diff --git a/book/README.md b/book/README.md
index 65ebda153..8f060baa0 100644
--- a/book/README.md
+++ b/book/README.md
@@ -12,7 +12,7 @@ This directory contains the book-length presentation of the framework developed
 
 ## Overview
 
-The book develops Observation Incompleteness (OI) from its foundational claim through physics and applications. The foundational result is an exact finite-horizon equivalence: finite stochastic laws, finite reversible deterministic realizations, and fixed-basis unitary/Born representations coincide. History readback then identifies the nontrivial OI sector by forcing hidden predictive memory. In the spatial theory, the coupling graph supplies exact causal cones for finite-range substrata. Bell then imposes a fork on the deterministic completion: retaining measurement independence means quantum Bell violation requires ontic parameter dependence. In the specific SM/GR branch the target realization is preparation-indexed adjacency in the existing state-dependent graph $G(x)$; H-Bell is the open metric/Ollivier--Ricci stability condition for those prepared graphs. The measurement-dependent alternative is recorded quantitatively but not adopted.
+The book develops Observation Incompleteness (OI) from its foundational claim through physics and applications. The foundational result is an exact finite-horizon equivalence: finite stochastic laws, finite reversible deterministic realizations, and fixed-basis unitary/Born representations coincide. History readback then identifies the nontrivial OI sector by forcing hidden predictive memory. In the spatial theory, the coupling graph supplies exact causal cones for finite-range substrata. Bell then imposes a fork on the deterministic completion: retaining measurement independence means quantum Bell violation requires ontic parameter dependence. In the specific SM/GR branch the target realization is preparation-indexed adjacency in the existing state-dependent graph $G(x)$; H-Bell is the open requirement that those prepared graphs preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The measurement-dependent alternative is recorded quantitatively but not adopted.
 
 The manuscript therefore uses “equivalence of quantum mechanics and embedded observation” in a precise sense rather than as a slogan. The stochastic/quantum-representation equivalence is exact and bidirectional for finite observable laws, and finite quantum experimental envelopes have constructive finite OI realizations to arbitrary specified accuracy. The remaining qualification concerns full operational quantum mechanics: the entire coherent instrument/composite hierarchy must be represented by one compatible standard local quantum theory. That residual is kept explicit without weakening the equivalence already proved.
 
diff --git a/book/The-Incompleteness-of-Observation-FULL.md b/book/The-Incompleteness-of-Observation-FULL.md
index 135e03c43..09f6c960a 100644
--- a/book/The-Incompleteness-of-Observation-FULL.md
+++ b/book/The-Incompleteness-of-Observation-FULL.md
@@ -274,7 +274,7 @@ These features — coupling, memory persistence, large capacity, and the readbac
 
 The framework's central theorem says something more exact. The finite stochastic law available to the experimenter, a finite reversible hidden-state realization, and a fixed-basis unitary/Born description are mathematically equivalent representations of the same finite observable data. If the hidden record is read back, the reduced law is not merely stochastic: every faithful completion must retain predictive memory. Quantum mechanics is therefore an exact observer-level representation of the incomplete finite law, not an extra microscopic postulate placed on top of it.
 
-The thought experiment captures the framework's central move. Quantum mechanics is reframed from a statement about reality to a statement about the observer's relationship to reality. The mathematics is unchanged; what it represents is different. The wave function is not the universe's state; it is the experimenter's compressed description of what they cannot see. The Born rule is not an independent postulate about fundamental indeterminism at the finite observable-law layer; it is the $|U|^2$ readout dictionary of the exact unitary representation every such law admits ([Main §3.4]). The remaining quantum question is the coherent local operational extension of that representation. For Bell experiments the deterministic layer faces Bell's sharper fork: a measurement-independent response-complete completion with finite-range Bell couplings is classical, so quantum violation requires ontic parameter dependence. The framework takes that branch while retaining operational no-signaling; the stochastic Tsirelson construction is kept as a separate weaker-description result.
+The thought experiment captures the framework's central move. Quantum mechanics is reframed from a statement about reality to a statement about the observer's relationship to reality. The mathematics is unchanged; what it represents is different. The wave function is not the universe's state; it is the experimenter's compressed description of what they cannot see. The Born rule is not an independent postulate about fundamental indeterminism at the finite observable-law layer; it is the $|U|^2$ readout dictionary of the exact unitary representation every such law admits ([Main §3.4]). The remaining quantum question is the coherent local operational extension of that representation. For Bell experiments the deterministic layer faces Bell's sharper fork: a measurement-independent response-complete completion with one-step own-wing setting interventions, Bell couplings that do not connect the wings before readout and a $\pm1$ outcome in every run is Bell-local, so quantum violation under measurement independence requires ontic parameter dependence. The framework takes that branch while retaining operational no-signaling; the stochastic Tsirelson construction is kept as a separate weaker-description result.
 
 The chapters that follow make this thought experiment precise. The room becomes a partition of the universe into visible and hidden sectors. The experimenter becomes a mathematical observer. The characterization theorem then separates what is universal from what is physically discriminating. The universal part is the exact finite-horizon equivalence $S\iff D\iff Q_{\mathrm{fb}}$; the discriminating part is history readback, which forces hidden predictive memory. The spatial extension adds graph causal cones and a separately stated operational screening condition for Bell experiments. The strongest remaining question is therefore not whether the observer has a quantum representation, but whether the whole coherent instrument/composite hierarchy is one standard local quantum operational theory.
 
@@ -288,7 +288,7 @@ finite stochastic laws, finite reversible deterministic realizations, and fixed-
 
 The representation equivalence is universal, so the distinctly memory-bearing content is carried by history readback. When two visible histories with the same present lead to different future laws, every faithful completion must retain predictive information in the hidden sector; on a fixed finite reversible system, recurrence forces the rooted visible process to be indivisible somewhere in its full cycle whenever any visible step is non-deterministic, so that indivisibility also holds for laws with no accessible memory. The observer therefore sees quantum-representable stochastic dynamics because of incomplete access, while the C1–C4 structure tells us when that description contains genuine hidden memory rather than merely a Markovian stochastic law.
 
-For spatially separated systems, the coupling graph supplies an exact causal cone. Bell adds a sharper deterministic constraint: if the response-complete pre-setting ontic ensemble is setting-independent and the wings lie outside each other's graph cone for the duration of the measurement, then Bell factorization follows and $|S_{\rm CHSH}|\le2$. The adopted branch therefore retains measurement independence and uses ontic parameter dependence, realized in the SM/GR target through preparation-indexed structure in the state-dependent graph $G(x)$ while preserving operational no-signaling. The measurement-dependent horn is recorded separately: $0.0309$ bits is a model-independent necessary lower bound from the manuscript's inequality, not an achievable cost. What is not yet claimed as a completed theorem is one common standard local quantum instrument/composite representation for every coherent intervention at once. That is the remaining operational-lifting layer; it does not weaken the exact stochastic–quantum equivalence already established.
+For spatially separated systems, the coupling graph supplies an exact causal cone. Bell adds a sharper deterministic constraint: if each wing's setting intervention, applied at one step, reads and writes only its own region, every run records a $\pm1$ outcome at each wing, the response-complete pre-setting ontic ensemble is setting-independent, and the wings lie outside each other's graph cone for the duration of the measurement, then Bell factorization follows and $|S_{\rm CHSH}|\le2$. The adopted branch therefore retains measurement independence and uses ontic parameter dependence while preserving operational no-signaling. The SM/GR target proposes preparation-indexed structure in the state-dependent graph $G(x)$ for it; whether that structure keeps no-signaling and the continuum-curvature limit is the open hypothesis H-Bell. The measurement-dependent horn is recorded separately: $0.0309$ bits is a model-independent necessary lower bound from the manuscript's inequality, not an achievable cost. What is not claimed as a completed theorem is one common standard local quantum instrument/composite representation for every coherent intervention at once. That is the remaining operational-lifting layer; it does not weaken the exact stochastic–quantum equivalence already established.
 
 ## 0.4 The intellectual context
 
@@ -357,7 +357,7 @@ S\iff D\iff Q_{\mathrm{fb}}.
 $$
 A finite stochastic law, a finite reversible hidden-state realization, and a fixed-basis unitary/Born representation are three descriptions of the same finite observable object. Conversely, every finite quantum record has a finite reversible realization. Second, history readback identifies the nontrivial sector: it forces hidden predictive memory in every faithful completion.
 
-This chapter proves those statements, then adds their spatial scope. The coupling graph of the underlying dynamics gives exact causal cones. At the response-complete deterministic level, a pointwise finite-range cone together with local interventions and one setting-independent pre-setting ensemble is Bell-local and gives $|S_{\rm CHSH}|\le2$. The adopted quantum-Bell branch therefore retains measurement independence and relinquishes ontic parameter independence, while preserving operational no-signaling. The one boundary not folded into the theorem is the full coherent instrument/composite category of operational quantum mechanics. Keeping that boundary explicit lets the chapter recover the original equivalence claim without confusing a universal representation theorem with a uniqueness theorem.
+This chapter proves those statements, then adds their spatial scope. The coupling graph of the underlying dynamics gives exact causal cones. At the response-complete deterministic level, setting interventions, applied at one step, that each read and write only their own wing, readouts outside the other wing's graph cone, a $\pm1$ outcome recorded in every run, and one setting-independent pre-setting ensemble give a Bell-local model and $|S_{\rm CHSH}|\le2$. The adopted quantum-Bell branch therefore retains measurement independence and relinquishes ontic parameter independence, while preserving operational no-signaling. The one boundary not folded into the theorem is the full coherent instrument/composite category of operational quantum mechanics. Keeping that boundary explicit lets the chapter recover the original equivalence claim without confusing a universal representation theorem with a uniqueness theorem.
 
 ## 1.2 The starting point
 
@@ -510,9 +510,9 @@ The Born rule in the fixed-basis representation is therefore part of the represe
 
 ## 1.7 Bell-inequality violations
 
-The Bell claim must separate the deterministic completion from the reduced stochastic description. For a Bell-relevant substratum whose coupling range does not connect the wings before readout, the dependency graph gives exact pointwise separation. If the response-complete pre-setting ensemble is also independent of the settings, determinism yields an ordinary Bell-local hidden-variable model and $|S_{\rm CHSH}|\le2$. Hidden memory and indivisibility do not alter that ceiling.
+The Bell claim must separate the deterministic completion from the reduced stochastic description. For a Bell-relevant substratum whose coupling range does not connect the wings before readout, the dependency graph gives exact pointwise separation. If each setting intervention, applied at one step, also reads and writes only its own wing, every run records a $\pm1$ outcome at each wing, and the response-complete pre-setting ensemble is independent of the settings, determinism yields an ordinary Bell-local hidden-variable model and $|S_{\rm CHSH}|\le2$. Hidden memory and indivisibility do not alter that ceiling.
 
-The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the vacuum/uniform reference graph remains geometric and bounded-range, while an entangling preparation may supply Bell-relevant long adjacency so a microstate response at one wing can depend on the remote setting. The averaged operational distribution remains no-signaling. H-Bell is the open metric/Ollivier--Ricci stability condition for those prepared graphs. That condition is now downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The setting-dependent alternative is recorded but not adopted; Main §3.3 gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits, while the smaller $\sim0.046$-bit benchmark is retrocausal.
+The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the vacuum/uniform reference graph remains geometric and bounded-range, while an entangling preparation may supply Bell-relevant long adjacency so a microstate response at one wing can depend on the remote setting. H-Bell is the open requirement that those prepared graphs preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The curvature condition is downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The setting-dependent alternative is recorded but not adopted; Main §3.3 gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits, while the smaller $\sim0.046$-bit benchmark is retrocausal.
 
 The cited causal-local indivisible **stochastic** construction separately obeys Tsirelson's bound because its causal-independence notion is weaker than Bell factorization. That theorem is not the hidden-variable locality structure of the deterministic completion. If the spatial/intervention restriction is removed, the general finite OI response construction can realize PR-box behavior, showing that representability, no-signaling, hidden memory, and indivisibility do not by themselves select the quantum Bell set.
 
@@ -524,7 +524,7 @@ The characterization is best read as a layered biconditional rather than a singl
 
 **Readback theorem.** C4 is the condition that makes the OI sector memory-bearing. It forces different hidden posteriors for visible histories that share a current state but have different future laws, a persistence/readback requirement, and the capacity lower bound of C3. Because the physical representative is finite and reversible, it also recurs: its rooted visible maps, defined for every root under one hidden prior, return to the identity, and a non-permutation stochastic matrix has no stochastic inverse, so any non-permutation rooted map makes the rooted law indivisible somewhere in the recurrence cycle. A C4 gap supplies such a map, and so does every non-deterministic visible step, including in laws that are Markov on every accessible window. With a full-support visible prior, that indivisibility is equivalent to memory at some order below the recurrence time; an observer sees the memory only when it appears at an accessible order, which is what C4 asserts.
 
-**Spatial extension.** The dependency graph supplies finite causal cones exactly for finite-range substrata. Bell adds a separate constraint: for a response-complete deterministic completion, measurement independence plus parameter independence would imply $|S_{\rm CHSH}|\le2$. Section §1.7 therefore takes the measurement-independent, ontically parameter-dependent branch for Bell-violating substrata and keeps operational no-signaling separate.
+**Spatial extension.** The dependency graph supplies finite causal cones exactly for finite-range substrata. Bell adds a separate constraint: for a response-complete deterministic completion that records a $\pm1$ outcome in every run, measurement independence plus parameter independence would imply $|S_{\rm CHSH}|\le2$. Section §1.7 therefore takes the measurement-independent, ontically parameter-dependent branch for Bell-violating substrata and keeps operational no-signaling separate.
 
 **Operational boundary.** These theorems do not yet prove that the entire family of coherent instruments and composites equals the unique standard local quantum operational theory. That residual is an active-lifting statement, not a qualification on the exact finite stochastic/representation equivalence itself.
 
@@ -828,7 +828,7 @@ The reconstruction theorem and the substratum gauge group have established what
 
 The framework's claim is that quantum mechanics, general relativity, and the arrow of time are not three independent theories. Conditional on H-Bell at the Bell/local-lattice interface, they are three projections of the same finite deterministic construction. Each projection applies the same trace-out machinery to the same $(S, \varphi)$ along a different axis, and each produces a distinct emergent structure as the observer sees the substratum from inside.
 
-**The visible-sector projection: quantum mechanics.** Chapter 1 developed this projection in detail. At finite observable horizon the reduced stochastic law, a finite reversible realization, and a fixed-basis unitary/Born representation are exactly equivalent: $S\iff D\iff Q_{\mathrm{fb}}$. C4 readback then identifies the memory-bearing sector by forcing hidden predictive memory. In the spatial construction the coupling graph supplies exact causal cones for finite-range substrata. Bell is separate from the full-QM lift: a measurement-independent response-complete deterministic completion with parameter independence would obey $|S_{\rm CHSH}|\le2$, so the framework's Bell-violating branch is ontically parameter-dependent but operationally no-signaling. Two independent qualifications remain beyond the finite-law equivalence: the simultaneous coherent instrument/composite lift ([Main §3.4]) and H-Bell, the compatibility of the local lattice sector with the ontically parameter-dependent Bell completion. Applied to the local lattice sector constructed in this chapter — a $d = 3$ cubic lattice with $K = 6$ internal components and the wave equation as its local propagating dynamics — the visible-sector projection produces the Standard Model: the gauge group $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)$ as the commutant of the cubic-symmetric coupling matrix, three chiral fermion generations, one composite Higgs, and anomaly-free hypercharges. Chapters 5 and 6 develop the Standard Model derivation; Chapter 8 develops the specific JUNO neutrino measurement that the framework's parameter-free PMNS-angle value matches at $0.07\sigma$ (a retrodiction). The local nearest-neighbor sector cannot itself supply Bell parameter dependence for wings outside each other's graph cone under measurement independence; identifying it with one Bell-violating total completion is the open H-Bell compatibility hypothesis.
+**The visible-sector projection: quantum mechanics.** Chapter 1 developed this projection in detail. At finite observable horizon the reduced stochastic law, a finite reversible realization, and a fixed-basis unitary/Born representation are exactly equivalent: $S\iff D\iff Q_{\mathrm{fb}}$. C4 readback then identifies the memory-bearing sector by forcing hidden predictive memory. In the spatial construction the coupling graph supplies exact causal cones for finite-range substrata. Bell is separate from the full-QM lift: a measurement-independent response-complete deterministic completion with parameter independence and a $\pm1$ outcome in every run would obey $|S_{\rm CHSH}|\le2$, so the framework's Bell-violating branch is ontically parameter-dependent but operationally no-signaling. Two independent qualifications remain beyond the finite-law equivalence: the simultaneous coherent instrument/composite lift ([Main §3.4]) and H-Bell, the compatibility of the local lattice sector with the ontically parameter-dependent Bell completion. Applied to the local lattice sector constructed in this chapter — a $d = 3$ cubic lattice with $K = 6$ internal components and the wave equation as its local propagating dynamics — the visible-sector projection produces the Standard Model: the gauge group $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)$ as the commutant of the cubic-symmetric coupling matrix, three chiral fermion generations, one composite Higgs, and anomaly-free hypercharges. Chapters 5 and 6 develop the Standard Model derivation; Chapter 8 develops the specific JUNO neutrino measurement that the framework's parameter-free PMNS-angle value matches at $0.07\sigma$ (a retrodiction). The local nearest-neighbor sector cannot itself supply Bell parameter dependence for wings with one-step own-wing setting interventions outside each other's graph cone under measurement independence; identifying it with one Bell-violating total completion is the open H-Bell compatibility hypothesis.
 
 **The boundary-thermodynamic projection: general relativity.** A second projection takes the same substratum but applies the trace-out machinery to the partition boundary rather than to the bulk. The boundary of the visible sector — the surface across which the coupling $H_{\text{int}}$ acts — carries its own thermodynamic structure: a temperature set by the boundary's classical surface gravity, an entropy set by the number of boundary modes, and a dynamical evolution set by the coupling between boundary and bulk. Jacobson's thermodynamic argument applied to local causal horizons yields Einstein's equations as the Clausius relation $dE = T \, dS$ at the boundary.
 
@@ -913,7 +913,7 @@ Universality classes have internal sub-structure at three levels of refinement.
 
 Level C commits to a structural realism at the class level: the universality class is what is real, with specific substratum representatives playing the role of gauge expressions. Different members of the same universality class are observationally indistinguishable by definition, so the question "which specific substratum is real?" has no empirical content at the universality-class level. The realism is precisely about what survives the universality-class quotient.
 
-**Level D: OI's specific local structural residue.** The framework's narrowest reconstructed commitment is the three-dimensional cubic local lattice/gauge sector with $K=6$, the wave-equation dynamics and the listed Standard-Model representation data, with the qualifications developed in the technical chapters. The reconstruction theorem establishes that the stated observed and structural inputs uniquely fix this **local residue** up to $\mathcal{G}_{\text{sub}}$ under Theorem 23's conditions. It does not uniquely determine a Bell-inclusive full representative. The reference cubic graph is Bell-local under measurement independence; the adopted branch uses preparation-indexed state-dependent adjacency, with H-Bell conditioning its metric/Ollivier--Ricci compatibility and its uniqueness left open.
+**Level D: OI's specific local structural residue.** The framework's narrowest reconstructed commitment is the three-dimensional cubic local lattice/gauge sector with $K=6$, the wave-equation dynamics and the listed Standard-Model representation data, with the qualifications developed in the technical chapters. The reconstruction theorem establishes that the stated observed and structural inputs uniquely fix this **local residue** up to $\mathcal{G}_{\text{sub}}$ under Theorem 23's conditions. It does not uniquely determine a Bell-inclusive full representative. With one-step own-wing setting interventions, readouts outside the other wing's graph cone and a $\pm1$ outcome in every run, the reference cubic graph is Bell-local under measurement independence; the adopted branch proposes preparation-indexed state-dependent adjacency under the open hypothesis H-Bell (operational no-signaling and the metric/Ollivier--Ricci continuum limit), with its uniqueness left open.
 
 Level D is where the framework's twenty-two classified quantitative predictions live (two parameter-free structural and five conditional structural among them): the Cabibbo angle $1/(\pi\sqrt{2})$, the Koide angle $2/9$, the gauge-coupling-running calculation giving the three SM coupling constants at the $Z$ pole, the six fermion masses derived from one empirical input, the Higgs quartic coupling from cubic-group representation theory, the Bekenstein-Hawking $1/4$ factor as a consistency relation, the MOND acceleration scale $cH/6$, and the JUNO neutrino-mixing prediction. The empirical content that distinguishes OI from other observer-admitting frameworks is concentrated at Level D, because Level D is where the structural commitments become specific enough to produce specific numerical predictions.
 
@@ -1035,9 +1035,9 @@ The framework is a hidden-variable theory in the literal sense: there is a deter
 
 The framework's engagement with these theorems is not a single trick repeated, nor four separate tricks. Each theorem identifies a different structural property of would-be hidden-variable accounts. The two-level substratum-emergent structure joined by the trace-out is the common bookkeeping architecture, but it is **not** one automatic escape: Bell forces ontic parameter dependence in the adopted deterministic branch; Kochen-Specker constrains the noncommuting operational algebra; PBR constrains preparation independence of ontic composites; Frauchiger-Renner constrains universal nested-agent descriptions. The hierarchy matters because it locates each premise at the right level, not because the same property simply holds above and fails below in every case.
 
-**Bell's theorem.** Bell's theorem binds directly on the deterministic hidden-variable completion. If the Bell-relevant coupling range does not connect the wings before readout and one setting-independent response-complete ensemble is used, the model factorizes and obeys $|S_{\rm CHSH}|\le2$. The framework therefore cannot use graph locality, screening, outcome dependence, or indivisibility to explain the quantum violation. It retains measurement independence and accepts **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling as the distinct empirical locality statement. The cited stochastic causal-local indivisible construction can still obey Tsirelson because its causal-independence criterion is weaker than Bell factorization. Unrestricted globally controlled OI realizations remain the PR-box countercontrol.
+**Bell's theorem.** Bell's theorem binds directly on the deterministic hidden-variable completion. If the setting interventions, applied at one step, each read and write only their own wing, the Bell-relevant coupling range does not connect the wings before readout, every run records a $\pm1$ outcome, and one setting-independent response-complete ensemble is used, the model factorizes and obeys $|S_{\rm CHSH}|\le2$. The framework therefore cannot use graph locality, screening, outcome dependence, or indivisibility to explain the quantum violation. It retains measurement independence and accepts **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling as the distinct empirical locality statement. The cited stochastic causal-local indivisible construction can still obey Tsirelson because its causal-independence criterion is weaker than Bell factorization. Unrestricted globally controlled OI realizations remain the PR-box countercontrol.
 
-In hierarchy language, the Bell question splits the deterministic substratum from the reduced stochastic description. A finite-range Bell graph plus a setting-independent response-complete ensemble would force the substratum into Bell's local class and cap CHSH at $2$. The framework therefore does not identify no-signaling, Jarrett parameter independence, Fine's theorem, hidden memory, or indivisibility with a derivation of the quantum correlation set. Its adopted deterministic branch is instead ontic parameter dependence with operational no-signaling; the $2\sqrt2$ result for the causal-local indivisible stochastic construction remains a distinct weaker-description theorem.
+In hierarchy language, the Bell question splits the deterministic substratum from the reduced stochastic description. A Bell graph that does not connect the wings before readout, with one-step own-wing setting interventions and a $\pm1$ outcome in every run, plus a setting-independent response-complete ensemble, would force the substratum into Bell's local class and cap CHSH at $2$. The framework therefore does not identify no-signaling, Jarrett parameter independence, Fine's theorem, hidden memory, or indivisibility with a derivation of the quantum correlation set. Its adopted deterministic branch is instead ontic parameter dependence with operational no-signaling; the $2\sqrt2$ result for the causal-local indivisible stochastic construction remains a distinct weaker-description theorem.
 
 **Kochen-Specker.** The Kochen-Specker theorem rules out non-contextual hidden-variable assignments: there is no function $v$ mapping observables to definite values such that $v(O)$ depends only on $O$ rather than on the measurement context (the set of compatible observables being measured simultaneously). Any hidden-variable theory matching quantum mechanics must be contextual: the hidden variable's outcome on a given observable depends on which other observables are co-measured.
 
@@ -1053,9 +1053,9 @@ The framework's PBR response must be stated conditionally. PBR assumes Preparati
 
 **What the framework does not argue.** Two standard escapes are explicitly declined. It does not deny counterfactual definiteness: substratum outcomes are definite, and the framework nowhere trades on refusing to consider unperformed measurements — the response to Bell runs through the structure of the premises, not through denying that measurements have results. Nor does it treat hidden setting correlations as an explanation of Bell statistics. Measurement independence is an explicit premise of the adopted Bell branch; chaotic mixing may motivate laboratory decorrelation between pair-preparation and setting-generating degrees of freedom, but the violation itself is assigned to ontic parameter dependence. The setting-dependent horn is quantified and declined (Main §3.3).
 
-**Bell's theorem, conceded and then confronted.** Bell's mathematics binds on the framework because the substratum is a response-complete hidden-variable completion. If the Bell-relevant graph does not connect the wings before readout and the pre-setting ensemble is independent of the settings, determinism gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore cannot explain quantum Bell violation by combining pointwise graph locality and indivisibility. It declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization, the target is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the reference vacuum/uniform graph remains geometric and bounded-range, while an entangling preparation may add Bell-relevant long adjacency. The averaged operational statistics remain no-signaling. H-Bell is the remaining metric/Ollivier--Ricci stability condition for those prepared graphs. That condition is now downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The causal-local indivisible *stochastic* construction can still obey Tsirelson because its causal-independence condition is weaker than Bell factorization; that result is not the locality structure of the deterministic completion. The unrestricted PR realization remains the negative control showing that representability, no-signaling, and indivisibility do not select the quantum set.
+**Bell's theorem, conceded and then confronted.** Bell's mathematics binds on the framework because the substratum is a response-complete hidden-variable completion. If the setting interventions, applied at one step, each read and write only their own wing, the Bell-relevant graph does not connect the wings before readout, every run records a $\pm1$ outcome, and the pre-setting ensemble is independent of the settings, determinism gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore cannot explain quantum Bell violation by combining pointwise graph locality and indivisibility. It declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization, the target is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the reference vacuum/uniform graph remains geometric and bounded-range, while an entangling preparation may add Bell-relevant long adjacency. H-Bell is the open requirement that those prepared graphs preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The curvature condition is downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The causal-local indivisible *stochastic* construction can still obey Tsirelson because its causal-independence condition is weaker than Bell factorization; that result is not the locality structure of the deterministic completion. The unrestricted PR realization remains the negative control showing that representability, no-signaling, and indivisibility do not select the quantum set.
 
-**The rejoinder, at full strength.** A response-complete deterministic Bell completion is not local in Bell's parameter-independence sense. A response-complete hidden-variable theory reproducing Bell violation while retaining measurement independence must fail parameter independence, and the framework explicitly accepts that conclusion. Its Bell-violating prepared states are therefore **ontically nonlocal in Bell's parameter sense**. In the concrete lattice branch, that nonlocality is represented by preparation-indexed state-dependent adjacency (or an equivalent response rule), not by pretending the nearest-neighbor reference wave equation itself carries Bell influence. What remains local operationally is the no-signaling statement — changing a controllable setting cannot be used to transmit a message to the remote wing. The cosmological partition or shared boundary may be proposed as a physical realization, but calling that carrier atemporal, global, or prior to emergent spacetime does not remove Bell nonlocality; it only locates it in the ontology. The separate Barandes–Hasan–Kagan theorem shows that the reduced stochastic law can satisfy their weaker causal-independence criterion and remain below Tsirelson, but that criterion is not Bell factorization for the deterministic completion. The manuscript can therefore defend a non-signaling deterministic ontology with a specific locus of nonlocality; it does not claim a local hidden-variable resolution of Bell.
+**The rejoinder, at full strength.** A response-complete deterministic Bell completion is not local in Bell's parameter-independence sense. A response-complete hidden-variable theory reproducing Bell violation while retaining measurement independence must fail parameter independence, and the framework explicitly accepts that conclusion. Its Bell-violating prepared states are therefore **ontically nonlocal in Bell's parameter sense**. In the concrete lattice branch, that nonlocality is targeted through preparation-indexed state-dependent adjacency (or an equivalent response rule) under H-Bell, not by pretending the nearest-neighbor reference wave equation itself carries Bell influence. What remains local operationally is the no-signaling statement — changing a controllable setting cannot be used to transmit a message to the remote wing. The cosmological partition or shared boundary may be proposed as a physical realization, but calling that carrier atemporal, global, or prior to emergent spacetime does not remove Bell nonlocality; it only locates it in the ontology. The separate Barandes–Hasan–Kagan theorem shows that the reduced stochastic law can satisfy their weaker causal-independence criterion and remain below Tsirelson, but that criterion is not Bell factorization for the deterministic completion. The manuscript can therefore defend a non-signaling deterministic ontology with a specific locus of nonlocality; it does not claim a local hidden-variable resolution of Bell.
 
 **The bill, paid in the open.** A deterministic substratum that violates **ontic parameter independence** owes an account of relativity, and the account cannot be evasive: the framework's substratum has a preferred frame — the frame in which update steps are simultaneous — and on identification with the observed universe this is operationally the cosmic rest frame, an identification the framework records rather than derives (SM §3.1). Lorentz invariance is therefore wholly emergent, and the framework's obligations are quantitative: no linear violation (established at tree level), rotational protection by octahedral symmetry to all orders conditional on the emergent theory preserving that symmetry at loop level, boost-sector violation controlled, conditional on the symmetric-point matching under H-blind (SM §4.4), by a decoupling law in the cross-charged mass $M_X$ whose quadratic-with-logarithm form was reported by a one-loop calculation that is not independently verified, its two-sided window illustrative until it is. These are not side technicalities; they are the price of the preferred-frame answer to the foliation objection, and the open item among them — the interacting (condensate-dressed) extension of the coarse-graining characterization (SM §3.1; Chapter 19 §19.3.7) — is correctly understood as Bell-defense infrastructure. A reader who wants to falsify the framework's account of Bell should attack there: a demonstrated failure of emergent Lorentz protection would leave the preferred frame exposed at accessible energies, and the framework's answer to this subsection would fail with it.
 
@@ -1206,9 +1206,9 @@ First, identify the theorem's structural assumption. Bell's theorem assumes fact
 
 Second, identify the level of the framework's hierarchy where the assumption sits. Bell's factorizability is a property at Level G3 × Level D, where the joint transition matrix between visible-sector subsystems is defined. Kochen-Specker non-contextuality is a property at Level G2 × Level D, where observables are defined as operators on the emergent Hilbert space. PBR preparation independence is a property at Level D × Level G3, where the substratum's joint-system structure is specified. Frauchiger-Renner universal applicability is a claim at Level G2 × Level D applied to substratum-level objects.
 
-Third, locate where the framework meets or violates the theorem's premises at the correct level. Bell is the sharpest case: for a response-complete deterministic completion, finite-range Bell couplings plus a setting-independent pre-setting ensemble imply Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore does not obtain quantum Bell violation from outcome-independence failure in an indivisible stochastic law; it retains measurement independence and gives up **ontic parameter independence**, while preserving operational no-signaling. PBR's preparation independence — the postulate that independently prepared systems have a product joint ontic-state distribution — is not a premise of bare OI. Co-embedded preparation devices may share preparation-relevant hidden or boundary data, so unconditional product independence is not guaranteed; the graph causal cone by itself does not derive either a conditional product distribution or the standard quantum tensor-product composite. Frauchiger-Renner's universal applicability fails because the substratum-level and emergent-level descriptions are incommensurable in the relevant sense. The fourth theorem, Kochen-Specker, does not fit this "satisfied below, violated above" form: its assumed property, a noncontextual valuation of the observables, holds at neither level — the framework — conditionally on the operational bridge reconstructing the standard observable algebra — carries the operational theory, which by Kochen-Specker's own content admits no noncontextual valuation, and the substratum carries a definite configuration that is not a valuation of the emergent observables at all. The framework's contextuality is forced, under that same conditional bridge, by equivalence at the operational layer — and what the framework adds is the account: contextuality is the partition-dependence of the trace-out. The common factor across all four is therefore the architecture — two levels and a trace-out — not a single property-placement move repeated.
+Third, locate where the framework meets or violates the theorem's premises at the correct level. Bell is the sharpest case: for a response-complete deterministic completion, Bell couplings that do not connect the wings before readout, one-step own-wing setting interventions and a $\pm1$ outcome in every run, plus a setting-independent pre-setting ensemble, imply Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore does not obtain quantum Bell violation from outcome-independence failure in an indivisible stochastic law; it retains measurement independence and gives up **ontic parameter independence**, while preserving operational no-signaling. PBR's preparation independence — the postulate that independently prepared systems have a product joint ontic-state distribution — is not a premise of bare OI. Co-embedded preparation devices may share preparation-relevant hidden or boundary data, so unconditional product independence is not guaranteed; the graph causal cone by itself does not derive either a conditional product distribution or the standard quantum tensor-product composite. Frauchiger-Renner's universal applicability fails because the substratum-level and emergent-level descriptions are incommensurable in the relevant sense. The fourth theorem, Kochen-Specker, does not fit this "satisfied below, violated above" form: its assumed property, a noncontextual valuation of the observables, holds at neither level — the framework — conditionally on the operational bridge reconstructing the standard observable algebra — carries the operational theory, which by Kochen-Specker's own content admits no noncontextual valuation, and the substratum carries a definite configuration that is not a valuation of the emergent observables at all. The framework's contextuality is forced, under that same conditional bridge, by equivalence at the operational layer — and what the framework adds is the account: contextuality is the partition-dependence of the trace-out. The common factor across all four is therefore the architecture — two levels and a trace-out — not a single property-placement move repeated.
 
-Fourth, verify that the framework's predictions match quantum mechanics in the regime where the no-go theorem applies, without silently importing the very condition under test. For Bell, verify the deterministic completion directly: if its Bell-relevant graph is finite-range at the wings and its pre-setting ensemble is setting-independent, CHSH is capped at $2$. The framework's quantum branch therefore has ontic parameter dependence. For the specific SM/GR representative, the nearest-neighbor **reference** graph cannot itself supply that parameter dependence in a Bell protocol whose wings lie outside each other's graph cone. The existing state-dependent graph $G(x)$ supplies the native target: preparation-indexed adjacency (or an equivalent nonlocal response), with H-Bell now the open metric/Ollivier--Ricci stability condition for the prepared graph family. The measurement-dependent alternative is not adopted; Chapter 1 gives a model-independent necessary lower bound and a separate causal benchmark; the stochastic causal-local Tsirelson theorem is retained only at its weaker stochastic level. Kochen-Specker, PBR, and Frauchiger-Renner concern the coherent operational structure and therefore inherit the operational-lifting qualification: their standard quantum statistics are recovered once the common instrument/composite representation is established, not merely from universal fixed-basis representability.
+Fourth, verify that the framework's predictions match quantum mechanics in the regime where the no-go theorem applies, without silently importing the very condition under test. For Bell, verify the deterministic completion directly: if its setting interventions, applied at one step, each read and write only their own wing, its Bell-relevant graph does not connect the wings before readout, every run records a $\pm1$ outcome, and its pre-setting ensemble is setting-independent, CHSH is capped at $2$. The framework's quantum branch therefore has ontic parameter dependence. For the specific SM/GR representative, the nearest-neighbor **reference** graph cannot itself supply that parameter dependence in a Bell protocol with one-step own-wing setting interventions whose wings lie outside each other's graph cone. The existing state-dependent graph $G(x)$ supplies the native target: preparation-indexed adjacency (or an equivalent nonlocal response), with H-Bell the open requirement that the prepared graph family preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The measurement-dependent alternative is not adopted; Chapter 1 gives a model-independent necessary lower bound and a separate causal benchmark; the stochastic causal-local Tsirelson theorem is retained only at its weaker stochastic level. Kochen-Specker, PBR, and Frauchiger-Renner concern the coherent operational structure and therefore inherit the operational-lifting qualification: their standard quantum statistics are recovered once the common instrument/composite representation is established, not merely from universal fixed-basis representability.
 
 **One architecture, verified per theorem.** Two things must be held apart here, because they pull in opposite directions and both are true. The framework's *response* to the no-go literature is not piecemeal: it is one architectural feature — two levels of description joined by the trace-out — fixed before any no-go theorem is examined, and the four cases are four manifestations of working within it rather than four separately chosen escapes. But the *verification* that the architecture in fact answers a given theorem is per-theorem work: each theorem's assumption must be located against the two-level structure, and the match checked. The unity is in the response; the labor is in the checking. As new no-go theorems are published — the literature continues to grow — each must be checked against the same architecture, with the framework's engagement verified rather than assumed.
 
@@ -1240,7 +1240,7 @@ The conditions are organized into three classes. Class A identifies structural t
 
 *Majorana neutrinos with normal mass ordering.* The framework derives this from the taste-breaking structure of the neutrino mass matrix. Inverted mass ordering, confirmed to high significance, falsifies the derivation. Confirmed Dirac nature of the neutrino — for example, a null result for neutrinoless double-beta decay at the sensitivity that would require Majorana masses well below the framework's prediction — falsifies the prediction that no right-handed neutrino exists in the spectrum.
 
-*The Tsirelson bound.* The value $2\sqrt{2}$ belongs to the cited **stochastic causal-local indivisible construction** ([Main §3.3]), not to a Bell-local deterministic completion and not to generic P-indivisibility. The deterministic OI layer reaches quantum Bell violation only on the ontically parameter-dependent branch. An observed loophole-free CHSH value above $2\sqrt2$ would falsify standard quantum mechanics and any claim that the relevant OI operational lift lands in the standard quantum Bell set; it would not, by itself, falsify P-indivisibility.
+*The Tsirelson bound.* The value $2\sqrt{2}$ belongs to the cited **stochastic causal-local indivisible construction** ([Main §3.3]), not to a Bell-local deterministic completion and not to generic P-indivisibility. The deterministic OI layer reaches quantum Bell violation, under measurement independence, only on the ontically parameter-dependent branch. An observed loophole-free CHSH value above $2\sqrt2$ would falsify standard quantum mechanics and any claim that the relevant OI operational lift lands in the standard quantum Bell set; it would not, by itself, falsify P-indivisibility.
 
 *Exact unitarity of the visible-sector dynamics at accessible scales.* The framework derives unitary quantum evolution as the exact embedded-observer description at every accessible mass and coherence scale, with dissipative corrections structurally suppressed to the dissipator scale of Chapter 1 §1.6. Any confirmed intrinsic-collapse signature — anomalous decoherence not attributable to environmental channels, scaling with mass or superposition size as objective-collapse models (GRW/CSL, Diósi–Penrose) require, at sufficient confidence to exclude systematics — falsifies the emergence theorem directly. Because the framework's predicted deviations are pinned orders of magnitude below the collapse-model band, a positive detection cannot be absorbed as a framework correction. The current frontier is matter-wave interference at macroscopicity $\mu = 15.5$ (Pedalino et al. 2026; Chapter 1 §1.6), consistent with exact quantum behavior; the frontier's continued advance is a standing test rather than a completed one.
 
@@ -4925,7 +4925,7 @@ The apparent randomness arises because the observer sees only $x$, not $h$. Diff
 
 This is what "deterministic but inaccessible" means in the framework: the outcomes are fully determined by the substratum dynamics, but the observer cannot in principle access the hidden-sector information that determines them. The randomness is unavoidable for any embedded observer, but it is not fundamental — it is the cost of partial observation.
 
-**Bell's theorem and the chosen nonlocality.** Bell does not rule out determinism by itself; it rules out reproducing the observed correlations with a response-complete deterministic completion that is both measurement-independent and parameter-independent. Chapter 1 proves the corresponding Bell ceiling: if the Bell-relevant coupling range does not connect the wings before readout and one setting-independent pre-setting ensemble is used, then $|S_{\rm CHSH}|\le2$. The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response), so a prepared microstate response may depend on the remote setting while the reference vacuum/uniform graph remains geometric and bounded-range. The operational distribution remains no-signaling. The $2\sqrt2$ theorem for the causal-local indivisible stochastic description is a separate weaker-layer result, not a locality theorem for the deterministic completion.
+**Bell's theorem and the chosen nonlocality.** Bell does not rule out determinism by itself; it rules out reproducing the observed correlations with a response-complete deterministic completion that records a $\pm1$ outcome in every run and is both measurement-independent and parameter-independent. Chapter 1 proves the corresponding Bell ceiling: if the setting interventions, applied at one step, each read and write only their own wing, the Bell-relevant coupling range does not connect the wings before readout, every run records a $\pm1$ outcome, and one setting-independent pre-setting ensemble is used, then $|S_{\rm CHSH}|\le2$. The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response), so a prepared microstate response may depend on the remote setting while the reference vacuum/uniform graph remains geometric and bounded-range. Whether those prepared graphs keep the operational distribution no-signaling and preserve the continuum-curvature limit is the open hypothesis H-Bell. The $2\sqrt2$ theorem for the causal-local indivisible stochastic description is a separate weaker-layer result, not a locality theorem for the deterministic completion.
 
 One proposed physical realization of that preparation-indexed parameter dependence uses non-localized cosmological-boundary modes. This is a candidate realization, not an established Bell mechanism: any such prepared long-edge/response structure must satisfy H-Bell, i.e. preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit used by the gravitational reconstruction. What distinguishes it from a superluminal signaling mechanism is operational no-signaling, not ontic parameter independence.
 
@@ -6275,9 +6275,9 @@ The most frequent objection to deterministic-substratum theories is: "Bell's the
 
 **The objection.** Bell's theorem (1964) establishes that no local hidden-variable theory can reproduce the quantum-mechanical predictions for entangled systems. The empirical violations of Bell inequalities (CHSH measured to $\geq 2.4$ in multiple experiments, with quantum prediction at $2\sqrt{2} \approx 2.83$) are taken as definitively excluding local hidden-variable theories. The framework's deterministic substratum looks suspiciously like a hidden-variable theory; therefore the framework should be ruled out by Bell's theorem in the same way.
 
-**The framework's response.** Bell applies directly to the response-complete deterministic substratum. If the Bell-relevant coupling range is finite at the wings' separation, local interventions occur before the corresponding cones meet, and one setting-independent pre-setting ensemble is used, then the hidden responses factorize and $|S_{\rm CHSH}|\le2$. OI therefore cannot combine deterministic response completeness, measurement independence, and ontic parameter independence and still reproduce quantum Bell violation. The framework keeps measurement independence and takes the remaining horn: **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling retained (Chapter 1 §1.7; Main §3.3).
+**The framework's response.** Bell applies directly to the response-complete deterministic substratum. If the Bell-relevant coupling range is finite at the wings' separation, the setting interventions, applied at one step, each read and write only their own wing and each wing's readout lies outside the other wing's graph cone, every run records a $\pm1$ outcome, and one setting-independent pre-setting ensemble is used, then the hidden responses factorize and $|S_{\rm CHSH}|\le2$. OI therefore cannot combine deterministic response completeness, a $\pm1$ outcome in every run, measurement independence, and ontic parameter independence and still reproduce quantum Bell violation. The framework keeps measurement independence and takes the remaining horn: **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling retained (Chapter 1 §1.7; Main §3.3).
 
-The cited causal-local **stochastic** indivisible construction separately obeys the Tsirelson bound $2\sqrt2$. By the Bell ceiling theorem (Main §3.3), a response-complete deterministic completion that keeps a pointwise finite-range cone on one setting-independent pre-setting ensemble is a local hidden-variable model, so $|S_{\rm CHSH}|\le2$. The framework therefore adopts ontic **parameter dependence**, implemented in the SM/GR branch through preparation-indexed structure in the state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response), while retaining operational no-signaling. If measurement independence were dropped instead, $S_{\rm CHSH}\le\min\{4,\,2+4\sqrt{2\ln2\,I_{\rm ont}}\}$ gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits; the smaller $\sim0.046$-bit benchmark is retrocausal. Dropping the spatial/intervention restriction permits the general finite OI response construction to reach PR-box behavior; PR is therefore a negative control for causal-local selection, not for the existence of a Hilbert/Born representation.
+The cited causal-local **stochastic** indivisible construction separately obeys the Tsirelson bound $2\sqrt2$. By the Bell ceiling theorem (Main §3.3), a response-complete deterministic completion with one-step own-wing setting interventions, each wing's readout outside the other wing's graph cone, a $\pm1$ outcome in every run, and one setting-independent pre-setting ensemble is a local hidden-variable model, so $|S_{\rm CHSH}|\le2$. The framework therefore adopts ontic **parameter dependence**, targeted in the SM/GR branch through preparation-indexed structure in the state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response) under the open hypothesis H-Bell, while retaining operational no-signaling. If measurement independence were dropped instead, $S_{\rm CHSH}\le\min\{4,\,2+4\sqrt{2\ln2\,I_{\rm ont}}\}$ gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits; the smaller $\sim0.046$-bit benchmark is retrocausal. Dropping the spatial/intervention restriction permits the general finite OI response construction to reach PR-box behavior; PR is therefore a negative control for causal-local selection, not for the existence of a Hilbert/Born representation.
 
 *Not superdeterminism.* Determinism alone does not establish Bell measurement independence, because setting generators are physical degrees of freedom. The manuscript therefore treats measurement independence as an explicit premise of the adopted Bell branch rather than as a theorem of the substratum. It does **not** use setting–hidden correlations to explain the observed violation. A mixing/decorrelation argument may motivate why laboratory setting generators approximate that premise, but the Bell mechanism itself is ontic parameter dependence. If the premise were dropped instead, that would be the measurement-dependent/superdeterministic horn quantified by the $I_{\rm ont}$ bound — a horn the framework records and declines.
 
@@ -6285,7 +6285,7 @@ The cited causal-local **stochastic** indivisible construction separately obeys
 
 *Not Bohmian mechanics.* Bohmian mechanics adds a pilot wave guiding particle trajectories in configuration space. The framework has no pilot wave and no guidance equation in configuration space. The framework's hidden sector is the substratum's broader configuration space, not a separate guiding field; the dynamics is direct (the bijection $\varphi$) rather than mediated by a guidance equation.
 
-The framework is therefore not a Bell-local hidden-variable theory. Its deterministic completion is measurement-independent by the adopted Bell premise but ontically parameter-dependent, with operational no-signaling. Hidden predictive memory and indivisibility remain central to the OI dynamics, but they are **not** the mechanism that evades Bell: a parameter-independent deterministic completion would still satisfy CHSH $\le2$. The Tsirelson value is retained for the cited stochastic causal-local indivisible construction and, conditionally, for any successful operational lift to standard quantum mechanics (§C.2).
+The framework is therefore not a Bell-local hidden-variable theory. Its deterministic completion is measurement-independent by the adopted Bell premise but ontically parameter-dependent, with operational no-signaling. Hidden predictive memory and indivisibility remain central to the OI dynamics, but they are **not** the mechanism that evades Bell: a measurement-independent, parameter-independent deterministic completion recording a $\pm1$ outcome in every run would still satisfy CHSH $\le2$. The Tsirelson value is retained for the cited stochastic causal-local indivisible construction and, conditionally, for any successful operational lift to standard quantum mechanics (§C.2).
 
 ## C.3 The no-go theorems: PBR, Frauchiger-Renner, Colbeck-Renner, Bong-Wiseman
 
@@ -6616,7 +6616,7 @@ This glossary defines the framework's distinctive terminology and the technical
 
 **Bekenstein-Hawking entropy.** The entropy $S = A/(4 l_p^2)$ assigned to a horizon of area $A$ in units of the Planck length $l_p$. The factor $1/4$ follows from the Hawking temperature and the first law. In the framework it is the ratio $2\pi/8\pi$ fixed by the horizon calibration of Chapter 7 (conditional on H-slope); the mode count reproduces it for any cell size once the calibration is imposed. GW250114 (September 2025) confirms the classical area theorem; the $1/4$ coefficient has no direct empirical test. Developed in Chapter 7 §7.5.
 
-**Bell-inequality violations.** Empirical correlations exceeding bounds derivable from local hidden-variable theories. For a response-complete deterministic OI completion, measurement independence plus ontic parameter independence gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore retains measurement independence but relinquishes **ontic parameter independence** for Bell-violating substrata, while preserving operational no-signaling. The measurement-dependent alternative is recorded rather than adopted: the manuscript proves the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum CHSH value, while an optimized causal model in Hall--Branciard uses about $0.080$ bits (the smaller $\sim0.046$-bit benchmark is retrocausal). Developed in Chapter 1 §1.7 and Appendix C §C.2.
+**Bell-inequality violations.** Empirical correlations exceeding bounds derivable from local hidden-variable theories. For a response-complete deterministic OI completion, measurement independence plus ontic parameter independence, with a $\pm1$ outcome in every run, gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore retains measurement independence but relinquishes **ontic parameter independence** for Bell-violating substrata, while preserving operational no-signaling. The measurement-dependent alternative is recorded rather than adopted: the manuscript proves the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum CHSH value, while an optimized causal model in Hall--Branciard uses about $0.080$ bits (the smaller $\sim0.046$-bit benchmark is retrocausal). Developed in Chapter 1 §1.7 and Appendix C §C.2.
 
 **Born rule.** The quantum-mechanical prescription that the probability of measurement outcome $i$ on state $|\psi\rangle$ is $|\langle i|\psi\rangle|^2$. Conventionally treated as a postulate of quantum mechanics. In the framework, at the finite fixed-basis observable-law layer, the Born form is part of an exact equivalent representation: $S\iff D\iff Q_{\mathrm{fb}}$ ([Main §3.4]). The framework therefore does not list a separate 'quadratic-exponent selector' as an unresolved foundational theorem at that layer. What remains is the **operational lifting** problem: prove that the fixed-basis representation extends coherently and simultaneously to the standard local noncommuting instrument/composite algebra. The read-write-cycle equilibrium account in Chapter 18 §18.2 is an additional physical mechanism proposal and is not needed for the finite representation equivalence.
 
@@ -6646,7 +6646,7 @@ This glossary defines the framework's distinctive terminology and the technical
 
 **CKM (Cabibbo-Kobayashi-Maskawa) matrix.** The unitary mixing matrix between Standard Model quark mass and weak interaction eigenstates. Conventionally parameterized by three mixing angles and one CP-violating phase. The framework derives the Cabibbo angle structurally and provides partial content for the broader CKM structure. Developed in Chapter 6 §6.5.
 
-**CHSH inequality.** The Clauser-Horne-Shimony-Holt formulation of Bell's inequality, with the Bell-local bound of 2 and the quantum (Tsirelson) bound of $2\sqrt{2}$. In the deterministic OI completion, measurement independence plus parameter independence gives the bound 2; quantum violation therefore uses ontic parameter dependence. The cited stochastic causal-local indivisible construction separately has the Tsirelson bound. Discussed in Appendix C §C.2.
+**CHSH inequality.** The Clauser-Horne-Shimony-Holt formulation of Bell's inequality, with the Bell-local bound of 2 and the quantum (Tsirelson) bound of $2\sqrt{2}$. In the deterministic OI completion, measurement independence plus parameter independence, with a $\pm1$ outcome in every run, gives the bound 2; quantum violation under measurement independence therefore uses ontic parameter dependence. The cited stochastic causal-local indivisible construction separately has the Tsirelson bound. Discussed in Appendix C §C.2.
 
 **Cosmological constant problem.** The discrepancy of approximately $10^{122}$ between quantum field theory's predicted vacuum energy ($\sim 10^{113}$ J/m³) and the observed value inferred from cosmic expansion ($\sim 6 \times 10^{-10}$ J/m³). The framework proposes to *dissolve* this problem by identifying the two quantities as properties of logically distinct descriptions: the quantum vacuum energy is the emergent QFT's prediction within a partition; the observed cosmological constant is the gravitational consequence of the substratum's full content. The descriptive distinction is established; the dissolution is conditional on the open coupling step. Developed in Chapter 7 §7.7.
 
@@ -6744,7 +6744,7 @@ This glossary defines the framework's distinctive terminology and the technical
 
 **Trace-out.** The mathematical operation of marginalizing over (summing or integrating out) the hidden-sector degrees of freedom, producing the reduced description on the visible sector. The framework's central technical operation. Equivalent to partial trace in quantum mechanics. Defined throughout Chapter 1.
 
-**Tsirelson bound.** The maximum CHSH inequality violation achievable by standard quantum mechanics: $2\sqrt{2}$. In the manuscript this value is retained for the cited **stochastic causal-local indivisible** construction and for any successful lift to the standard quantum Bell set. It is not the ceiling of a measurement-independent, parameter-independent deterministic completion, whose Bell bound is 2. The deterministic OI branch reaches quantum violation by ontic parameter dependence; the measurement-dependent alternative is separately **bounded and benchmarked** in Chapter 1 §1.7. Discussed in Appendix C §C.2.
+**Tsirelson bound.** The maximum CHSH inequality violation achievable by standard quantum mechanics: $2\sqrt{2}$. In the manuscript this value is retained for the cited **stochastic causal-local indivisible** construction and for any successful lift to the standard quantum Bell set. It is not the ceiling of a measurement-independent, parameter-independent deterministic completion recording a $\pm1$ outcome in every run, whose Bell bound is 2. The deterministic OI branch reaches quantum violation by ontic parameter dependence; the measurement-dependent alternative is separately **bounded and benchmarked** in Chapter 1 §1.7. Discussed in Appendix C §C.2.
 
 **U-parity.** The framework's grading structure in the neutrino sector, distinguishing $U^+$ and $U^-$ states in the cubic-group flavor classification. Produces the framework's distinctive sum rule and structural relation among the three PMNS mixing angles. Developed in Chapter 8 §8.4.
 
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--- a/book/The-Incompleteness-of-Observation-FULL.tex
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@@ -1008,8 +1008,10 @@ \subsection{0.2 An informal thought
 every such law admits ({[}Main §3.4{]}). The remaining quantum question
 is the coherent local operational extension of that representation. For
 Bell experiments the deterministic layer faces Bell's sharper fork: a
-measurement-independent response-complete completion with finite-range
-Bell couplings is classical, so quantum violation requires ontic
+measurement-independent response-complete completion with one-step
+own-wing setting interventions, Bell couplings that do not connect the
+wings before readout and a \(\pm1\) outcome in every run is Bell-local,
+so quantum violation under measurement independence requires ontic
 parameter dependence. The framework takes that branch while retaining
 operational no-signaling; the stochastic Tsirelson construction is kept
 as a separate weaker-description result.
@@ -1055,21 +1057,24 @@ \subsection{0.3 The framework's central
 law.
 
 For spatially separated systems, the coupling graph supplies an exact
-causal cone. Bell adds a sharper deterministic constraint: if the
-response-complete pre-setting ontic ensemble is setting-independent and
+causal cone. Bell adds a sharper deterministic constraint: if each
+wing's setting intervention, applied at one step, reads and writes only
+its own region, every run records a \(\pm1\) outcome at each wing, the
+response-complete pre-setting ontic ensemble is setting-independent, and
 the wings lie outside each other's graph cone for the duration of the
 measurement, then Bell factorization follows and \(|S_{\rm CHSH}|\le2\).
 The adopted branch therefore retains measurement independence and uses
-ontic parameter dependence, realized in the SM/GR target through
-preparation-indexed structure in the state-dependent graph \(G(x)\)
-while preserving operational no-signaling. The measurement-dependent
-horn is recorded separately: \(0.0309\) bits is a model-independent
-necessary lower bound from the manuscript's inequality, not an
-achievable cost. What is not yet claimed as a completed theorem is one
-common standard local quantum instrument/composite representation for
-every coherent intervention at once. That is the remaining
-operational-lifting layer; it does not weaken the exact
-stochastic--quantum equivalence already established.
+ontic parameter dependence while preserving operational no-signaling.
+The SM/GR target proposes preparation-indexed structure in the
+state-dependent graph \(G(x)\) for it; whether that structure keeps
+no-signaling and the continuum-curvature limit is the open hypothesis
+H-Bell. The measurement-dependent horn is recorded separately:
+\(0.0309\) bits is a model-independent necessary lower bound from the
+manuscript's inequality, not an achievable cost. What is not claimed as
+a completed theorem is one common standard local quantum
+instrument/composite representation for every coherent intervention at
+once. That is the remaining operational-lifting layer; it does not
+weaken the exact stochastic--quantum equivalence already established.
 
 \hypertarget{the-intellectual-context}{%
 \subsection{0.4 The intellectual
@@ -1493,16 +1498,18 @@ \subsection{1.1 The problem and the
 
 This chapter proves those statements, then adds their spatial scope. The
 coupling graph of the underlying dynamics gives exact causal cones. At
-the response-complete deterministic level, a pointwise finite-range cone
-together with local interventions and one setting-independent
-pre-setting ensemble is Bell-local and gives \(|S_{\rm CHSH}|\le2\). The
-adopted quantum-Bell branch therefore retains measurement independence
-and relinquishes ontic parameter independence, while preserving
-operational no-signaling. The one boundary not folded into the theorem
-is the full coherent instrument/composite category of operational
-quantum mechanics. Keeping that boundary explicit lets the chapter
-recover the original equivalence claim without confusing a universal
-representation theorem with a uniqueness theorem.
+the response-complete deterministic level, setting interventions,
+applied at one step, that each read and write only their own wing,
+readouts outside the other wing's graph cone, a \(\pm1\) outcome
+recorded in every run, and one setting-independent pre-setting ensemble
+give a Bell-local model and \(|S_{\rm CHSH}|\le2\). The adopted
+quantum-Bell branch therefore retains measurement independence and
+relinquishes ontic parameter independence, while preserving operational
+no-signaling. The one boundary not folded into the theorem is the full
+coherent instrument/composite category of operational quantum mechanics.
+Keeping that boundary explicit lets the chapter recover the original
+equivalence claim without confusing a universal representation theorem
+with a uniqueness theorem.
 
 \hypertarget{the-starting-point}{%
 \subsection{1.2 The starting point}\label{the-starting-point}}
@@ -2258,11 +2265,12 @@ \subsection{1.7 Bell-inequality
 The Bell claim must separate the deterministic completion from the
 reduced stochastic description. For a Bell-relevant substratum whose
 coupling range does not connect the wings before readout, the dependency
-graph gives exact pointwise separation. If the response-complete
-pre-setting ensemble is also independent of the settings, determinism
-yields an ordinary Bell-local hidden-variable model and
-\(|S_{\rm CHSH}|\le2\). Hidden memory and indivisibility do not alter
-that ceiling.
+graph gives exact pointwise separation. If each setting intervention,
+applied at one step, also reads and writes only its own wing, every run
+records a \(\pm1\) outcome at each wing, and the response-complete
+pre-setting ensemble is independent of the settings, determinism yields
+an ordinary Bell-local hidden-variable model and \(|S_{\rm CHSH}|\le2\).
+Hidden memory and indivisibility do not alter that ceiling.
 
 The framework therefore declines the
 measurement-dependent/superdeterministic horn and takes \textbf{ontic
@@ -2272,18 +2280,18 @@ \subsection{1.7 Bell-inequality
 response): the vacuum/uniform reference graph remains geometric and
 bounded-range, while an entangling preparation may supply Bell-relevant
 long adjacency so a microstate response at one wing can depend on the
-remote setting. The averaged operational distribution remains
-no-signaling. H-Bell is the open metric/Ollivier--Ricci stability
-condition for those prepared graphs. That condition is now downstream of
-a harder one. The cited convergence theorem is arbitrary-dimensional
-only for the manifold-distance-weighted graph metric, and for the
-degree-\(6\) cubic reference graph the intrinsic hop metric is exactly
-\(\ell_1\) --- a \(\sqrt2\) diagonal stretch that does not decay at any
-scale --- so the hop-metric curvature route fails for the reference
-family, before any Bell edge is added, and no \(D=3\) extension of that
-theorem would rescue it. The emergent geometry itself is not in
-question: the substratum's dispersion relation is isotropic at leading
-order. What must be re-founded is the curvature functional, on the
+remote setting. H-Bell is the open requirement that those prepared
+graphs preserve operational no-signaling and the metric/Ollivier--Ricci
+continuum limit. The curvature condition is downstream of a harder one.
+The cited convergence theorem is arbitrary-dimensional only for the
+manifold-distance-weighted graph metric, and for the degree-\(6\) cubic
+reference graph the intrinsic hop metric is exactly \(\ell_1\) --- a
+\(\sqrt2\) diagonal stretch that does not decay at any scale --- so the
+hop-metric curvature route fails for the reference family, before any
+Bell edge is added, and no \(D=3\) extension of that theorem would
+rescue it. The emergent geometry itself is not in question: the
+substratum's dispersion relation is isotropic at leading order. What
+must be re-founded is the curvature functional, on the
 propagation/Laplacian geometry rather than on shortest-path counts {[}SM
 §3.2{]}. The setting-dependent alternative is recorded but not adopted;
 Main §3.3 gives the model-independent necessary lower bound
@@ -2330,11 +2338,12 @@ \subsection{1.8 The characterization
 
 \textbf{Spatial extension.} The dependency graph supplies finite causal
 cones exactly for finite-range substrata. Bell adds a separate
-constraint: for a response-complete deterministic completion,
-measurement independence plus parameter independence would imply
-\(|S_{\rm CHSH}|\le2\). Section §1.7 therefore takes the
-measurement-independent, ontically parameter-dependent branch for
-Bell-violating substrata and keeps operational no-signaling separate.
+constraint: for a response-complete deterministic completion that
+records a \(\pm1\) outcome in every run, measurement independence plus
+parameter independence would imply \(|S_{\rm CHSH}|\le2\). Section §1.7
+therefore takes the measurement-independent, ontically
+parameter-dependent branch for Bell-violating substrata and keeps
+operational no-signaling separate.
 
 \textbf{Operational boundary.} These theorems do not yet prove that the
 entire family of coherent instruments and composites equals the unique
@@ -3739,12 +3748,12 @@ \subsection{2.6 The three projections}\label{the-three-projections}}
 spatial construction the coupling graph supplies exact causal cones for
 finite-range substrata. Bell is separate from the full-QM lift: a
 measurement-independent response-complete deterministic completion with
-parameter independence would obey \(|S_{\rm CHSH}|\le2\), so the
-framework's Bell-violating branch is ontically parameter-dependent but
-operationally no-signaling. Two independent qualifications remain beyond
-the finite-law equivalence: the simultaneous coherent
-instrument/composite lift ({[}Main §3.4{]}) and H-Bell, the
-compatibility of the local lattice sector with the ontically
+parameter independence and a \(\pm1\) outcome in every run would obey
+\(|S_{\rm CHSH}|\le2\), so the framework's Bell-violating branch is
+ontically parameter-dependent but operationally no-signaling. Two
+independent qualifications remain beyond the finite-law equivalence: the
+simultaneous coherent instrument/composite lift ({[}Main §3.4{]}) and
+H-Bell, the compatibility of the local lattice sector with the ontically
 parameter-dependent Bell completion. Applied to the local lattice sector
 constructed in this chapter --- a \(d = 3\) cubic lattice with \(K = 6\)
 internal components and the wave equation as its local propagating
@@ -3757,9 +3766,10 @@ \subsection{2.6 The three projections}\label{the-three-projections}}
 develops the specific JUNO neutrino measurement that the framework's
 parameter-free PMNS-angle value matches at \(0.07\sigma\) (a
 retrodiction). The local nearest-neighbor sector cannot itself supply
-Bell parameter dependence for wings outside each other's graph cone
-under measurement independence; identifying it with one Bell-violating
-total completion is the open H-Bell compatibility hypothesis.
+Bell parameter dependence for wings with one-step own-wing setting
+interventions outside each other's graph cone under measurement
+independence; identifying it with one Bell-violating total completion is
+the open H-Bell compatibility hypothesis.
 
 \textbf{The boundary-thermodynamic projection: general relativity.} A
 second projection takes the same substratum but applies the trace-out
@@ -4282,11 +4292,13 @@ \subsection{3.2 The observation axis}\label{the-observation-axis}}
 theorem establishes that the stated observed and structural inputs
 uniquely fix this \textbf{local residue} up to
 \(\mathcal{G}_{\text{sub}}\) under Theorem 23's conditions. It does not
-uniquely determine a Bell-inclusive full representative. The reference
-cubic graph is Bell-local under measurement independence; the adopted
-branch uses preparation-indexed state-dependent adjacency, with H-Bell
-conditioning its metric/Ollivier--Ricci compatibility and its uniqueness
-left open.
+uniquely determine a Bell-inclusive full representative. With one-step
+own-wing setting interventions, readouts outside the other wing's graph
+cone and a \(\pm1\) outcome in every run, the reference cubic graph is
+Bell-local under measurement independence; the adopted branch proposes
+preparation-indexed state-dependent adjacency under the open hypothesis
+H-Bell (operational no-signaling and the metric/Ollivier--Ricci
+continuum limit), with its uniqueness left open.
 
 Level D is where the framework's twenty-two classified quantitative
 predictions live (two parameter-free structural and five conditional
@@ -4881,25 +4893,28 @@ \subsection{3.7 No-go theorems at different descriptive
 every case.
 
 \textbf{Bell's theorem.} Bell's theorem binds directly on the
-deterministic hidden-variable completion. If the Bell-relevant coupling
-range does not connect the wings before readout and one
-setting-independent response-complete ensemble is used, the model
-factorizes and obeys \(|S_{\rm CHSH}|\le2\). The framework therefore
-cannot use graph locality, screening, outcome dependence, or
-indivisibility to explain the quantum violation. It retains measurement
-independence and accepts \textbf{ontic parameter dependence} for
-Bell-violating substrata, with operational no-signaling as the distinct
-empirical locality statement. The cited stochastic causal-local
-indivisible construction can still obey Tsirelson because its
-causal-independence criterion is weaker than Bell factorization.
-Unrestricted globally controlled OI realizations remain the PR-box
-countercontrol.
+deterministic hidden-variable completion. If the setting interventions,
+applied at one step, each read and write only their own wing, the
+Bell-relevant coupling range does not connect the wings before readout,
+every run records a \(\pm1\) outcome, and one setting-independent
+response-complete ensemble is used, the model factorizes and obeys
+\(|S_{\rm CHSH}|\le2\). The framework therefore cannot use graph
+locality, screening, outcome dependence, or indivisibility to explain
+the quantum violation. It retains measurement independence and accepts
+\textbf{ontic parameter dependence} for Bell-violating substrata, with
+operational no-signaling as the distinct empirical locality statement.
+The cited stochastic causal-local indivisible construction can still
+obey Tsirelson because its causal-independence criterion is weaker than
+Bell factorization. Unrestricted globally controlled OI realizations
+remain the PR-box countercontrol.
 
 In hierarchy language, the Bell question splits the deterministic
-substratum from the reduced stochastic description. A finite-range Bell
-graph plus a setting-independent response-complete ensemble would force
-the substratum into Bell's local class and cap CHSH at \(2\). The
-framework therefore does not identify no-signaling, Jarrett parameter
+substratum from the reduced stochastic description. A Bell graph that
+does not connect the wings before readout, with one-step own-wing
+setting interventions and a \(\pm1\) outcome in every run, plus a
+setting-independent response-complete ensemble, would force the
+substratum into Bell's local class and cap CHSH at \(2\). The framework
+therefore does not identify no-signaling, Jarrett parameter
 independence, Fine's theorem, hidden memory, or indivisibility with a
 derivation of the quantum correlation set. Its adopted deterministic
 branch is instead ontic parameter dependence with operational
@@ -5015,9 +5030,11 @@ \subsection{3.7 No-go theorems at different descriptive
 
 \textbf{Bell's theorem, conceded and then confronted.} Bell's
 mathematics binds on the framework because the substratum is a
-response-complete hidden-variable completion. If the Bell-relevant graph
-does not connect the wings before readout and the pre-setting ensemble
-is independent of the settings, determinism gives Bell factorization and
+response-complete hidden-variable completion. If the setting
+interventions, applied at one step, each read and write only their own
+wing, the Bell-relevant graph does not connect the wings before readout,
+every run records a \(\pm1\) outcome, and the pre-setting ensemble is
+independent of the settings, determinism gives Bell factorization and
 \(|S_{\rm CHSH}|\le2\). The framework therefore cannot explain quantum
 Bell violation by combining pointwise graph locality and indivisibility.
 It declines the measurement-dependent/superdeterministic horn and takes
@@ -5026,9 +5043,9 @@ \subsection{3.7 No-go theorems at different descriptive
 state-dependent graph \(G(x)\) (or an equivalent ontically nonlocal
 response): the reference vacuum/uniform graph remains geometric and
 bounded-range, while an entangling preparation may add Bell-relevant
-long adjacency. The averaged operational statistics remain no-signaling.
-H-Bell is the remaining metric/Ollivier--Ricci stability condition for
-those prepared graphs. That condition is now downstream of a harder one.
+long adjacency. H-Bell is the open requirement that those prepared
+graphs preserve operational no-signaling and the metric/Ollivier--Ricci
+continuum limit. The curvature condition is downstream of a harder one.
 The cited convergence theorem is arbitrary-dimensional only for the
 manifold-distance-weighted graph metric, and for the degree-\(6\) cubic
 reference graph the intrinsic hop metric is exactly \(\ell_1\) --- a
@@ -5053,22 +5070,22 @@ \subsection{3.7 No-go theorems at different descriptive
 fail parameter independence, and the framework explicitly accepts that
 conclusion. Its Bell-violating prepared states are therefore
 \textbf{ontically nonlocal in Bell's parameter sense}. In the concrete
-lattice branch, that nonlocality is represented by preparation-indexed
-state-dependent adjacency (or an equivalent response rule), not by
-pretending the nearest-neighbor reference wave equation itself carries
-Bell influence. What remains local operationally is the no-signaling
-statement --- changing a controllable setting cannot be used to transmit
-a message to the remote wing. The cosmological partition or shared
-boundary may be proposed as a physical realization, but calling that
-carrier atemporal, global, or prior to emergent spacetime does not
-remove Bell nonlocality; it only locates it in the ontology. The
-separate Barandes--Hasan--Kagan theorem shows that the reduced
-stochastic law can satisfy their weaker causal-independence criterion
-and remain below Tsirelson, but that criterion is not Bell factorization
-for the deterministic completion. The manuscript can therefore defend a
-non-signaling deterministic ontology with a specific locus of
-nonlocality; it does not claim a local hidden-variable resolution of
-Bell.
+lattice branch, that nonlocality is targeted through preparation-indexed
+state-dependent adjacency (or an equivalent response rule) under H-Bell,
+not by pretending the nearest-neighbor reference wave equation itself
+carries Bell influence. What remains local operationally is the
+no-signaling statement --- changing a controllable setting cannot be
+used to transmit a message to the remote wing. The cosmological
+partition or shared boundary may be proposed as a physical realization,
+but calling that carrier atemporal, global, or prior to emergent
+spacetime does not remove Bell nonlocality; it only locates it in the
+ontology. The separate Barandes--Hasan--Kagan theorem shows that the
+reduced stochastic law can satisfy their weaker causal-independence
+criterion and remain below Tsirelson, but that criterion is not Bell
+factorization for the deterministic completion. The manuscript can
+therefore defend a non-signaling deterministic ontology with a specific
+locus of nonlocality; it does not claim a local hidden-variable
+resolution of Bell.
 
 \textbf{The bill, paid in the open.} A deterministic substratum that
 violates \textbf{ontic parameter independence} owes an account of
@@ -6029,58 +6046,61 @@ \subsection{4.4 Engaging the no-go results through one
 
 Third, locate where the framework meets or violates the theorem's
 premises at the correct level. Bell is the sharpest case: for a
-response-complete deterministic completion, finite-range Bell couplings
-plus a setting-independent pre-setting ensemble imply Bell factorization
-and \(|S_{\rm CHSH}|\le2\). The framework therefore does not obtain
-quantum Bell violation from outcome-independence failure in an
-indivisible stochastic law; it retains measurement independence and
-gives up \textbf{ontic parameter independence}, while preserving
-operational no-signaling. PBR's preparation independence --- the
-postulate that independently prepared systems have a product joint
-ontic-state distribution --- is not a premise of bare OI. Co-embedded
-preparation devices may share preparation-relevant hidden or boundary
-data, so unconditional product independence is not guaranteed; the graph
-causal cone by itself does not derive either a conditional product
-distribution or the standard quantum tensor-product composite.
-Frauchiger-Renner's universal applicability fails because the
-substratum-level and emergent-level descriptions are incommensurable in
-the relevant sense. The fourth theorem, Kochen-Specker, does not fit
-this ``satisfied below, violated above'' form: its assumed property, a
-noncontextual valuation of the observables, holds at neither level ---
-the framework --- conditionally on the operational bridge reconstructing
-the standard observable algebra --- carries the operational theory,
-which by Kochen-Specker's own content admits no noncontextual valuation,
-and the substratum carries a definite configuration that is not a
-valuation of the emergent observables at all. The framework's
-contextuality is forced, under that same conditional bridge, by
-equivalence at the operational layer --- and what the framework adds is
-the account: contextuality is the partition-dependence of the trace-out.
-The common factor across all four is therefore the architecture --- two
-levels and a trace-out --- not a single property-placement move
-repeated.
+response-complete deterministic completion, Bell couplings that do not
+connect the wings before readout, one-step own-wing setting
+interventions and a \(\pm1\) outcome in every run, plus a
+setting-independent pre-setting ensemble, imply Bell factorization and
+\(|S_{\rm CHSH}|\le2\). The framework therefore does not obtain quantum
+Bell violation from outcome-independence failure in an indivisible
+stochastic law; it retains measurement independence and gives up
+\textbf{ontic parameter independence}, while preserving operational
+no-signaling. PBR's preparation independence --- the postulate that
+independently prepared systems have a product joint ontic-state
+distribution --- is not a premise of bare OI. Co-embedded preparation
+devices may share preparation-relevant hidden or boundary data, so
+unconditional product independence is not guaranteed; the graph causal
+cone by itself does not derive either a conditional product distribution
+or the standard quantum tensor-product composite. Frauchiger-Renner's
+universal applicability fails because the substratum-level and
+emergent-level descriptions are incommensurable in the relevant sense.
+The fourth theorem, Kochen-Specker, does not fit this ``satisfied below,
+violated above'' form: its assumed property, a noncontextual valuation
+of the observables, holds at neither level --- the framework ---
+conditionally on the operational bridge reconstructing the standard
+observable algebra --- carries the operational theory, which by
+Kochen-Specker's own content admits no noncontextual valuation, and the
+substratum carries a definite configuration that is not a valuation of
+the emergent observables at all. The framework's contextuality is
+forced, under that same conditional bridge, by equivalence at the
+operational layer --- and what the framework adds is the account:
+contextuality is the partition-dependence of the trace-out. The common
+factor across all four is therefore the architecture --- two levels and
+a trace-out --- not a single property-placement move repeated.
 
 Fourth, verify that the framework's predictions match quantum mechanics
 in the regime where the no-go theorem applies, without silently
 importing the very condition under test. For Bell, verify the
-deterministic completion directly: if its Bell-relevant graph is
-finite-range at the wings and its pre-setting ensemble is
-setting-independent, CHSH is capped at \(2\). The framework's quantum
-branch therefore has ontic parameter dependence. For the specific SM/GR
-representative, the nearest-neighbor \textbf{reference} graph cannot
-itself supply that parameter dependence in a Bell protocol whose wings
-lie outside each other's graph cone. The existing state-dependent graph
-\(G(x)\) supplies the native target: preparation-indexed adjacency (or
-an equivalent nonlocal response), with H-Bell now the open
-metric/Ollivier--Ricci stability condition for the prepared graph
-family. The measurement-dependent alternative is not adopted; Chapter 1
-gives a model-independent necessary lower bound and a separate causal
-benchmark; the stochastic causal-local Tsirelson theorem is retained
-only at its weaker stochastic level. Kochen-Specker, PBR, and
-Frauchiger-Renner concern the coherent operational structure and
-therefore inherit the operational-lifting qualification: their standard
-quantum statistics are recovered once the common instrument/composite
-representation is established, not merely from universal fixed-basis
-representability.
+deterministic completion directly: if its setting interventions, applied
+at one step, each read and write only their own wing, its Bell-relevant
+graph does not connect the wings before readout, every run records a
+\(\pm1\) outcome, and its pre-setting ensemble is setting-independent,
+CHSH is capped at \(2\). The framework's quantum branch therefore has
+ontic parameter dependence. For the specific SM/GR representative, the
+nearest-neighbor \textbf{reference} graph cannot itself supply that
+parameter dependence in a Bell protocol with one-step own-wing setting
+interventions whose wings lie outside each other's graph cone. The
+existing state-dependent graph \(G(x)\) supplies the native target:
+preparation-indexed adjacency (or an equivalent nonlocal response), with
+H-Bell the open requirement that the prepared graph family preserve
+operational no-signaling and the metric/Ollivier--Ricci continuum limit.
+The measurement-dependent alternative is not adopted; Chapter 1 gives a
+model-independent necessary lower bound and a separate causal benchmark;
+the stochastic causal-local Tsirelson theorem is retained only at its
+weaker stochastic level. Kochen-Specker, PBR, and Frauchiger-Renner
+concern the coherent operational structure and therefore inherit the
+operational-lifting qualification: their standard quantum statistics are
+recovered once the common instrument/composite representation is
+established, not merely from universal fixed-basis representability.
 
 \textbf{One architecture, verified per theorem.} Two things must be held
 apart here, because they pull in opposite directions and both are true.
@@ -6225,11 +6245,11 @@ \subsection{4.5 Pre-registered falsification
 \textbf{stochastic causal-local indivisible construction} ({[}Main
 §3.3{]}), not to a Bell-local deterministic completion and not to
 generic P-indivisibility. The deterministic OI layer reaches quantum
-Bell violation only on the ontically parameter-dependent branch. An
-observed loophole-free CHSH value above \(2\sqrt2\) would falsify
-standard quantum mechanics and any claim that the relevant OI
-operational lift lands in the standard quantum Bell set; it would not,
-by itself, falsify P-indivisibility.
+Bell violation, under measurement independence, only on the ontically
+parameter-dependent branch. An observed loophole-free CHSH value above
+\(2\sqrt2\) would falsify standard quantum mechanics and any claim that
+the relevant OI operational lift lands in the standard quantum Bell set;
+it would not, by itself, falsify P-indivisibility.
 
 \emph{Exact unitarity of the visible-sector dynamics at accessible
 scales.} The framework derives unitary quantum evolution as the exact
@@ -22286,21 +22306,25 @@ \subsection{18.4 The epistemic character of quantum
 
 \textbf{Bell's theorem and the chosen nonlocality.} Bell does not rule
 out determinism by itself; it rules out reproducing the observed
-correlations with a response-complete deterministic completion that is
-both measurement-independent and parameter-independent. Chapter 1 proves
-the corresponding Bell ceiling: if the Bell-relevant coupling range does
-not connect the wings before readout and one setting-independent
-pre-setting ensemble is used, then \(|S_{\rm CHSH}|\le2\). The framework
-therefore declines the measurement-dependent/superdeterministic horn and
-takes \textbf{ontic parameter dependence}. In the specific SM/GR
-realization the target mechanism is preparation-indexed adjacency in the
-already state-dependent graph \(G(x)\) (or an equivalent ontically
-nonlocal response), so a prepared microstate response may depend on the
-remote setting while the reference vacuum/uniform graph remains
-geometric and bounded-range. The operational distribution remains
-no-signaling. The \(2\sqrt2\) theorem for the causal-local indivisible
-stochastic description is a separate weaker-layer result, not a locality
-theorem for the deterministic completion.
+correlations with a response-complete deterministic completion that
+records a \(\pm1\) outcome in every run and is both
+measurement-independent and parameter-independent. Chapter 1 proves the
+corresponding Bell ceiling: if the setting interventions, applied at one
+step, each read and write only their own wing, the Bell-relevant
+coupling range does not connect the wings before readout, every run
+records a \(\pm1\) outcome, and one setting-independent pre-setting
+ensemble is used, then \(|S_{\rm CHSH}|\le2\). The framework therefore
+declines the measurement-dependent/superdeterministic horn and takes
+\textbf{ontic parameter dependence}. In the specific SM/GR realization
+the target mechanism is preparation-indexed adjacency in the already
+state-dependent graph \(G(x)\) (or an equivalent ontically nonlocal
+response), so a prepared microstate response may depend on the remote
+setting while the reference vacuum/uniform graph remains geometric and
+bounded-range. Whether those prepared graphs keep the operational
+distribution no-signaling and preserve the continuum-curvature limit is
+the open hypothesis H-Bell. The \(2\sqrt2\) theorem for the causal-local
+indivisible stochastic description is a separate weaker-layer result,
+not a locality theorem for the deterministic completion.
 
 One proposed physical realization of that preparation-indexed parameter
 dependence uses non-localized cosmological-boundary modes. This is a
@@ -27934,26 +27958,31 @@ \subsection{C.2 Bell's theorem and the framework's relationship to
 
 \textbf{The framework's response.} Bell applies directly to the
 response-complete deterministic substratum. If the Bell-relevant
-coupling range is finite at the wings' separation, local interventions
-occur before the corresponding cones meet, and one setting-independent
+coupling range is finite at the wings' separation, the setting
+interventions, applied at one step, each read and write only their own
+wing and each wing's readout lies outside the other wing's graph cone,
+every run records a \(\pm1\) outcome, and one setting-independent
 pre-setting ensemble is used, then the hidden responses factorize and
 \(|S_{\rm CHSH}|\le2\). OI therefore cannot combine deterministic
-response completeness, measurement independence, and ontic parameter
-independence and still reproduce quantum Bell violation. The framework
-keeps measurement independence and takes the remaining horn:
-\textbf{ontic parameter dependence} for Bell-violating substrata, with
-operational no-signaling retained (Chapter 1 §1.7; Main §3.3).
+response completeness, a \(\pm1\) outcome in every run, measurement
+independence, and ontic parameter independence and still reproduce
+quantum Bell violation. The framework keeps measurement independence and
+takes the remaining horn: \textbf{ontic parameter dependence} for
+Bell-violating substrata, with operational no-signaling retained
+(Chapter 1 §1.7; Main §3.3).
 
 The cited causal-local \textbf{stochastic} indivisible construction
 separately obeys the Tsirelson bound \(2\sqrt2\). By the Bell ceiling
-theorem (Main §3.3), a response-complete deterministic completion that
-keeps a pointwise finite-range cone on one setting-independent
-pre-setting ensemble is a local hidden-variable model, so
-\(|S_{\rm CHSH}|\le2\). The framework therefore adopts ontic
-\textbf{parameter dependence}, implemented in the SM/GR branch through
+theorem (Main §3.3), a response-complete deterministic completion with
+one-step own-wing setting interventions, each wing's readout outside the
+other wing's graph cone, a \(\pm1\) outcome in every run, and one
+setting-independent pre-setting ensemble is a local hidden-variable
+model, so \(|S_{\rm CHSH}|\le2\). The framework therefore adopts ontic
+\textbf{parameter dependence}, targeted in the SM/GR branch through
 preparation-indexed structure in the state-dependent graph \(G(x)\) (or
-an equivalent ontically nonlocal response), while retaining operational
-no-signaling. If measurement independence were dropped instead,
+an equivalent ontically nonlocal response) under the open hypothesis
+H-Bell, while retaining operational no-signaling. If measurement
+independence were dropped instead,
 \(S_{\rm CHSH}\le\min\{4,\,2+4\sqrt{2\ln2\,I_{\rm ont}}\}\) gives the
 model-independent necessary lower bound \(I_{\rm ont}\ge0.0309\) bits
 for the quantum value. Hall--Branciard's optimized causal CHSH model
@@ -27999,10 +28028,11 @@ \subsection{C.2 Bell's theorem and the framework's relationship to
 premise but ontically parameter-dependent, with operational
 no-signaling. Hidden predictive memory and indivisibility remain central
 to the OI dynamics, but they are \textbf{not} the mechanism that evades
-Bell: a parameter-independent deterministic completion would still
-satisfy CHSH \(\le2\). The Tsirelson value is retained for the cited
-stochastic causal-local indivisible construction and, conditionally, for
-any successful operational lift to standard quantum mechanics (§C.2).
+Bell: a measurement-independent, parameter-independent deterministic
+completion recording a \(\pm1\) outcome in every run would still satisfy
+CHSH \(\le2\). The Tsirelson value is retained for the cited stochastic
+causal-local indivisible construction and, conditionally, for any
+successful operational lift to standard quantum mechanics (§C.2).
 
 \hypertarget{c.3-the-no-go-theorems-pbr-frauchiger-renner-colbeck-renner-bong-wiseman}{%
 \subsection{C.3 The no-go theorems: PBR, Frauchiger-Renner,
@@ -29296,16 +29326,17 @@ \section{Glossary}\label{glossary}}
 \textbf{Bell-inequality violations.} Empirical correlations exceeding
 bounds derivable from local hidden-variable theories. For a
 response-complete deterministic OI completion, measurement independence
-plus ontic parameter independence gives Bell factorization and
-\(|S_{\rm CHSH}|\le2\). The framework therefore retains measurement
-independence but relinquishes \textbf{ontic parameter independence} for
-Bell-violating substrata, while preserving operational no-signaling. The
-measurement-dependent alternative is recorded rather than adopted: the
-manuscript proves the model-independent necessary lower bound
-\(I_{\rm ont}\ge0.0309\) bits for the quantum CHSH value, while an
-optimized causal model in Hall--Branciard uses about \(0.080\) bits (the
-smaller \(\sim0.046\)-bit benchmark is retrocausal). Developed in
-Chapter 1 §1.7 and Appendix C §C.2.
+plus ontic parameter independence, with a \(\pm1\) outcome in every run,
+gives Bell factorization and \(|S_{\rm CHSH}|\le2\). The framework
+therefore retains measurement independence but relinquishes
+\textbf{ontic parameter independence} for Bell-violating substrata,
+while preserving operational no-signaling. The measurement-dependent
+alternative is recorded rather than adopted: the manuscript proves the
+model-independent necessary lower bound \(I_{\rm ont}\ge0.0309\) bits
+for the quantum CHSH value, while an optimized causal model in
+Hall--Branciard uses about \(0.080\) bits (the smaller \(\sim0.046\)-bit
+benchmark is retrocausal). Developed in Chapter 1 §1.7 and Appendix C
+§C.2.
 
 \textbf{Born rule.} The quantum-mechanical prescription that the
 probability of measurement outcome \(i\) on state \(|\psi\rangle\) is
@@ -29495,10 +29526,11 @@ \section{Glossary}\label{glossary}}
 \textbf{CHSH inequality.} The Clauser-Horne-Shimony-Holt formulation of
 Bell's inequality, with the Bell-local bound of 2 and the quantum
 (Tsirelson) bound of \(2\sqrt{2}\). In the deterministic OI completion,
-measurement independence plus parameter independence gives the bound 2;
-quantum violation therefore uses ontic parameter dependence. The cited
-stochastic causal-local indivisible construction separately has the
-Tsirelson bound. Discussed in Appendix C §C.2.
+measurement independence plus parameter independence, with a \(\pm1\)
+outcome in every run, gives the bound 2; quantum violation under
+measurement independence therefore uses ontic parameter dependence. The
+cited stochastic causal-local indivisible construction separately has
+the Tsirelson bound. Discussed in Appendix C §C.2.
 
 \textbf{Cosmological constant problem.} The discrepancy of approximately
 \(10^{122}\) between quantum field theory's predicted vacuum energy
@@ -29937,11 +29969,12 @@ \section{Glossary}\label{glossary}}
 manuscript this value is retained for the cited \textbf{stochastic
 causal-local indivisible} construction and for any successful lift to
 the standard quantum Bell set. It is not the ceiling of a
-measurement-independent, parameter-independent deterministic completion,
-whose Bell bound is 2. The deterministic OI branch reaches quantum
-violation by ontic parameter dependence; the measurement-dependent
-alternative is separately \textbf{bounded and benchmarked} in Chapter 1
-§1.7. Discussed in Appendix C §C.2.
+measurement-independent, parameter-independent deterministic completion
+recording a \(\pm1\) outcome in every run, whose Bell bound is 2. The
+deterministic OI branch reaches quantum violation by ontic parameter
+dependence; the measurement-dependent alternative is separately
+\textbf{bounded and benchmarked} in Chapter 1 §1.7. Discussed in
+Appendix C §C.2.
 
 \textbf{U-parity.} The framework's grading structure in the neutrino
 sector, distinguishing \(U^+\) and \(U^-\) states in the cubic-group
@@ -30782,4 +30815,4 @@ \subsection{Historical and philosophical
 {[}Origin of the molecular clock hypothesis.{]}
 
 \end{document}
-% source-sha256: da16313cd63b57dde7cd34212ebb478edcde411e0ecbadbdb95e88502df98118
+% source-sha256: 4429793c2f6486d2e99b74b637fede7c899e6adb5f6aca5c1adf51f27d689d82
diff --git a/book/appendix-c-objections.md b/book/appendix-c-objections.md
index 5b8f5758e..3a355d381 100644
--- a/book/appendix-c-objections.md
+++ b/book/appendix-c-objections.md
@@ -29,9 +29,9 @@ The most frequent objection to deterministic-substratum theories is: "Bell's the
 
 **The objection.** Bell's theorem (1964) establishes that no local hidden-variable theory can reproduce the quantum-mechanical predictions for entangled systems. The empirical violations of Bell inequalities (CHSH measured to $\geq 2.4$ in multiple experiments, with quantum prediction at $2\sqrt{2} \approx 2.83$) are taken as definitively excluding local hidden-variable theories. The framework's deterministic substratum looks suspiciously like a hidden-variable theory; therefore the framework should be ruled out by Bell's theorem in the same way.
 
-**The framework's response.** Bell applies directly to the response-complete deterministic substratum. If the Bell-relevant coupling range is finite at the wings' separation, local interventions occur before the corresponding cones meet, and one setting-independent pre-setting ensemble is used, then the hidden responses factorize and $|S_{\rm CHSH}|\le2$. OI therefore cannot combine deterministic response completeness, measurement independence, and ontic parameter independence and still reproduce quantum Bell violation. The framework keeps measurement independence and takes the remaining horn: **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling retained (Chapter 1 §1.7; Main §3.3).
+**The framework's response.** Bell applies directly to the response-complete deterministic substratum. If the Bell-relevant coupling range is finite at the wings' separation, the setting interventions, applied at one step, each read and write only their own wing and each wing's readout lies outside the other wing's graph cone, every run records a $\pm1$ outcome, and one setting-independent pre-setting ensemble is used, then the hidden responses factorize and $|S_{\rm CHSH}|\le2$. OI therefore cannot combine deterministic response completeness, a $\pm1$ outcome in every run, measurement independence, and ontic parameter independence and still reproduce quantum Bell violation. The framework keeps measurement independence and takes the remaining horn: **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling retained (Chapter 1 §1.7; Main §3.3).
 
-The cited causal-local **stochastic** indivisible construction separately obeys the Tsirelson bound $2\sqrt2$. By the Bell ceiling theorem (Main §3.3), a response-complete deterministic completion that keeps a pointwise finite-range cone on one setting-independent pre-setting ensemble is a local hidden-variable model, so $|S_{\rm CHSH}|\le2$. The framework therefore adopts ontic **parameter dependence**, implemented in the SM/GR branch through preparation-indexed structure in the state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response), while retaining operational no-signaling. If measurement independence were dropped instead, $S_{\rm CHSH}\le\min\{4,\,2+4\sqrt{2\ln2\,I_{\rm ont}}\}$ gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits; the smaller $\sim0.046$-bit benchmark is retrocausal. Dropping the spatial/intervention restriction permits the general finite OI response construction to reach PR-box behavior; PR is therefore a negative control for causal-local selection, not for the existence of a Hilbert/Born representation.
+The cited causal-local **stochastic** indivisible construction separately obeys the Tsirelson bound $2\sqrt2$. By the Bell ceiling theorem (Main §3.3), a response-complete deterministic completion with one-step own-wing setting interventions, each wing's readout outside the other wing's graph cone, a $\pm1$ outcome in every run, and one setting-independent pre-setting ensemble is a local hidden-variable model, so $|S_{\rm CHSH}|\le2$. The framework therefore adopts ontic **parameter dependence**, targeted in the SM/GR branch through preparation-indexed structure in the state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response) under the open hypothesis H-Bell, while retaining operational no-signaling. If measurement independence were dropped instead, $S_{\rm CHSH}\le\min\{4,\,2+4\sqrt{2\ln2\,I_{\rm ont}}\}$ gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits; the smaller $\sim0.046$-bit benchmark is retrocausal. Dropping the spatial/intervention restriction permits the general finite OI response construction to reach PR-box behavior; PR is therefore a negative control for causal-local selection, not for the existence of a Hilbert/Born representation.
 
 *Not superdeterminism.* Determinism alone does not establish Bell measurement independence, because setting generators are physical degrees of freedom. The manuscript therefore treats measurement independence as an explicit premise of the adopted Bell branch rather than as a theorem of the substratum. It does **not** use setting–hidden correlations to explain the observed violation. A mixing/decorrelation argument may motivate why laboratory setting generators approximate that premise, but the Bell mechanism itself is ontic parameter dependence. If the premise were dropped instead, that would be the measurement-dependent/superdeterministic horn quantified by the $I_{\rm ont}$ bound — a horn the framework records and declines.
 
@@ -39,7 +39,7 @@ The cited causal-local **stochastic** indivisible construction separately obeys
 
 *Not Bohmian mechanics.* Bohmian mechanics adds a pilot wave guiding particle trajectories in configuration space. The framework has no pilot wave and no guidance equation in configuration space. The framework's hidden sector is the substratum's broader configuration space, not a separate guiding field; the dynamics is direct (the bijection $\varphi$) rather than mediated by a guidance equation.
 
-The framework is therefore not a Bell-local hidden-variable theory. Its deterministic completion is measurement-independent by the adopted Bell premise but ontically parameter-dependent, with operational no-signaling. Hidden predictive memory and indivisibility remain central to the OI dynamics, but they are **not** the mechanism that evades Bell: a parameter-independent deterministic completion would still satisfy CHSH $\le2$. The Tsirelson value is retained for the cited stochastic causal-local indivisible construction and, conditionally, for any successful operational lift to standard quantum mechanics (§C.2).
+The framework is therefore not a Bell-local hidden-variable theory. Its deterministic completion is measurement-independent by the adopted Bell premise but ontically parameter-dependent, with operational no-signaling. Hidden predictive memory and indivisibility remain central to the OI dynamics, but they are **not** the mechanism that evades Bell: a measurement-independent, parameter-independent deterministic completion recording a $\pm1$ outcome in every run would still satisfy CHSH $\le2$. The Tsirelson value is retained for the cited stochastic causal-local indivisible construction and, conditionally, for any successful operational lift to standard quantum mechanics (§C.2).
 
 ## C.3 The no-go theorems: PBR, Frauchiger-Renner, Colbeck-Renner, Bong-Wiseman
 
diff --git a/book/ch00-introduction.md b/book/ch00-introduction.md
index 04cb76cf3..5f5eaad73 100644
--- a/book/ch00-introduction.md
+++ b/book/ch00-introduction.md
@@ -38,7 +38,7 @@ These features — coupling, memory persistence, large capacity, and the readbac
 
 The framework's central theorem says something more exact. The finite stochastic law available to the experimenter, a finite reversible hidden-state realization, and a fixed-basis unitary/Born description are mathematically equivalent representations of the same finite observable data. If the hidden record is read back, the reduced law is not merely stochastic: every faithful completion must retain predictive memory. Quantum mechanics is therefore an exact observer-level representation of the incomplete finite law, not an extra microscopic postulate placed on top of it.
 
-The thought experiment captures the framework's central move. Quantum mechanics is reframed from a statement about reality to a statement about the observer's relationship to reality. The mathematics is unchanged; what it represents is different. The wave function is not the universe's state; it is the experimenter's compressed description of what they cannot see. The Born rule is not an independent postulate about fundamental indeterminism at the finite observable-law layer; it is the $|U|^2$ readout dictionary of the exact unitary representation every such law admits ([Main §3.4]). The remaining quantum question is the coherent local operational extension of that representation. For Bell experiments the deterministic layer faces Bell's sharper fork: a measurement-independent response-complete completion with finite-range Bell couplings is classical, so quantum violation requires ontic parameter dependence. The framework takes that branch while retaining operational no-signaling; the stochastic Tsirelson construction is kept as a separate weaker-description result.
+The thought experiment captures the framework's central move. Quantum mechanics is reframed from a statement about reality to a statement about the observer's relationship to reality. The mathematics is unchanged; what it represents is different. The wave function is not the universe's state; it is the experimenter's compressed description of what they cannot see. The Born rule is not an independent postulate about fundamental indeterminism at the finite observable-law layer; it is the $|U|^2$ readout dictionary of the exact unitary representation every such law admits ([Main §3.4]). The remaining quantum question is the coherent local operational extension of that representation. For Bell experiments the deterministic layer faces Bell's sharper fork: a measurement-independent response-complete completion with one-step own-wing setting interventions, Bell couplings that do not connect the wings before readout and a $\pm1$ outcome in every run is Bell-local, so quantum violation under measurement independence requires ontic parameter dependence. The framework takes that branch while retaining operational no-signaling; the stochastic Tsirelson construction is kept as a separate weaker-description result.
 
 The chapters that follow make this thought experiment precise. The room becomes a partition of the universe into visible and hidden sectors. The experimenter becomes a mathematical observer. The characterization theorem then separates what is universal from what is physically discriminating. The universal part is the exact finite-horizon equivalence $S\iff D\iff Q_{\mathrm{fb}}$; the discriminating part is history readback, which forces hidden predictive memory. The spatial extension adds graph causal cones and a separately stated operational screening condition for Bell experiments. The strongest remaining question is therefore not whether the observer has a quantum representation, but whether the whole coherent instrument/composite hierarchy is one standard local quantum operational theory.
 
@@ -52,7 +52,7 @@ finite stochastic laws, finite reversible deterministic realizations, and fixed-
 
 The representation equivalence is universal, so the distinctly memory-bearing content is carried by history readback. When two visible histories with the same present lead to different future laws, every faithful completion must retain predictive information in the hidden sector; on a fixed finite reversible system, recurrence forces the rooted visible process to be indivisible somewhere in its full cycle whenever any visible step is non-deterministic, so that indivisibility also holds for laws with no accessible memory. The observer therefore sees quantum-representable stochastic dynamics because of incomplete access, while the C1–C4 structure tells us when that description contains genuine hidden memory rather than merely a Markovian stochastic law.
 
-For spatially separated systems, the coupling graph supplies an exact causal cone. Bell adds a sharper deterministic constraint: if the response-complete pre-setting ontic ensemble is setting-independent and the wings lie outside each other's graph cone for the duration of the measurement, then Bell factorization follows and $|S_{\rm CHSH}|\le2$. The adopted branch therefore retains measurement independence and uses ontic parameter dependence, realized in the SM/GR target through preparation-indexed structure in the state-dependent graph $G(x)$ while preserving operational no-signaling. The measurement-dependent horn is recorded separately: $0.0309$ bits is a model-independent necessary lower bound from the manuscript's inequality, not an achievable cost. What is not yet claimed as a completed theorem is one common standard local quantum instrument/composite representation for every coherent intervention at once. That is the remaining operational-lifting layer; it does not weaken the exact stochastic–quantum equivalence already established.
+For spatially separated systems, the coupling graph supplies an exact causal cone. Bell adds a sharper deterministic constraint: if each wing's setting intervention, applied at one step, reads and writes only its own region, every run records a $\pm1$ outcome at each wing, the response-complete pre-setting ontic ensemble is setting-independent, and the wings lie outside each other's graph cone for the duration of the measurement, then Bell factorization follows and $|S_{\rm CHSH}|\le2$. The adopted branch therefore retains measurement independence and uses ontic parameter dependence while preserving operational no-signaling. The SM/GR target proposes preparation-indexed structure in the state-dependent graph $G(x)$ for it; whether that structure keeps no-signaling and the continuum-curvature limit is the open hypothesis H-Bell. The measurement-dependent horn is recorded separately: $0.0309$ bits is a model-independent necessary lower bound from the manuscript's inequality, not an achievable cost. What is not claimed as a completed theorem is one common standard local quantum instrument/composite representation for every coherent intervention at once. That is the remaining operational-lifting layer; it does not weaken the exact stochastic–quantum equivalence already established.
 
 ## 0.4 The intellectual context
 
diff --git a/book/ch01-observation.md b/book/ch01-observation.md
index d52093572..48f0a3ae3 100644
--- a/book/ch01-observation.md
+++ b/book/ch01-observation.md
@@ -13,7 +13,7 @@ S\iff D\iff Q_{\mathrm{fb}}.
 $$
 A finite stochastic law, a finite reversible hidden-state realization, and a fixed-basis unitary/Born representation are three descriptions of the same finite observable object. Conversely, every finite quantum record has a finite reversible realization. Second, history readback identifies the nontrivial sector: it forces hidden predictive memory in every faithful completion.
 
-This chapter proves those statements, then adds their spatial scope. The coupling graph of the underlying dynamics gives exact causal cones. At the response-complete deterministic level, a pointwise finite-range cone together with local interventions and one setting-independent pre-setting ensemble is Bell-local and gives $|S_{\rm CHSH}|\le2$. The adopted quantum-Bell branch therefore retains measurement independence and relinquishes ontic parameter independence, while preserving operational no-signaling. The one boundary not folded into the theorem is the full coherent instrument/composite category of operational quantum mechanics. Keeping that boundary explicit lets the chapter recover the original equivalence claim without confusing a universal representation theorem with a uniqueness theorem.
+This chapter proves those statements, then adds their spatial scope. The coupling graph of the underlying dynamics gives exact causal cones. At the response-complete deterministic level, setting interventions, applied at one step, that each read and write only their own wing, readouts outside the other wing's graph cone, a $\pm1$ outcome recorded in every run, and one setting-independent pre-setting ensemble give a Bell-local model and $|S_{\rm CHSH}|\le2$. The adopted quantum-Bell branch therefore retains measurement independence and relinquishes ontic parameter independence, while preserving operational no-signaling. The one boundary not folded into the theorem is the full coherent instrument/composite category of operational quantum mechanics. Keeping that boundary explicit lets the chapter recover the original equivalence claim without confusing a universal representation theorem with a uniqueness theorem.
 
 ## 1.2 The starting point
 
@@ -166,9 +166,9 @@ The Born rule in the fixed-basis representation is therefore part of the represe
 
 ## 1.7 Bell-inequality violations
 
-The Bell claim must separate the deterministic completion from the reduced stochastic description. For a Bell-relevant substratum whose coupling range does not connect the wings before readout, the dependency graph gives exact pointwise separation. If the response-complete pre-setting ensemble is also independent of the settings, determinism yields an ordinary Bell-local hidden-variable model and $|S_{\rm CHSH}|\le2$. Hidden memory and indivisibility do not alter that ceiling.
+The Bell claim must separate the deterministic completion from the reduced stochastic description. For a Bell-relevant substratum whose coupling range does not connect the wings before readout, the dependency graph gives exact pointwise separation. If each setting intervention, applied at one step, also reads and writes only its own wing, every run records a $\pm1$ outcome at each wing, and the response-complete pre-setting ensemble is independent of the settings, determinism yields an ordinary Bell-local hidden-variable model and $|S_{\rm CHSH}|\le2$. Hidden memory and indivisibility do not alter that ceiling.
 
-The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the vacuum/uniform reference graph remains geometric and bounded-range, while an entangling preparation may supply Bell-relevant long adjacency so a microstate response at one wing can depend on the remote setting. The averaged operational distribution remains no-signaling. H-Bell is the open metric/Ollivier--Ricci stability condition for those prepared graphs. That condition is now downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The setting-dependent alternative is recorded but not adopted; Main §3.3 gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits, while the smaller $\sim0.046$-bit benchmark is retrocausal.
+The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the vacuum/uniform reference graph remains geometric and bounded-range, while an entangling preparation may supply Bell-relevant long adjacency so a microstate response at one wing can depend on the remote setting. H-Bell is the open requirement that those prepared graphs preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The curvature condition is downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The setting-dependent alternative is recorded but not adopted; Main §3.3 gives the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum value. Hall--Branciard's optimized causal CHSH model uses about $0.080$ bits, while the smaller $\sim0.046$-bit benchmark is retrocausal.
 
 The cited causal-local indivisible **stochastic** construction separately obeys Tsirelson's bound because its causal-independence notion is weaker than Bell factorization. That theorem is not the hidden-variable locality structure of the deterministic completion. If the spatial/intervention restriction is removed, the general finite OI response construction can realize PR-box behavior, showing that representability, no-signaling, hidden memory, and indivisibility do not by themselves select the quantum Bell set.
 
@@ -180,7 +180,7 @@ The characterization is best read as a layered biconditional rather than a singl
 
 **Readback theorem.** C4 is the condition that makes the OI sector memory-bearing. It forces different hidden posteriors for visible histories that share a current state but have different future laws, a persistence/readback requirement, and the capacity lower bound of C3. Because the physical representative is finite and reversible, it also recurs: its rooted visible maps, defined for every root under one hidden prior, return to the identity, and a non-permutation stochastic matrix has no stochastic inverse, so any non-permutation rooted map makes the rooted law indivisible somewhere in the recurrence cycle. A C4 gap supplies such a map, and so does every non-deterministic visible step, including in laws that are Markov on every accessible window. With a full-support visible prior, that indivisibility is equivalent to memory at some order below the recurrence time; an observer sees the memory only when it appears at an accessible order, which is what C4 asserts.
 
-**Spatial extension.** The dependency graph supplies finite causal cones exactly for finite-range substrata. Bell adds a separate constraint: for a response-complete deterministic completion, measurement independence plus parameter independence would imply $|S_{\rm CHSH}|\le2$. Section §1.7 therefore takes the measurement-independent, ontically parameter-dependent branch for Bell-violating substrata and keeps operational no-signaling separate.
+**Spatial extension.** The dependency graph supplies finite causal cones exactly for finite-range substrata. Bell adds a separate constraint: for a response-complete deterministic completion that records a $\pm1$ outcome in every run, measurement independence plus parameter independence would imply $|S_{\rm CHSH}|\le2$. Section §1.7 therefore takes the measurement-independent, ontically parameter-dependent branch for Bell-violating substrata and keeps operational no-signaling separate.
 
 **Operational boundary.** These theorems do not yet prove that the entire family of coherent instruments and composites equals the unique standard local quantum operational theory. That residual is an active-lifting statement, not a qualification on the exact finite stochastic/representation equivalence itself.
 
diff --git a/book/ch02-substratum.md b/book/ch02-substratum.md
index 2d35019e0..ca8fb3296 100644
--- a/book/ch02-substratum.md
+++ b/book/ch02-substratum.md
@@ -185,7 +185,7 @@ The reconstruction theorem and the substratum gauge group have established what
 
 The framework's claim is that quantum mechanics, general relativity, and the arrow of time are not three independent theories. Conditional on H-Bell at the Bell/local-lattice interface, they are three projections of the same finite deterministic construction. Each projection applies the same trace-out machinery to the same $(S, \varphi)$ along a different axis, and each produces a distinct emergent structure as the observer sees the substratum from inside.
 
-**The visible-sector projection: quantum mechanics.** Chapter 1 developed this projection in detail. At finite observable horizon the reduced stochastic law, a finite reversible realization, and a fixed-basis unitary/Born representation are exactly equivalent: $S\iff D\iff Q_{\mathrm{fb}}$. C4 readback then identifies the memory-bearing sector by forcing hidden predictive memory. In the spatial construction the coupling graph supplies exact causal cones for finite-range substrata. Bell is separate from the full-QM lift: a measurement-independent response-complete deterministic completion with parameter independence would obey $|S_{\rm CHSH}|\le2$, so the framework's Bell-violating branch is ontically parameter-dependent but operationally no-signaling. Two independent qualifications remain beyond the finite-law equivalence: the simultaneous coherent instrument/composite lift ([Main §3.4]) and H-Bell, the compatibility of the local lattice sector with the ontically parameter-dependent Bell completion. Applied to the local lattice sector constructed in this chapter — a $d = 3$ cubic lattice with $K = 6$ internal components and the wave equation as its local propagating dynamics — the visible-sector projection produces the Standard Model: the gauge group $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)$ as the commutant of the cubic-symmetric coupling matrix, three chiral fermion generations, one composite Higgs, and anomaly-free hypercharges. Chapters 5 and 6 develop the Standard Model derivation; Chapter 8 develops the specific JUNO neutrino measurement that the framework's parameter-free PMNS-angle value matches at $0.07\sigma$ (a retrodiction). The local nearest-neighbor sector cannot itself supply Bell parameter dependence for wings outside each other's graph cone under measurement independence; identifying it with one Bell-violating total completion is the open H-Bell compatibility hypothesis.
+**The visible-sector projection: quantum mechanics.** Chapter 1 developed this projection in detail. At finite observable horizon the reduced stochastic law, a finite reversible realization, and a fixed-basis unitary/Born representation are exactly equivalent: $S\iff D\iff Q_{\mathrm{fb}}$. C4 readback then identifies the memory-bearing sector by forcing hidden predictive memory. In the spatial construction the coupling graph supplies exact causal cones for finite-range substrata. Bell is separate from the full-QM lift: a measurement-independent response-complete deterministic completion with parameter independence and a $\pm1$ outcome in every run would obey $|S_{\rm CHSH}|\le2$, so the framework's Bell-violating branch is ontically parameter-dependent but operationally no-signaling. Two independent qualifications remain beyond the finite-law equivalence: the simultaneous coherent instrument/composite lift ([Main §3.4]) and H-Bell, the compatibility of the local lattice sector with the ontically parameter-dependent Bell completion. Applied to the local lattice sector constructed in this chapter — a $d = 3$ cubic lattice with $K = 6$ internal components and the wave equation as its local propagating dynamics — the visible-sector projection produces the Standard Model: the gauge group $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)$ as the commutant of the cubic-symmetric coupling matrix, three chiral fermion generations, one composite Higgs, and anomaly-free hypercharges. Chapters 5 and 6 develop the Standard Model derivation; Chapter 8 develops the specific JUNO neutrino measurement that the framework's parameter-free PMNS-angle value matches at $0.07\sigma$ (a retrodiction). The local nearest-neighbor sector cannot itself supply Bell parameter dependence for wings with one-step own-wing setting interventions outside each other's graph cone under measurement independence; identifying it with one Bell-violating total completion is the open H-Bell compatibility hypothesis.
 
 **The boundary-thermodynamic projection: general relativity.** A second projection takes the same substratum but applies the trace-out machinery to the partition boundary rather than to the bulk. The boundary of the visible sector — the surface across which the coupling $H_{\text{int}}$ acts — carries its own thermodynamic structure: a temperature set by the boundary's classical surface gravity, an entropy set by the number of boundary modes, and a dynamical evolution set by the coupling between boundary and bulk. Jacobson's thermodynamic argument applied to local causal horizons yields Einstein's equations as the Clausius relation $dE = T \, dS$ at the boundary.
 
diff --git a/book/ch03-structural-realism.md b/book/ch03-structural-realism.md
index 595adc85d..027995987 100644
--- a/book/ch03-structural-realism.md
+++ b/book/ch03-structural-realism.md
@@ -37,7 +37,7 @@ Universality classes have internal sub-structure at three levels of refinement.
 
 Level C commits to a structural realism at the class level: the universality class is what is real, with specific substratum representatives playing the role of gauge expressions. Different members of the same universality class are observationally indistinguishable by definition, so the question "which specific substratum is real?" has no empirical content at the universality-class level. The realism is precisely about what survives the universality-class quotient.
 
-**Level D: OI's specific local structural residue.** The framework's narrowest reconstructed commitment is the three-dimensional cubic local lattice/gauge sector with $K=6$, the wave-equation dynamics and the listed Standard-Model representation data, with the qualifications developed in the technical chapters. The reconstruction theorem establishes that the stated observed and structural inputs uniquely fix this **local residue** up to $\mathcal{G}_{\text{sub}}$ under Theorem 23's conditions. It does not uniquely determine a Bell-inclusive full representative. The reference cubic graph is Bell-local under measurement independence; the adopted branch uses preparation-indexed state-dependent adjacency, with H-Bell conditioning its metric/Ollivier--Ricci compatibility and its uniqueness left open.
+**Level D: OI's specific local structural residue.** The framework's narrowest reconstructed commitment is the three-dimensional cubic local lattice/gauge sector with $K=6$, the wave-equation dynamics and the listed Standard-Model representation data, with the qualifications developed in the technical chapters. The reconstruction theorem establishes that the stated observed and structural inputs uniquely fix this **local residue** up to $\mathcal{G}_{\text{sub}}$ under Theorem 23's conditions. It does not uniquely determine a Bell-inclusive full representative. With one-step own-wing setting interventions, readouts outside the other wing's graph cone and a $\pm1$ outcome in every run, the reference cubic graph is Bell-local under measurement independence; the adopted branch proposes preparation-indexed state-dependent adjacency under the open hypothesis H-Bell (operational no-signaling and the metric/Ollivier--Ricci continuum limit), with its uniqueness left open.
 
 Level D is where the framework's twenty-two classified quantitative predictions live (two parameter-free structural and five conditional structural among them): the Cabibbo angle $1/(\pi\sqrt{2})$, the Koide angle $2/9$, the gauge-coupling-running calculation giving the three SM coupling constants at the $Z$ pole, the six fermion masses derived from one empirical input, the Higgs quartic coupling from cubic-group representation theory, the Bekenstein-Hawking $1/4$ factor as a consistency relation, the MOND acceleration scale $cH/6$, and the JUNO neutrino-mixing prediction. The empirical content that distinguishes OI from other observer-admitting frameworks is concentrated at Level D, because Level D is where the structural commitments become specific enough to produce specific numerical predictions.
 
@@ -159,9 +159,9 @@ The framework is a hidden-variable theory in the literal sense: there is a deter
 
 The framework's engagement with these theorems is not a single trick repeated, nor four separate tricks. Each theorem identifies a different structural property of would-be hidden-variable accounts. The two-level substratum-emergent structure joined by the trace-out is the common bookkeeping architecture, but it is **not** one automatic escape: Bell forces ontic parameter dependence in the adopted deterministic branch; Kochen-Specker constrains the noncommuting operational algebra; PBR constrains preparation independence of ontic composites; Frauchiger-Renner constrains universal nested-agent descriptions. The hierarchy matters because it locates each premise at the right level, not because the same property simply holds above and fails below in every case.
 
-**Bell's theorem.** Bell's theorem binds directly on the deterministic hidden-variable completion. If the Bell-relevant coupling range does not connect the wings before readout and one setting-independent response-complete ensemble is used, the model factorizes and obeys $|S_{\rm CHSH}|\le2$. The framework therefore cannot use graph locality, screening, outcome dependence, or indivisibility to explain the quantum violation. It retains measurement independence and accepts **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling as the distinct empirical locality statement. The cited stochastic causal-local indivisible construction can still obey Tsirelson because its causal-independence criterion is weaker than Bell factorization. Unrestricted globally controlled OI realizations remain the PR-box countercontrol.
+**Bell's theorem.** Bell's theorem binds directly on the deterministic hidden-variable completion. If the setting interventions, applied at one step, each read and write only their own wing, the Bell-relevant coupling range does not connect the wings before readout, every run records a $\pm1$ outcome, and one setting-independent response-complete ensemble is used, the model factorizes and obeys $|S_{\rm CHSH}|\le2$. The framework therefore cannot use graph locality, screening, outcome dependence, or indivisibility to explain the quantum violation. It retains measurement independence and accepts **ontic parameter dependence** for Bell-violating substrata, with operational no-signaling as the distinct empirical locality statement. The cited stochastic causal-local indivisible construction can still obey Tsirelson because its causal-independence criterion is weaker than Bell factorization. Unrestricted globally controlled OI realizations remain the PR-box countercontrol.
 
-In hierarchy language, the Bell question splits the deterministic substratum from the reduced stochastic description. A finite-range Bell graph plus a setting-independent response-complete ensemble would force the substratum into Bell's local class and cap CHSH at $2$. The framework therefore does not identify no-signaling, Jarrett parameter independence, Fine's theorem, hidden memory, or indivisibility with a derivation of the quantum correlation set. Its adopted deterministic branch is instead ontic parameter dependence with operational no-signaling; the $2\sqrt2$ result for the causal-local indivisible stochastic construction remains a distinct weaker-description theorem.
+In hierarchy language, the Bell question splits the deterministic substratum from the reduced stochastic description. A Bell graph that does not connect the wings before readout, with one-step own-wing setting interventions and a $\pm1$ outcome in every run, plus a setting-independent response-complete ensemble, would force the substratum into Bell's local class and cap CHSH at $2$. The framework therefore does not identify no-signaling, Jarrett parameter independence, Fine's theorem, hidden memory, or indivisibility with a derivation of the quantum correlation set. Its adopted deterministic branch is instead ontic parameter dependence with operational no-signaling; the $2\sqrt2$ result for the causal-local indivisible stochastic construction remains a distinct weaker-description theorem.
 
 **Kochen-Specker.** The Kochen-Specker theorem rules out non-contextual hidden-variable assignments: there is no function $v$ mapping observables to definite values such that $v(O)$ depends only on $O$ rather than on the measurement context (the set of compatible observables being measured simultaneously). Any hidden-variable theory matching quantum mechanics must be contextual: the hidden variable's outcome on a given observable depends on which other observables are co-measured.
 
@@ -177,9 +177,9 @@ The framework's PBR response must be stated conditionally. PBR assumes Preparati
 
 **What the framework does not argue.** Two standard escapes are explicitly declined. It does not deny counterfactual definiteness: substratum outcomes are definite, and the framework nowhere trades on refusing to consider unperformed measurements — the response to Bell runs through the structure of the premises, not through denying that measurements have results. Nor does it treat hidden setting correlations as an explanation of Bell statistics. Measurement independence is an explicit premise of the adopted Bell branch; chaotic mixing may motivate laboratory decorrelation between pair-preparation and setting-generating degrees of freedom, but the violation itself is assigned to ontic parameter dependence. The setting-dependent horn is quantified and declined (Main §3.3).
 
-**Bell's theorem, conceded and then confronted.** Bell's mathematics binds on the framework because the substratum is a response-complete hidden-variable completion. If the Bell-relevant graph does not connect the wings before readout and the pre-setting ensemble is independent of the settings, determinism gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore cannot explain quantum Bell violation by combining pointwise graph locality and indivisibility. It declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization, the target is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the reference vacuum/uniform graph remains geometric and bounded-range, while an entangling preparation may add Bell-relevant long adjacency. The averaged operational statistics remain no-signaling. H-Bell is the remaining metric/Ollivier--Ricci stability condition for those prepared graphs. That condition is now downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The causal-local indivisible *stochastic* construction can still obey Tsirelson because its causal-independence condition is weaker than Bell factorization; that result is not the locality structure of the deterministic completion. The unrestricted PR realization remains the negative control showing that representability, no-signaling, and indivisibility do not select the quantum set.
+**Bell's theorem, conceded and then confronted.** Bell's mathematics binds on the framework because the substratum is a response-complete hidden-variable completion. If the setting interventions, applied at one step, each read and write only their own wing, the Bell-relevant graph does not connect the wings before readout, every run records a $\pm1$ outcome, and the pre-setting ensemble is independent of the settings, determinism gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore cannot explain quantum Bell violation by combining pointwise graph locality and indivisibility. It declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization, the target is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response): the reference vacuum/uniform graph remains geometric and bounded-range, while an entangling preparation may add Bell-relevant long adjacency. H-Bell is the open requirement that those prepared graphs preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The curvature condition is downstream of a harder one. The cited convergence theorem is arbitrary-dimensional only for the manifold-distance-weighted graph metric, and for the degree-$6$ cubic reference graph the intrinsic hop metric is exactly $\ell_1$ — a $\sqrt2$ diagonal stretch that does not decay at any scale — so the hop-metric curvature route fails for the reference family, before any Bell edge is added, and no $D=3$ extension of that theorem would rescue it. The emergent geometry itself is not in question: the substratum's dispersion relation is isotropic at leading order. What must be re-founded is the curvature functional, on the propagation/Laplacian geometry rather than on shortest-path counts [SM §3.2]. The causal-local indivisible *stochastic* construction can still obey Tsirelson because its causal-independence condition is weaker than Bell factorization; that result is not the locality structure of the deterministic completion. The unrestricted PR realization remains the negative control showing that representability, no-signaling, and indivisibility do not select the quantum set.
 
-**The rejoinder, at full strength.** A response-complete deterministic Bell completion is not local in Bell's parameter-independence sense. A response-complete hidden-variable theory reproducing Bell violation while retaining measurement independence must fail parameter independence, and the framework explicitly accepts that conclusion. Its Bell-violating prepared states are therefore **ontically nonlocal in Bell's parameter sense**. In the concrete lattice branch, that nonlocality is represented by preparation-indexed state-dependent adjacency (or an equivalent response rule), not by pretending the nearest-neighbor reference wave equation itself carries Bell influence. What remains local operationally is the no-signaling statement — changing a controllable setting cannot be used to transmit a message to the remote wing. The cosmological partition or shared boundary may be proposed as a physical realization, but calling that carrier atemporal, global, or prior to emergent spacetime does not remove Bell nonlocality; it only locates it in the ontology. The separate Barandes–Hasan–Kagan theorem shows that the reduced stochastic law can satisfy their weaker causal-independence criterion and remain below Tsirelson, but that criterion is not Bell factorization for the deterministic completion. The manuscript can therefore defend a non-signaling deterministic ontology with a specific locus of nonlocality; it does not claim a local hidden-variable resolution of Bell.
+**The rejoinder, at full strength.** A response-complete deterministic Bell completion is not local in Bell's parameter-independence sense. A response-complete hidden-variable theory reproducing Bell violation while retaining measurement independence must fail parameter independence, and the framework explicitly accepts that conclusion. Its Bell-violating prepared states are therefore **ontically nonlocal in Bell's parameter sense**. In the concrete lattice branch, that nonlocality is targeted through preparation-indexed state-dependent adjacency (or an equivalent response rule) under H-Bell, not by pretending the nearest-neighbor reference wave equation itself carries Bell influence. What remains local operationally is the no-signaling statement — changing a controllable setting cannot be used to transmit a message to the remote wing. The cosmological partition or shared boundary may be proposed as a physical realization, but calling that carrier atemporal, global, or prior to emergent spacetime does not remove Bell nonlocality; it only locates it in the ontology. The separate Barandes–Hasan–Kagan theorem shows that the reduced stochastic law can satisfy their weaker causal-independence criterion and remain below Tsirelson, but that criterion is not Bell factorization for the deterministic completion. The manuscript can therefore defend a non-signaling deterministic ontology with a specific locus of nonlocality; it does not claim a local hidden-variable resolution of Bell.
 
 **The bill, paid in the open.** A deterministic substratum that violates **ontic parameter independence** owes an account of relativity, and the account cannot be evasive: the framework's substratum has a preferred frame — the frame in which update steps are simultaneous — and on identification with the observed universe this is operationally the cosmic rest frame, an identification the framework records rather than derives (SM §3.1). Lorentz invariance is therefore wholly emergent, and the framework's obligations are quantitative: no linear violation (established at tree level), rotational protection by octahedral symmetry to all orders conditional on the emergent theory preserving that symmetry at loop level, boost-sector violation controlled, conditional on the symmetric-point matching under H-blind (SM §4.4), by a decoupling law in the cross-charged mass $M_X$ whose quadratic-with-logarithm form was reported by a one-loop calculation that is not independently verified, its two-sided window illustrative until it is. These are not side technicalities; they are the price of the preferred-frame answer to the foliation objection, and the open item among them — the interacting (condensate-dressed) extension of the coarse-graining characterization (SM §3.1; Chapter 19 §19.3.7) — is correctly understood as Bell-defense infrastructure. A reader who wants to falsify the framework's account of Bell should attack there: a demonstrated failure of emergent Lorentz protection would leave the preferred frame exposed at accessible energies, and the framework's answer to this subsection would fail with it.
 
diff --git a/book/ch04-methodology.md b/book/ch04-methodology.md
index 7eb9b50e6..e687df13c 100644
--- a/book/ch04-methodology.md
+++ b/book/ch04-methodology.md
@@ -87,9 +87,9 @@ First, identify the theorem's structural assumption. Bell's theorem assumes fact
 
 Second, identify the level of the framework's hierarchy where the assumption sits. Bell's factorizability is a property at Level G3 × Level D, where the joint transition matrix between visible-sector subsystems is defined. Kochen-Specker non-contextuality is a property at Level G2 × Level D, where observables are defined as operators on the emergent Hilbert space. PBR preparation independence is a property at Level D × Level G3, where the substratum's joint-system structure is specified. Frauchiger-Renner universal applicability is a claim at Level G2 × Level D applied to substratum-level objects.
 
-Third, locate where the framework meets or violates the theorem's premises at the correct level. Bell is the sharpest case: for a response-complete deterministic completion, finite-range Bell couplings plus a setting-independent pre-setting ensemble imply Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore does not obtain quantum Bell violation from outcome-independence failure in an indivisible stochastic law; it retains measurement independence and gives up **ontic parameter independence**, while preserving operational no-signaling. PBR's preparation independence — the postulate that independently prepared systems have a product joint ontic-state distribution — is not a premise of bare OI. Co-embedded preparation devices may share preparation-relevant hidden or boundary data, so unconditional product independence is not guaranteed; the graph causal cone by itself does not derive either a conditional product distribution or the standard quantum tensor-product composite. Frauchiger-Renner's universal applicability fails because the substratum-level and emergent-level descriptions are incommensurable in the relevant sense. The fourth theorem, Kochen-Specker, does not fit this "satisfied below, violated above" form: its assumed property, a noncontextual valuation of the observables, holds at neither level — the framework — conditionally on the operational bridge reconstructing the standard observable algebra — carries the operational theory, which by Kochen-Specker's own content admits no noncontextual valuation, and the substratum carries a definite configuration that is not a valuation of the emergent observables at all. The framework's contextuality is forced, under that same conditional bridge, by equivalence at the operational layer — and what the framework adds is the account: contextuality is the partition-dependence of the trace-out. The common factor across all four is therefore the architecture — two levels and a trace-out — not a single property-placement move repeated.
+Third, locate where the framework meets or violates the theorem's premises at the correct level. Bell is the sharpest case: for a response-complete deterministic completion, Bell couplings that do not connect the wings before readout, one-step own-wing setting interventions and a $\pm1$ outcome in every run, plus a setting-independent pre-setting ensemble, imply Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore does not obtain quantum Bell violation from outcome-independence failure in an indivisible stochastic law; it retains measurement independence and gives up **ontic parameter independence**, while preserving operational no-signaling. PBR's preparation independence — the postulate that independently prepared systems have a product joint ontic-state distribution — is not a premise of bare OI. Co-embedded preparation devices may share preparation-relevant hidden or boundary data, so unconditional product independence is not guaranteed; the graph causal cone by itself does not derive either a conditional product distribution or the standard quantum tensor-product composite. Frauchiger-Renner's universal applicability fails because the substratum-level and emergent-level descriptions are incommensurable in the relevant sense. The fourth theorem, Kochen-Specker, does not fit this "satisfied below, violated above" form: its assumed property, a noncontextual valuation of the observables, holds at neither level — the framework — conditionally on the operational bridge reconstructing the standard observable algebra — carries the operational theory, which by Kochen-Specker's own content admits no noncontextual valuation, and the substratum carries a definite configuration that is not a valuation of the emergent observables at all. The framework's contextuality is forced, under that same conditional bridge, by equivalence at the operational layer — and what the framework adds is the account: contextuality is the partition-dependence of the trace-out. The common factor across all four is therefore the architecture — two levels and a trace-out — not a single property-placement move repeated.
 
-Fourth, verify that the framework's predictions match quantum mechanics in the regime where the no-go theorem applies, without silently importing the very condition under test. For Bell, verify the deterministic completion directly: if its Bell-relevant graph is finite-range at the wings and its pre-setting ensemble is setting-independent, CHSH is capped at $2$. The framework's quantum branch therefore has ontic parameter dependence. For the specific SM/GR representative, the nearest-neighbor **reference** graph cannot itself supply that parameter dependence in a Bell protocol whose wings lie outside each other's graph cone. The existing state-dependent graph $G(x)$ supplies the native target: preparation-indexed adjacency (or an equivalent nonlocal response), with H-Bell now the open metric/Ollivier--Ricci stability condition for the prepared graph family. The measurement-dependent alternative is not adopted; Chapter 1 gives a model-independent necessary lower bound and a separate causal benchmark; the stochastic causal-local Tsirelson theorem is retained only at its weaker stochastic level. Kochen-Specker, PBR, and Frauchiger-Renner concern the coherent operational structure and therefore inherit the operational-lifting qualification: their standard quantum statistics are recovered once the common instrument/composite representation is established, not merely from universal fixed-basis representability.
+Fourth, verify that the framework's predictions match quantum mechanics in the regime where the no-go theorem applies, without silently importing the very condition under test. For Bell, verify the deterministic completion directly: if its setting interventions, applied at one step, each read and write only their own wing, its Bell-relevant graph does not connect the wings before readout, every run records a $\pm1$ outcome, and its pre-setting ensemble is setting-independent, CHSH is capped at $2$. The framework's quantum branch therefore has ontic parameter dependence. For the specific SM/GR representative, the nearest-neighbor **reference** graph cannot itself supply that parameter dependence in a Bell protocol with one-step own-wing setting interventions whose wings lie outside each other's graph cone. The existing state-dependent graph $G(x)$ supplies the native target: preparation-indexed adjacency (or an equivalent nonlocal response), with H-Bell the open requirement that the prepared graph family preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The measurement-dependent alternative is not adopted; Chapter 1 gives a model-independent necessary lower bound and a separate causal benchmark; the stochastic causal-local Tsirelson theorem is retained only at its weaker stochastic level. Kochen-Specker, PBR, and Frauchiger-Renner concern the coherent operational structure and therefore inherit the operational-lifting qualification: their standard quantum statistics are recovered once the common instrument/composite representation is established, not merely from universal fixed-basis representability.
 
 **One architecture, verified per theorem.** Two things must be held apart here, because they pull in opposite directions and both are true. The framework's *response* to the no-go literature is not piecemeal: it is one architectural feature — two levels of description joined by the trace-out — fixed before any no-go theorem is examined, and the four cases are four manifestations of working within it rather than four separately chosen escapes. But the *verification* that the architecture in fact answers a given theorem is per-theorem work: each theorem's assumption must be located against the two-level structure, and the match checked. The unity is in the response; the labor is in the checking. As new no-go theorems are published — the literature continues to grow — each must be checked against the same architecture, with the framework's engagement verified rather than assumed.
 
@@ -121,7 +121,7 @@ The conditions are organized into three classes. Class A identifies structural t
 
 *Majorana neutrinos with normal mass ordering.* The framework derives this from the taste-breaking structure of the neutrino mass matrix. Inverted mass ordering, confirmed to high significance, falsifies the derivation. Confirmed Dirac nature of the neutrino — for example, a null result for neutrinoless double-beta decay at the sensitivity that would require Majorana masses well below the framework's prediction — falsifies the prediction that no right-handed neutrino exists in the spectrum.
 
-*The Tsirelson bound.* The value $2\sqrt{2}$ belongs to the cited **stochastic causal-local indivisible construction** ([Main §3.3]), not to a Bell-local deterministic completion and not to generic P-indivisibility. The deterministic OI layer reaches quantum Bell violation only on the ontically parameter-dependent branch. An observed loophole-free CHSH value above $2\sqrt2$ would falsify standard quantum mechanics and any claim that the relevant OI operational lift lands in the standard quantum Bell set; it would not, by itself, falsify P-indivisibility.
+*The Tsirelson bound.* The value $2\sqrt{2}$ belongs to the cited **stochastic causal-local indivisible construction** ([Main §3.3]), not to a Bell-local deterministic completion and not to generic P-indivisibility. The deterministic OI layer reaches quantum Bell violation, under measurement independence, only on the ontically parameter-dependent branch. An observed loophole-free CHSH value above $2\sqrt2$ would falsify standard quantum mechanics and any claim that the relevant OI operational lift lands in the standard quantum Bell set; it would not, by itself, falsify P-indivisibility.
 
 *Exact unitarity of the visible-sector dynamics at accessible scales.* The framework derives unitary quantum evolution as the exact embedded-observer description at every accessible mass and coherence scale, with dissipative corrections structurally suppressed to the dissipator scale of Chapter 1 §1.6. Any confirmed intrinsic-collapse signature — anomalous decoherence not attributable to environmental channels, scaling with mass or superposition size as objective-collapse models (GRW/CSL, Diósi–Penrose) require, at sufficient confidence to exclude systematics — falsifies the emergence theorem directly. Because the framework's predicted deviations are pinned orders of magnitude below the collapse-model band, a positive detection cannot be absorbed as a framework correction. The current frontier is matter-wave interference at macroscopicity $\mu = 15.5$ (Pedalino et al. 2026; Chapter 1 §1.6), consistent with exact quantum behavior; the frontier's continued advance is a standing test rather than a completed one.
 
diff --git a/book/ch18-beyond.md b/book/ch18-beyond.md
index 0082d0b58..b0f262dcf 100644
--- a/book/ch18-beyond.md
+++ b/book/ch18-beyond.md
@@ -107,7 +107,7 @@ The apparent randomness arises because the observer sees only $x$, not $h$. Diff
 
 This is what "deterministic but inaccessible" means in the framework: the outcomes are fully determined by the substratum dynamics, but the observer cannot in principle access the hidden-sector information that determines them. The randomness is unavoidable for any embedded observer, but it is not fundamental — it is the cost of partial observation.
 
-**Bell's theorem and the chosen nonlocality.** Bell does not rule out determinism by itself; it rules out reproducing the observed correlations with a response-complete deterministic completion that is both measurement-independent and parameter-independent. Chapter 1 proves the corresponding Bell ceiling: if the Bell-relevant coupling range does not connect the wings before readout and one setting-independent pre-setting ensemble is used, then $|S_{\rm CHSH}|\le2$. The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response), so a prepared microstate response may depend on the remote setting while the reference vacuum/uniform graph remains geometric and bounded-range. The operational distribution remains no-signaling. The $2\sqrt2$ theorem for the causal-local indivisible stochastic description is a separate weaker-layer result, not a locality theorem for the deterministic completion.
+**Bell's theorem and the chosen nonlocality.** Bell does not rule out determinism by itself; it rules out reproducing the observed correlations with a response-complete deterministic completion that records a $\pm1$ outcome in every run and is both measurement-independent and parameter-independent. Chapter 1 proves the corresponding Bell ceiling: if the setting interventions, applied at one step, each read and write only their own wing, the Bell-relevant coupling range does not connect the wings before readout, every run records a $\pm1$ outcome, and one setting-independent pre-setting ensemble is used, then $|S_{\rm CHSH}|\le2$. The framework therefore declines the measurement-dependent/superdeterministic horn and takes **ontic parameter dependence**. In the specific SM/GR realization the target mechanism is preparation-indexed adjacency in the already state-dependent graph $G(x)$ (or an equivalent ontically nonlocal response), so a prepared microstate response may depend on the remote setting while the reference vacuum/uniform graph remains geometric and bounded-range. Whether those prepared graphs keep the operational distribution no-signaling and preserve the continuum-curvature limit is the open hypothesis H-Bell. The $2\sqrt2$ theorem for the causal-local indivisible stochastic description is a separate weaker-layer result, not a locality theorem for the deterministic completion.
 
 One proposed physical realization of that preparation-indexed parameter dependence uses non-localized cosmological-boundary modes. This is a candidate realization, not an established Bell mechanism: any such prepared long-edge/response structure must satisfy H-Bell, i.e. preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit used by the gravitational reconstruction. What distinguishes it from a superluminal signaling mechanism is operational no-signaling, not ontic parameter independence.
 
diff --git a/book/glossary.md b/book/glossary.md
index 74c426c84..137c60335 100644
--- a/book/glossary.md
+++ b/book/glossary.md
@@ -16,7 +16,7 @@ This glossary defines the framework's distinctive terminology and the technical
 
 **Bekenstein-Hawking entropy.** The entropy $S = A/(4 l_p^2)$ assigned to a horizon of area $A$ in units of the Planck length $l_p$. The factor $1/4$ follows from the Hawking temperature and the first law. In the framework it is the ratio $2\pi/8\pi$ fixed by the horizon calibration of Chapter 7 (conditional on H-slope); the mode count reproduces it for any cell size once the calibration is imposed. GW250114 (September 2025) confirms the classical area theorem; the $1/4$ coefficient has no direct empirical test. Developed in Chapter 7 §7.5.
 
-**Bell-inequality violations.** Empirical correlations exceeding bounds derivable from local hidden-variable theories. For a response-complete deterministic OI completion, measurement independence plus ontic parameter independence gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore retains measurement independence but relinquishes **ontic parameter independence** for Bell-violating substrata, while preserving operational no-signaling. The measurement-dependent alternative is recorded rather than adopted: the manuscript proves the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum CHSH value, while an optimized causal model in Hall--Branciard uses about $0.080$ bits (the smaller $\sim0.046$-bit benchmark is retrocausal). Developed in Chapter 1 §1.7 and Appendix C §C.2.
+**Bell-inequality violations.** Empirical correlations exceeding bounds derivable from local hidden-variable theories. For a response-complete deterministic OI completion, measurement independence plus ontic parameter independence, with a $\pm1$ outcome in every run, gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore retains measurement independence but relinquishes **ontic parameter independence** for Bell-violating substrata, while preserving operational no-signaling. The measurement-dependent alternative is recorded rather than adopted: the manuscript proves the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits for the quantum CHSH value, while an optimized causal model in Hall--Branciard uses about $0.080$ bits (the smaller $\sim0.046$-bit benchmark is retrocausal). Developed in Chapter 1 §1.7 and Appendix C §C.2.
 
 **Born rule.** The quantum-mechanical prescription that the probability of measurement outcome $i$ on state $|\psi\rangle$ is $|\langle i|\psi\rangle|^2$. Conventionally treated as a postulate of quantum mechanics. In the framework, at the finite fixed-basis observable-law layer, the Born form is part of an exact equivalent representation: $S\iff D\iff Q_{\mathrm{fb}}$ ([Main §3.4]). The framework therefore does not list a separate 'quadratic-exponent selector' as an unresolved foundational theorem at that layer. What remains is the **operational lifting** problem: prove that the fixed-basis representation extends coherently and simultaneously to the standard local noncommuting instrument/composite algebra. The read-write-cycle equilibrium account in Chapter 18 §18.2 is an additional physical mechanism proposal and is not needed for the finite representation equivalence.
 
@@ -46,7 +46,7 @@ This glossary defines the framework's distinctive terminology and the technical
 
 **CKM (Cabibbo-Kobayashi-Maskawa) matrix.** The unitary mixing matrix between Standard Model quark mass and weak interaction eigenstates. Conventionally parameterized by three mixing angles and one CP-violating phase. The framework derives the Cabibbo angle structurally and provides partial content for the broader CKM structure. Developed in Chapter 6 §6.5.
 
-**CHSH inequality.** The Clauser-Horne-Shimony-Holt formulation of Bell's inequality, with the Bell-local bound of 2 and the quantum (Tsirelson) bound of $2\sqrt{2}$. In the deterministic OI completion, measurement independence plus parameter independence gives the bound 2; quantum violation therefore uses ontic parameter dependence. The cited stochastic causal-local indivisible construction separately has the Tsirelson bound. Discussed in Appendix C §C.2.
+**CHSH inequality.** The Clauser-Horne-Shimony-Holt formulation of Bell's inequality, with the Bell-local bound of 2 and the quantum (Tsirelson) bound of $2\sqrt{2}$. In the deterministic OI completion, measurement independence plus parameter independence, with a $\pm1$ outcome in every run, gives the bound 2; quantum violation under measurement independence therefore uses ontic parameter dependence. The cited stochastic causal-local indivisible construction separately has the Tsirelson bound. Discussed in Appendix C §C.2.
 
 **Cosmological constant problem.** The discrepancy of approximately $10^{122}$ between quantum field theory's predicted vacuum energy ($\sim 10^{113}$ J/m³) and the observed value inferred from cosmic expansion ($\sim 6 \times 10^{-10}$ J/m³). The framework proposes to *dissolve* this problem by identifying the two quantities as properties of logically distinct descriptions: the quantum vacuum energy is the emergent QFT's prediction within a partition; the observed cosmological constant is the gravitational consequence of the substratum's full content. The descriptive distinction is established; the dissolution is conditional on the open coupling step. Developed in Chapter 7 §7.7.
 
@@ -144,7 +144,7 @@ This glossary defines the framework's distinctive terminology and the technical
 
 **Trace-out.** The mathematical operation of marginalizing over (summing or integrating out) the hidden-sector degrees of freedom, producing the reduced description on the visible sector. The framework's central technical operation. Equivalent to partial trace in quantum mechanics. Defined throughout Chapter 1.
 
-**Tsirelson bound.** The maximum CHSH inequality violation achievable by standard quantum mechanics: $2\sqrt{2}$. In the manuscript this value is retained for the cited **stochastic causal-local indivisible** construction and for any successful lift to the standard quantum Bell set. It is not the ceiling of a measurement-independent, parameter-independent deterministic completion, whose Bell bound is 2. The deterministic OI branch reaches quantum violation by ontic parameter dependence; the measurement-dependent alternative is separately **bounded and benchmarked** in Chapter 1 §1.7. Discussed in Appendix C §C.2.
+**Tsirelson bound.** The maximum CHSH inequality violation achievable by standard quantum mechanics: $2\sqrt{2}$. In the manuscript this value is retained for the cited **stochastic causal-local indivisible** construction and for any successful lift to the standard quantum Bell set. It is not the ceiling of a measurement-independent, parameter-independent deterministic completion recording a $\pm1$ outcome in every run, whose Bell bound is 2. The deterministic OI branch reaches quantum violation by ontic parameter dependence; the measurement-dependent alternative is separately **bounded and benchmarked** in Chapter 1 §1.7. Discussed in Appendix C §C.2.
 
 **U-parity.** The framework's grading structure in the neutrino sector, distinguishing $U^+$ and $U^-$ states in the cubic-group flavor classification. Produces the framework's distinctive sum rule and structural relation among the three PMNS mixing angles. Developed in Chapter 8 §8.4.
 
diff --git a/papers/Main.md b/papers/Main.md
index a0b61be37..4bd5ee58f 100644
--- a/papers/Main.md
+++ b/papers/Main.md
@@ -19,7 +19,7 @@ S\iff D\iff Q_{\mathrm{fb}}
 $$
 at the finite observable-law level. The quantum representation is exact, not merely approximate; it is also universal, so representability alone does not distinguish the memory-bearing sector from an ordinary Markov process. The Born dictionary $p=|U|^2$ is part of the definition of $Q_{\mathrm{fb}}$: the equivalence exhibits the Born form and does not select the quadratic exponent, which is named as a frontier item (§3.1). The discriminating content is history readback: (C4) holds exactly when the visible law has positive conditional memory $M_t=I(X_{<t};X_{t+1}\mid X_t)$ at some accessible time, and then every faithful deterministic completion contains readout-relevant hidden predictive memory. On one fixed finite reversible representative the full rooted visible process is indivisible somewhere in its recurrence cycle whenever some rooted map is not a permutation, since finite recurrence returns the visible map to the identity and a non-permutation stochastic matrix has no stochastic inverse. With a full-support visible prior this indivisibility is equivalent to a memory obstruction, $M_k > 0$ at some order $k$ below the recurrence time, and that order may lie as late as one step before the recurrence time. Observational access is a separate requirement: (C4) asks for the obstruction at an accessible order, and recurrence does not guarantee one, since every non-deterministic visible step gives the indivisibility, including in laws that are Markov on every accessible window. Conditions (C1) and (C3) are then necessary diagnostics of the hidden mediation and its capacity; (C2-structural), the persistence of the stored record until readback, holds by reversibility in every bijective realization and constrains coarse-grained descriptions of the hidden sector, with the slow-bath inequality one sufficient physical mechanism.
 
-For spatial OI systems, the coupling graph defined by one-step dynamical dependence supplies exact causal cones: influence propagates at most one graph edge per update. Bell accounting is correspondingly sharp: a deterministic completion that keeps the pointwise cone and a setting-independent pre-setting ensemble is a local hidden-variable model, so $|S_{\mathrm{CHSH}}|\le2$ and quantum correlations are unreachable. Reproducing them requires ontic parameter dependence — realized in the specific SM/GR branch through preparation-indexed state-dependent adjacency or an equivalent Bell-nonlocal response structure, with no operational signal — or else setting-dependent ontic ensembles, for which $S_{\mathrm{CHSH}}\le2+4\sqrt{2\ln2\,I_{\mathrm{ont}}}$ gives the model-independent necessary lower bound $I_{\mathrm{ont}}\ge0.0309$ bits for the quantum value. Conversely, every finite stochastic law, and therefore every finite quantum record, admits a finite reversible realization; for fixed finite dimension, instrument menu, horizon, and accuracy $\varepsilon$, one finite OI construction reproduces the whole corresponding quantum experimental envelope to that accuracy. In this precise sense the stochastic description of embedded observation and its quantum representation are mathematically equivalent. Two logically separate completion questions remain beyond that finite-law result: whether the complete family of coherent interventions and composites is represented simultaneously by the standard quantum instrument theory (§3.4), and whether preparation-indexed Bell adjacency in the state-dependent cubic SM/GR graph preserves the metric/Ollivier--Ricci continuum limit needed by the gravitational reconstruction (H-Bell, [Substratum §3.3]). Accordingly, the exact equivalence claim is at the finite observable-law level; universal Hilbert-space representability is not promoted into a uniqueness theorem for operational quantum mechanics entire. In particular one visible family can admit distinct coherent unitary lifts whose relating evolutions differ, so representability together with ordinary coherence does not by itself select the unitary evolution relating two times (§3.4 Remark). The specific nearest-neighbor cubic representative used for the Standard-Model sector is not by itself a Bell-violating completion under measurement independence; compatibility of preparation-indexed Bell adjacency with the continuum-curvature limit is the separate H-Bell hypothesis of [Substratum §3.3].
+For spatial OI systems, the coupling graph defined by one-step dynamical dependence supplies exact causal cones: influence propagates at most one graph edge per update. Bell accounting is correspondingly sharp: a deterministic completion whose setting interventions, applied at one step, each read and write only their own wing, whose readouts lie outside the other wing's cone and record a $\pm1$ outcome in every run, and whose pre-setting ensemble is setting-independent is a local hidden-variable model, so $|S_{\mathrm{CHSH}}|\le2$ and quantum correlations are unreachable. Reproducing them requires ontic parameter dependence — targeted in the specific SM/GR branch through preparation-indexed state-dependent adjacency or an equivalent Bell-nonlocal response structure, with no operational signal — or else setting-dependent ontic ensembles, for which $S_{\mathrm{CHSH}}\le2+4\sqrt{2\ln2\,I_{\mathrm{ont}}}$ gives the model-independent necessary lower bound $I_{\mathrm{ont}}\ge0.0309$ bits for the quantum value. Conversely, every finite stochastic law, and therefore every finite quantum record, admits a finite reversible realization; for fixed finite dimension, instrument menu, horizon, and accuracy $\varepsilon$, one finite OI construction reproduces the whole corresponding quantum experimental envelope to that accuracy. In this precise sense the stochastic description of embedded observation and its quantum representation are mathematically equivalent. Two logically separate completion questions remain beyond that finite-law result: whether the complete family of coherent interventions and composites is represented simultaneously by the standard quantum instrument theory (§3.4), and whether preparation-indexed Bell adjacency in the state-dependent cubic SM/GR graph preserves the metric/Ollivier--Ricci continuum limit needed by the gravitational reconstruction (H-Bell, [Substratum §3.3]). Accordingly, the exact equivalence claim is at the finite observable-law level; universal Hilbert-space representability is not promoted into a uniqueness theorem for operational quantum mechanics entire. In particular one visible family can admit distinct coherent unitary lifts whose relating evolutions differ, so representability together with ordinary coherence does not by itself select the unitary evolution relating two times (§3.4 Remark). The specific nearest-neighbor cubic representative used for the Standard-Model sector is not by itself a Bell-violating completion under measurement independence; compatibility of preparation-indexed Bell adjacency with the continuum-curvature limit is the separate H-Bell hypothesis of [Substratum §3.3].
 
 ## 1. INTRODUCTION
 
@@ -79,7 +79,7 @@ These properties contain no quantum postulates. The claim is that quantum mechan
 
 **(C4) History readback.** History-sensitive hidden mediation: on accessible windows, hidden degrees of freedom carry information about the visible past into future visible conditionals — at some order, two visible histories with the same current state induce different next-step laws, mediated through the hidden state. The condition is operational; it does not by itself assert a causal write-then-read cycle — a pre-sampled hidden variable revealed by the history satisfies it (the response-table construction, §3.4). (Status: necessity — immediate given observed non-Markovianity, since any realization of a non-Markov process carries differing past-conditionals. Realization — in the cosmological realization the mediation *is* a causal read-write cycle: the interaction reads the same boundary degrees it writes, a property to be independently demonstrated there; this is what C1's redefinition relocated here. Separation — (C1)–(C3) alone do not imply (C4): a tape-and-ledger realization of the fair coin satisfies all three with identically zero conditional memory on arbitrarily long accessible horizons (`review3_probes.py`; §2.3).)
 
-**Theorem statement.** The claims divide into three exact layers and one explicitly conditional extension. **(1) Representation equivalence:** on every finite accessible horizon, the stochastic laws $S$, their finite reversible deterministic realizations $D$, and fixed-basis unitary/Born representations $Q_{\mathrm{fb}}$ are the same class, $S\iff D\iff Q_{\mathrm{fb}}$ (§3.4). **(2) Readback content:** C4 is not needed for the existence of a quantum representation; it is what makes the OI sector nontrivial. C4 forces conditional memory in the visible law and readout-relevant hidden predictive memory in every faithful completion (§3.4); indivisibility somewhere in the recurrence cycle of a fixed finite reversible representative follows from any non-deterministic visible step, including in laws that are Markov on every accessible window, and does not require C4; with a full-support visible prior it is equivalent to memory at some order below the recurrence time, which an observer reaches only when that order is accessible, as C4 asserts (§2.3). C1 and C3 follow as necessary diagnostics of the mediation and its capacity; C2-structural, the persistence of the record to readback, holds by reversibility in every bijective realization and constrains coarse-grained descriptions of the hidden sector, with C2-slow one physical mechanism. **(3) Reverse finite realization:** every finite stochastic law, including every finite quantum record, has a finite reversible OI realization; bounded quantum instrument families are uniformly realizable to arbitrary finite accuracy (§3.4). **(4) Full operational extension:** identifying one common *standard local quantum instrument/composite theory* for all coherent interventions requires the additional operational-lifting and composition hypotheses stated in §3.4. Bell is a separate constraint rather than one of those lifting hypotheses: for a response-complete deterministic completion, measurement independence plus ontic parameter independence would force $|S_{\rm CHSH}|\le2$, so the Bell-violating branch adopted in §3.3 retains measurement independence and relinquishes ontic parameter independence while preserving operational no-signaling.
+**Theorem statement.** The claims divide into three exact layers and one explicitly conditional extension. **(1) Representation equivalence:** on every finite accessible horizon, the stochastic laws $S$, their finite reversible deterministic realizations $D$, and fixed-basis unitary/Born representations $Q_{\mathrm{fb}}$ are the same class, $S\iff D\iff Q_{\mathrm{fb}}$ (§3.4). **(2) Readback content:** C4 is not needed for the existence of a quantum representation; it is what makes the OI sector nontrivial. C4 forces conditional memory in the visible law and readout-relevant hidden predictive memory in every faithful completion (§3.4); indivisibility somewhere in the recurrence cycle of a fixed finite reversible representative follows from any non-deterministic visible step, including in laws that are Markov on every accessible window, and does not require C4; with a full-support visible prior it is equivalent to memory at some order below the recurrence time, which an observer reaches only when that order is accessible, as C4 asserts (§2.3). C1 and C3 follow as necessary diagnostics of the mediation and its capacity; C2-structural, the persistence of the record to readback, holds by reversibility in every bijective realization and constrains coarse-grained descriptions of the hidden sector, with C2-slow one physical mechanism. **(3) Reverse finite realization:** every finite stochastic law, including every finite quantum record, has a finite reversible OI realization; bounded quantum instrument families are uniformly realizable to arbitrary finite accuracy (§3.4). **(4) Full operational extension:** identifying one common *standard local quantum instrument/composite theory* for all coherent interventions requires the additional operational-lifting and composition hypotheses stated in §3.4. Bell is a separate constraint rather than one of those lifting hypotheses: for a response-complete deterministic completion that records a $\pm1$ outcome in every run, measurement independence plus ontic parameter independence would force $|S_{\rm CHSH}|\le2$, so the Bell-violating branch adopted in §3.3 retains measurement independence and relinquishes ontic parameter independence while preserving operational no-signaling.
 
 ### 1.4 Partition-Relativity
 
@@ -555,7 +555,7 @@ The framework's side supplies $\mathcal{C}_V$, the accessible times, the per-hor
 
 *Remark (why the geometry alone cannot do it).* Finitely many ontic states do not force a polytope state space, since a convex subset of a simplex need not be a polytope, so state-space geometry alone yields no obstruction. The SIC embedding is a certified instance: tetrahedral $a_i$, $p_i(r) = (1 + a_i \cdot r)/4$ maps the whole Bloch ball affinely and injectively into $\Delta_3$, so a four-state model with restricted preparations carries the qubit's state geometry intact. What it cannot carry is the sharp effects: the affine extension of $|0\rangle\langle 0|$ takes the value $\tfrac12 + \tfrac{\sqrt3}{2} > 1$ at an ontic vertex, no valid response function exists, and the dimension obstruction above is the correct general form (embedding, curvature, effect violation, and the factorization half all certified exactly over $\mathbb{Q}(\sqrt3)$: `nogo_probes.py`).
 
-*Remark (the operational-extension boundary).* The exact finite representation theorem and the finite-substratum obstruction answer different questions and should not be turned into a new 'selection' paper. At fixed observable horizon, $S\iff D\iff Q_{\mathrm{fb}}$ is exact. For a bounded family of interventions, the gluing theorem below gives one reversible realization for the entire classical action-labelled experiment; the uniform-continuum theorem then covers bounded quantum instrument envelopes to arbitrary requested finite accuracy. What no fixed finite carrier can do is reproduce the entire exact continuum operational theory of even a qubit at all preparations/effects and all precisions, by the classical-dimension obstruction above. The compositional target is settled as a characterization ([GR §3.3]): on any nonempty finite carrier, the operational theories whose available families on the system and on every ancilla level are exactly the finite Kraus instruments are precisely those satisfying five conditions — valid probabilities, trivial-ancilla consistency, inert spectators, full reversible control, iterated composition — each independent of the others and of the C1–C4 process, so that what the OI architecture must supply is named condition by condition rather than as one lifting hypothesis. Any exact-completion reconstruction beyond a fixed finite carrier must additionally show that its chosen completion retains finite predictive dimension; local tomography/composite completeness and all-level operational purification are sufficient reconstruction routes only after their hypotheses are actually established for that completion. The Bell side is now separate rather than analogous: the graph supplies a causal cone for finite-range substrata, but a measurement-independent deterministic completion with that pointwise cone is Bell-local. The framework's adopted Bell branch therefore requires ontic parameter dependence while retaining operational no-signaling (§3.3).
+*Remark (the operational-extension boundary).* The exact finite representation theorem and the finite-substratum obstruction answer different questions. At fixed observable horizon, $S\iff D\iff Q_{\mathrm{fb}}$ is exact. For a bounded family of interventions, the gluing theorem below gives one reversible realization for the entire classical action-labelled experiment; the uniform-continuum theorem then covers bounded quantum instrument envelopes to arbitrary requested finite accuracy. What no fixed finite carrier can do is reproduce the entire exact continuum operational theory of even a qubit at all preparations/effects and all precisions, by the classical-dimension obstruction above. The compositional target is a characterization ([GR §3.3]): on any nonempty finite carrier, the operational theories whose available families on the system and on every ancilla level are exactly the finite Kraus instruments are precisely those satisfying five conditions — valid probabilities, trivial-ancilla consistency, inert spectators, full reversible control, iterated composition — each independent of the others and of the C1–C4 process, so that what the OI architecture must supply is named condition by condition rather than as one lifting hypothesis. Any exact-completion reconstruction beyond a fixed finite carrier must additionally show that its chosen completion retains finite predictive dimension; local tomography/composite completeness and all-level operational purification are sufficient reconstruction routes only after their hypotheses are actually established for that completion. The Bell side is a separate question rather than an analogous one: the graph supplies a causal cone for finite-range substrata, but a measurement-independent deterministic completion with one-step own-wing setting interventions, readouts outside the other wing's cone and a $\pm1$ outcome in every run is Bell-local. The framework's adopted Bell branch therefore requires ontic parameter dependence while retaining operational no-signaling (§3.3).
 
 **Theorem (finite operational realization and gluing — ε-form).** *Fix a quantum experiment: a system of dimension $d$ with an initial state — alternative preparations entering, when wanted, as outcome-free channels in the family — a finite instrument family $\mathcal{F}$ — each instrument a finite family of CP maps $\{\mathcal{I}_o\}$ summing to a channel, each $\mathcal{I}_o$ with finitely many Kraus operators, so conditional states may be mixed — and a finite horizon $K$; fix a grid size $G \in \mathbb{N}$. There is a finite reversible deterministic embedded realization — visible sector: step counter, intervention record, outcome registers; hidden sector: the unnormalized digitized branch matrix (a density register), a predecessor stack, and $K$ pre-loaded seeds uniform on $\{0, \ldots, G{-}1\}$; one FIXED injective step map $\varphi_a$ per instrument, extended to a bijection by finite padding — with:*
 
@@ -643,7 +643,7 @@ At the level of finite-horizon fixed-basis observable laws, embedded observation
 
 *(i) Tensor product structure (visible–hidden).* The Stinespring route (§3.2) constructs $\mathcal{H} = \mathcal{H}_V \otimes \mathcal{H}_H$ and derives the CPTP channel $\Phi$ by partial trace. The visible–hidden tensor product is therefore given by the construction, not postulated.
 
-*(ii) Tensor product structure (visible-sector subsystems).* Spatially separated visible regions $V_A,V_B\subset V$ inherit an exact **dynamical causal separation** from the dependency graph: after $k$ updates, a local state can depend only on the graph ball of radius $k$ (§3.3). This establishes the causal-cone part of locality without the stronger simple-cubic nearest-neighbor stipulation. It does not alone establish statistical product structure after conditioning, local tomography, or one common tensor-product instrument category. Bell adds a sharper restriction: if that pointwise cone is kept at the wings' separation and the pre-setting ensemble is measurement-independent, determinism gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore does not use graph locality as the hidden-variable explanation of quantum Bell violation; it adopts ontic parameter dependence while requiring operational no-signaling. The common local quantum composite/instrument structure is the content of the inert-spectator and iterated-composition conditions of the operational-completion characterization (Remark on the operational-extension boundary; [GR §3.3]).
+*(ii) Tensor product structure (visible-sector subsystems).* Spatially separated visible regions $V_A,V_B\subset V$ inherit an exact **dynamical causal separation** from the dependency graph: after $k$ updates, a local state can depend only on the graph ball of radius $k$ (§3.3). This establishes the causal-cone part of locality without the stronger simple-cubic nearest-neighbor stipulation. It does not alone establish statistical product structure after conditioning, local tomography, or one common tensor-product instrument category. Bell adds a sharper restriction: if the setting interventions, applied at one step, each read and write only their own wing, each wing's readout lies outside the other wing's graph cone, a $\pm1$ outcome is recorded in every run, and the pre-setting ensemble is measurement-independent, determinism gives Bell factorization and $|S_{\rm CHSH}|\le2$. The framework therefore does not use graph locality as the hidden-variable explanation of quantum Bell violation; it adopts ontic parameter dependence while requiring operational no-signaling. The common local quantum composite/instrument structure is the content of the inert-spectator and iterated-composition conditions of the operational-completion characterization (Remark on the operational-extension boundary; [GR §3.3]).
 
 *(iii) State update, measurement, and multi-time predictions.* Projective measurement in the emergent description corresponds to conditioning on a visible-sector outcome and re-marginalizing over the hidden sector. The Lüders rule $\rho \to P_k \rho P_k / \text{Tr}(P_k \rho)$ transcribes Bayesian updating on the classical substratum (Lemma 3) for the represented diagonal sector — which is the transition-statistics layer, not the instrument algebra: the general operational update for noncommuting interventions belongs to that algebra, reached exactly under the operational completion conditions (§3.4; [GR §3.3]); its extension to arbitrary coherent density matrices belongs to the operational bridge (§3.2). No independent measurement postulate is required for the represented statistics. Multi-time correlation functions of the passive law are standard calculations within the delivered formalism ($\mathcal{H}_V$, $U(t)$, Born rule); weak values and Leggett-Garg protocols are intervention-rooted and belong to the intervention dilation (§3.4 Remark; §3.2 target) — the delivered formalism underdetermines them. The multi-time statement carries one qualification. The correspondence is engineered to reproduce rooted two-time transition data, which under-determines multi-time joint statistics [22]; the substratum, by contrast, fixes a unique multi-time law. Agreement of the substratum's conditioned multi-time statistics with the quantum formalism's intervention-rooted predictions is supported by the same chaotic-mixing suppression argument used to motivate decorrelation of controllable setting generators from preparation-relevant hidden data (§3.3); that decorrelation is not the Bell-violation mechanism, because the adopted Bell branch instead relinquishes ontic parameter independence. Residual pre-division memory, if present, would appear as deviations from quantum multi-time predictions — a falsifiable texture of the same standing as the residual dissipation $\mathcal{D}$.
 
@@ -697,7 +697,7 @@ $\epsilon$ does not smuggle in a quantum assumption, but the reason is foundatio
 
 ### 4.4 Relation to Prior Work
 
-**'t Hooft [1]:** Differs in mechanism (epistemic trace-out vs. information loss), generality (any embedded observer vs. particular rules), and Bell placement (outcome independence violation vs. superdeterminism). **QBism/relational QM:** Share observer-relative epistemic states; this framework provides a structural *why* and quantitative predictions.
+**'t Hooft [1]:** Differs in mechanism (epistemic trace-out vs. information loss), generality (any embedded observer vs. particular rules), and Bell placement (ontic parameter dependence with measurement independence retained vs. superdeterminism). **QBism/relational QM:** Share observer-relative epistemic states; this framework provides a structural *why* and quantitative predictions.
 
 **Relation to prior stochastic-quantum programs.** Three earlier programs sought to derive quantum mechanics from classical-looking substrates. **Nelson's stochastic mechanics [32]** postulates a continuous Brownian-motion-like process on configuration space with drift determined by the imaginary part of the log wave function; the Schrödinger equation follows from the Fokker-Planck structure. Wallstrom [33] showed that Nelson's program cannot uniquely select the quantization condition $\oint p \cdot dq = nh$ — the stochastic process admits a broader class of solutions than standard QM, and the quantization must be reimposed by hand. The present framework is not subject to this critique because it does not derive QM from a continuous stochastic process on $\psi$ or on configuration space; its exact identification is of the quantum REPRESENTATION — universal at the fixed-basis layer, with the common coherent operational lift stated separately — and proceeds through the characterization theorem for embedded observers on a deterministic bijection, with stochasticity emerging from the trace-out over the hidden sector rather than being fundamental. **Adler's trace dynamics [34]** derives QM from statistical mechanics of matrix-valued dynamical variables with a trace-class Hamiltonian, with the canonical commutation relations emerging as expectation values over a specific equilibrium ensemble. The framework here requires neither matrix-valued variables nor an equilibrium-ensemble derivation; the substratum is a finite configuration space with a deterministic bijection, and the emergence mechanism is the Stinespring dilation applied to observer-marginalized transition probabilities. **Barandes's stochastic-quantum correspondence [11, 12]**, used as a technical tool in §3.1, is not a competitor but a building block: the correspondence maps its finite-configuration tuple class — a broad class in which Markov chains are members and P-indivisibility marks the nontrivially indivisible dynamical sector, not a membership criterion — to unitary quantum evolutions in compressed ($\leq n^3$) form under (T); the present framework supplies the physical mechanism (embedded observation under C1–C4) that produces the memory-bearing processes occupying that nontrivial sector — P-indivisibility in the stronger regimes established separately — and supplies the fixed-basis representation itself internally ($S \iff D \iff Q_{\mathrm{fb}}$, §3.4), retaining the import for compression and interpretation. The three earlier programs identified emergent QM as a legitimate research target; what the present framework adds is an exact finite-horizon representation equivalence, $S \iff D \iff Q_{\mathrm{fb}}$, holding for every finite law, a characterization (ii) $\iff$ (iii) whose conditions are diagnostics of a realization, (C4) coinciding with (ii) in every faithful realization (§3.4), and a constructive derivation chain that does not require independent quantization conditions or equilibrium ensembles.
 
@@ -763,7 +763,7 @@ S\iff D\iff Q_{\mathrm{fb}}.
 $$
 Thus the reduced law of a finite embedded observer has an exact quantum representation, and every finite quantum record has a finite reversible realization. The representation statement is universal; it is not the selector. The content of observation incompleteness lies in history readback. C4 forces conditional memory and readout-relevant hidden predictive structure in every faithful completion. C1 and C3 are necessary diagnostics of that mediation and its capacity, while C2-structural, the persistence of the record to readback, holds by reversibility in every bijective realization and constrains coarse-grained descriptions of the hidden sector, with C2-slow one sufficient physical mechanism.
 
-The spatial theory adds an exact causal-cone result. Because the coupling graph is defined by one-step dynamical dependence, $k$ updates can carry influence no farther than graph distance $k$. Bell locality then follows when settings are genuine local interventions on a common setting-independent pre-setting ensemble **and** the Bell-relevant response graph is pointwise separated before readout; by §3.3 the resulting deterministic completion has $|S_{\rm CHSH}|\le2$. Reproducing quantum correlations therefore requires ontic parameter dependence, which is the option §3.3 takes and which the specific SM/GR target implements through preparation-indexed state-dependent adjacency. The superdeterministic alternative is not adopted: the manuscript proves only the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits, while Hall--Branciard's optimized causal benchmark is about $0.080$ bits. The PR-box construction remains the correct negative control for dropping the locality/intervention structure, not a counterexample to unitary representability.
+The spatial theory adds an exact causal-cone result. Because the coupling graph is defined by one-step dynamical dependence, $k$ updates can carry influence no farther than graph distance $k$. Bell locality then follows when settings are interventions, applied at one step, that each read and write only their own wing on a common setting-independent pre-setting ensemble, **and** each wing's $\pm1$ outcome, recorded in every run, is read outside the other wing's graph cone; by §3.3 the resulting deterministic completion has $|S_{\rm CHSH}|\le2$. Reproducing quantum correlations therefore requires giving up either ontic parameter independence, which the intervention and readout conditions secure through the cone lemma, or measurement independence. §3.3 gives up ontic parameter independence; for the specific SM/GR target the proposed implementation is preparation-indexed state-dependent adjacency, whose compatibility with operational no-signaling and the continuum-curvature limit is the open hypothesis H-Bell. The superdeterministic alternative is not adopted: the manuscript proves only the model-independent necessary lower bound $I_{\rm ont}\ge0.0309$ bits, while Hall--Branciard's optimized causal benchmark is about $0.080$ bits. The PR-box construction remains the correct negative control for dropping the locality/intervention structure, not a counterexample to unitary representability.
 
 The reverse direction is equally concrete. Every finite stochastic law has a finite reversible process dilation, and the operational gluing theorem shows that for any fixed finite dimension, finite instrument menu, finite horizon, and $\varepsilon>0$, one finite reversible OI realization covers the whole corresponding quantum experimental envelope to accuracy $\varepsilon$. A single fixed finite carrier cannot equal the full continuum operational theory at all precisions, but the framework does not require an ontically infinite carrier; the continuum is the mathematical idealization of its finite-resolution physical description.
 
diff --git a/papers/Main.pdf b/papers/Main.pdf
index a6b6c2396..7267c5aa9 100644
Binary files a/papers/Main.pdf and b/papers/Main.pdf differ
diff --git a/papers/Main.tex b/papers/Main.tex
index 6fee6fc31..cb5e3d906 100644
--- a/papers/Main.tex
+++ b/papers/Main.tex
@@ -251,14 +251,16 @@ \subsection{ABSTRACT}\label{abstract}}
 For spatial OI systems, the coupling graph defined by one-step dynamical
 dependence supplies exact causal cones: influence propagates at most one
 graph edge per update. Bell accounting is correspondingly sharp: a
-deterministic completion that keeps the pointwise cone and a
-setting-independent pre-setting ensemble is a local hidden-variable
-model, so \(|S_{\mathrm{CHSH}}|\le2\) and quantum correlations are
-unreachable. Reproducing them requires ontic parameter dependence ---
-realized in the specific SM/GR branch through preparation-indexed
-state-dependent adjacency or an equivalent Bell-nonlocal response
-structure, with no operational signal --- or else setting-dependent
-ontic ensembles, for which
+deterministic completion whose setting interventions, applied at one
+step, each read and write only their own wing, whose readouts lie
+outside the other wing's cone and record a \(\pm1\) outcome in every
+run, and whose pre-setting ensemble is setting-independent is a local
+hidden-variable model, so \(|S_{\mathrm{CHSH}}|\le2\) and quantum
+correlations are unreachable. Reproducing them requires ontic parameter
+dependence --- targeted in the specific SM/GR branch through
+preparation-indexed state-dependent adjacency or an equivalent
+Bell-nonlocal response structure, with no operational signal --- or else
+setting-dependent ontic ensembles, for which
 \(S_{\mathrm{CHSH}}\le2+4\sqrt{2\ln2\,I_{\mathrm{ont}}}\) gives the
 model-independent necessary lower bound \(I_{\mathrm{ont}}\ge0.0309\)
 bits for the quantum value. Conversely, every finite stochastic law, and
@@ -737,10 +739,11 @@ \subsubsection{1.3 Conditions on the Hidden
 coherent interventions requires the additional operational-lifting and
 composition hypotheses stated in §3.4. Bell is a separate constraint
 rather than one of those lifting hypotheses: for a response-complete
-deterministic completion, measurement independence plus ontic parameter
-independence would force \(|S_{\rm CHSH}|\le2\), so the Bell-violating
-branch adopted in §3.3 retains measurement independence and relinquishes
-ontic parameter independence while preserving operational no-signaling.
+deterministic completion that records a \(\pm1\) outcome in every run,
+measurement independence plus ontic parameter independence would force
+\(|S_{\rm CHSH}|\le2\), so the Bell-violating branch adopted in §3.3
+retains measurement independence and relinquishes ontic parameter
+independence while preserving operational no-signaling.
 
 \hypertarget{partition-relativity}{%
 \subsubsection{1.4 Partition-Relativity}\label{partition-relativity}}
@@ -3290,20 +3293,19 @@ \subsubsection{3.4 The Characterization Theorem: Necessity of the
 
 \emph{Remark (the operational-extension boundary).} The exact finite
 representation theorem and the finite-substratum obstruction answer
-different questions and should not be turned into a new `selection'
-paper. At fixed observable horizon, \(S\iff D\iff Q_{\mathrm{fb}}\) is
-exact. For a bounded family of interventions, the gluing theorem below
-gives one reversible realization for the entire classical
-action-labelled experiment; the uniform-continuum theorem then covers
-bounded quantum instrument envelopes to arbitrary requested finite
-accuracy. What no fixed finite carrier can do is reproduce the entire
-exact continuum operational theory of even a qubit at all
-preparations/effects and all precisions, by the classical-dimension
-obstruction above. The compositional target is settled as a
-characterization ({[}GR §3.3{]}): on any nonempty finite carrier, the
-operational theories whose available families on the system and on every
-ancilla level are exactly the finite Kraus instruments are precisely
-those satisfying five conditions --- valid probabilities,
+different questions. At fixed observable horizon,
+\(S\iff D\iff Q_{\mathrm{fb}}\) is exact. For a bounded family of
+interventions, the gluing theorem below gives one reversible realization
+for the entire classical action-labelled experiment; the
+uniform-continuum theorem then covers bounded quantum instrument
+envelopes to arbitrary requested finite accuracy. What no fixed finite
+carrier can do is reproduce the entire exact continuum operational
+theory of even a qubit at all preparations/effects and all precisions,
+by the classical-dimension obstruction above. The compositional target
+is a characterization ({[}GR §3.3{]}): on any nonempty finite carrier,
+the operational theories whose available families on the system and on
+every ancilla level are exactly the finite Kraus instruments are
+precisely those satisfying five conditions --- valid probabilities,
 trivial-ancilla consistency, inert spectators, full reversible control,
 iterated composition --- each independent of the others and of the
 C1--C4 process, so that what the OI architecture must supply is named
@@ -3313,11 +3315,13 @@ \subsubsection{3.4 The Characterization Theorem: Necessity of the
 dimension; local tomography/composite completeness and all-level
 operational purification are sufficient reconstruction routes only after
 their hypotheses are actually established for that completion. The Bell
-side is now separate rather than analogous: the graph supplies a causal
-cone for finite-range substrata, but a measurement-independent
-deterministic completion with that pointwise cone is Bell-local. The
-framework's adopted Bell branch therefore requires ontic parameter
-dependence while retaining operational no-signaling (§3.3).
+side is a separate question rather than an analogous one: the graph
+supplies a causal cone for finite-range substrata, but a
+measurement-independent deterministic completion with one-step own-wing
+setting interventions, readouts outside the other wing's cone and a
+\(\pm1\) outcome in every run is Bell-local. The framework's adopted
+Bell branch therefore requires ontic parameter dependence while
+retaining operational no-signaling (§3.3).
 
 \textbf{Theorem (finite operational realization and gluing --- ε-form).}
 \emph{Fix a quantum experiment: a system of dimension \(d\) with an
@@ -4333,8 +4337,10 @@ \subsubsection{3.4 The Characterization Theorem: Necessity of the
 without the stronger simple-cubic nearest-neighbor stipulation. It does
 not alone establish statistical product structure after conditioning,
 local tomography, or one common tensor-product instrument category. Bell
-adds a sharper restriction: if that pointwise cone is kept at the wings'
-separation and the pre-setting ensemble is measurement-independent,
+adds a sharper restriction: if the setting interventions, applied at one
+step, each read and write only their own wing, each wing's readout lies
+outside the other wing's graph cone, a \(\pm1\) outcome is recorded in
+every run, and the pre-setting ensemble is measurement-independent,
 determinism gives Bell factorization and \(|S_{\rm CHSH}|\le2\). The
 framework therefore does not use graph locality as the hidden-variable
 explanation of quantum Bell violation; it adopts ontic parameter
@@ -4692,10 +4698,10 @@ \subsubsection{4.4 Relation to Prior
 
 \textbf{'t Hooft {[}1{]}:} Differs in mechanism (epistemic trace-out
 vs.~information loss), generality (any embedded observer vs.~particular
-rules), and Bell placement (outcome independence violation
-vs.~superdeterminism). \textbf{QBism/relational QM:} Share
-observer-relative epistemic states; this framework provides a structural
-\emph{why} and quantitative predictions.
+rules), and Bell placement (ontic parameter dependence with measurement
+independence retained vs.~superdeterminism). \textbf{QBism/relational
+QM:} Share observer-relative epistemic states; this framework provides a
+structural \emph{why} and quantitative predictions.
 
 \textbf{Relation to prior stochastic-quantum programs.} Three earlier
 programs sought to derive quantum mechanics from classical-looking
@@ -5253,15 +5259,20 @@ \subsection{5. CONCLUSION}\label{conclusion}}
 The spatial theory adds an exact causal-cone result. Because the
 coupling graph is defined by one-step dynamical dependence, \(k\)
 updates can carry influence no farther than graph distance \(k\). Bell
-locality then follows when settings are genuine local interventions on a
-common setting-independent pre-setting ensemble \textbf{and} the
-Bell-relevant response graph is pointwise separated before readout; by
-§3.3 the resulting deterministic completion has \(|S_{\rm CHSH}|\le2\).
-Reproducing quantum correlations therefore requires ontic parameter
-dependence, which is the option §3.3 takes and which the specific SM/GR
-target implements through preparation-indexed state-dependent adjacency.
-The superdeterministic alternative is not adopted: the manuscript proves
-only the model-independent necessary lower bound
+locality then follows when settings are interventions, applied at one
+step, that each read and write only their own wing on a common
+setting-independent pre-setting ensemble, \textbf{and} each wing's
+\(\pm1\) outcome, recorded in every run, is read outside the other
+wing's graph cone; by §3.3 the resulting deterministic completion has
+\(|S_{\rm CHSH}|\le2\). Reproducing quantum correlations therefore
+requires giving up either ontic parameter independence, which the
+intervention and readout conditions secure through the cone lemma, or
+measurement independence. §3.3 gives up ontic parameter independence;
+for the specific SM/GR target the proposed implementation is
+preparation-indexed state-dependent adjacency, whose compatibility with
+operational no-signaling and the continuum-curvature limit is the open
+hypothesis H-Bell. The superdeterministic alternative is not adopted:
+the manuscript proves only the model-independent necessary lower bound
 \(I_{\rm ont}\ge0.0309\) bits, while Hall--Branciard's optimized causal
 benchmark is about \(0.080\) bits. The PR-box construction remains the
 correct negative control for dropping the locality/intervention
@@ -5580,4 +5591,4 @@ \subsection{REFERENCES}\label{references}}
 \emph{Phys. Rev.~Lett.} \textbf{103}, 210401 (2009); arXiv:0908.0238.
 
 \end{document}
-% source-sha256: 8e326e67b65986a55502aae8e085c9b0b5570289c6cf596416d27e4bd5a6a1f7
+% source-sha256: 090e4a0cc1684d86ca7f6e6f2d1353078529cd0b53b96f615d96bd82469b4f65
diff --git a/verification/audits/manuscript/intro-corpus-audit-20261026/tracks/SC33-bell-main-book/README.md b/verification/audits/manuscript/intro-corpus-audit-20261026/tracks/SC33-bell-main-book/README.md
new file mode 100644
index 000000000..fab4fb68c
--- /dev/null
+++ b/verification/audits/manuscript/intro-corpus-audit-20261026/tracks/SC33-bell-main-book/README.md
@@ -0,0 +1,116 @@
+# SC-33: Bell placement in Main and the book (#942 / #946)
+
+Base: `main` at `0d917665`. This unit carries the Main and book part of the SC-17 claim class; SC-17 corrects the Explainer.
+Each site is restated at the strength of its anchor, and no claim is strengthened. The anchor is Main §3.3, Theorem (Bell
+ceiling for a screened local completion). Its hypotheses are (i) determinism, (ii) own-wing read/write setting interventions
+applied at one step, (iii) a ±1 readout region outside the other wing's cone, and (iv) one common pre-setting ensemble. It
+applies when the protocol records a ±1 outcome in every run. The either/or follows the theorem: a completion reproducing
+quantum Bell correlations gives up (ii) and (iii), which with the cone lemma secure ontic parameter independence, or (iv),
+measurement independence. The framework gives up the first, so the adopted branch is ontic parameter dependence. H-Bell is the
+open compatibility condition on preparation-indexed adjacency: operational no-signaling and the continuum-curvature
+(Ollivier–Ricci) limit (§3.3, Corollary).
+
+A deterministic completion satisfies ontic outcome independence automatically, since each outcome is a point mass given the
+pre-setting variable and the settings. Outcome dependence is therefore not available as OI's Bell route.
+
+Where a site assumes ontic parameter independence directly, (ii) and (iii) are already inside that assumption, and only the
+±1-every-run hypothesis is added. Where it states the ceiling from graph separation, the own-wing intervention hypothesis is
+added as well, applied at one step. On a finite vertex set "finite-range" is not a separation hypothesis, so (iii) is
+stated as each wing's readout lying outside the other wing's graph cone, or as couplings that do not connect the wings before
+readout.
+
+| Site | Was | Anchor | Now |
+|---|---|---|---|
+| Main :700 | 't Hooft comparison: "Bell placement (outcome independence violation vs. superdeterminism)" | §3.3 either/or; theorem proof (determinism makes the conditionals point masses) | "Bell placement (ontic parameter dependence with measurement independence retained vs. superdeterminism)" |
+| Main :766 | ceiling from "genuine local interventions" and pointwise separation, no ±1; "Reproducing quantum correlations therefore requires ontic parameter dependence, which … the specific SM/GR target implements through preparation-indexed state-dependent adjacency" | §3.3 (i)–(iv), ±1 in every run, either/or; Corollary (H-Bell open) | Ceiling states one-step own-wing interventions and a ±1 outcome in every run read outside the other wing's cone. Reproduction requires giving up ontic parameter independence or measurement independence, and §3.3 gives up the first. Preparation-indexed adjacency is the proposed SM/GR implementation, and its compatibility with no-signaling and the continuum-curvature limit is the open hypothesis H-Bell. |
+| Main :558 | "is now separate rather than analogous"; "with that pointwise cone is Bell-local"; "should not be turned into a new 'selection' paper"; "is settled as a characterization" | §A.32/§A.33; §3.3 (ii), (iii), ±1 | "is a separate question rather than an analogous one"; one-step own-wing interventions, readouts outside the other wing's cone and ±1 in every run; the 'selection' clause is deleted; "is a characterization". The adopted-branch "therefore requires ontic parameter dependence" is kept. |
+| Main :22 | "keeps the pointwise cone and a setting-independent pre-setting ensemble"; parameter dependence "realized in the specific SM/GR branch" | §3.3 (ii)–(iv), ±1; Corollary | Setting interventions applied at one step, each reading and writing only their own wing; readouts outside the other wing's cone recording ±1 in every run. "realized" becomes "targeted"; the abstract's later sentence names H-Bell as open. |
+| Main :82 (Theorem statement, canonical) | "measurement independence plus ontic parameter independence would force $\|S\|\le2$" | §3.3 theorem ("If the protocol records a ±1 outcome in every run") | Adds "that records a ±1 outcome in every run". Ledger `MAIN:T-statement` re-affirmed: fingerprint 70572f0b3e1aa833 → 2748dd752bdd9f03, level SUM and empty delta unchanged (it summarizes the constituent rows), same ID. |
+| Main :646 | "that pointwise cone is kept at the wings' separation and the pre-setting ensemble is measurement-independent" | §3.3 (ii), (iii), ±1 | Interventions applied at one step, each wing's readout outside the other wing's graph cone, ±1 in every run. |
+| ch00 :41 (+FULL :277) | "a measurement-independent response-complete completion with finite-range Bell couplings is classical, so quantum violation requires ontic parameter dependence" | §3.3; either/or | One-step own-wing interventions, couplings that do not connect the wings before readout, ±1 in every run; "is Bell-local, so quantum violation under measurement independence requires ontic parameter dependence". |
+| ch00 :55 (+FULL :291) | ceiling from graph-cone separation and a setting-independent ensemble; "realized in the SM/GR target"; "What is not yet claimed" | §3.3; Corollary; §A.30 | One-step own-region interventions and ±1 in every run. The SM/GR target proposes preparation-indexed structure, and whether it keeps no-signaling and the continuum-curvature limit is the open hypothesis H-Bell. "What is not claimed". |
+| ch01 :16 (+FULL :360) | "a pointwise finite-range cone together with local interventions and one setting-independent pre-setting ensemble is Bell-local" | §3.3 (iii): on a finite vertex set "finite-range" is no separation hypothesis | One-step own-wing interventions, readouts outside the other wing's graph cone, ±1 in every run and one setting-independent ensemble "give a Bell-local model". |
+| ch01 :169 (+FULL :513) | the book's own statement of the ceiling: coupling-range separation plus a setting-independent ensemble | §3.3 | Adds one-step own-wing interventions and ±1 at each wing in every run. |
+| ch01 :171 (+FULL :515) | "The averaged operational distribution remains no-signaling. H-Bell is the open metric/Ollivier--Ricci stability condition …. That condition is now downstream of a harder one." | Main §3.3 Corollary (H-Bell requires no-signaling and the curvature/metric limit); §A.30 | "H-Bell is the open requirement that those prepared graphs preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit. The curvature condition is downstream of a harder one." |
+| ch01 :183 (+FULL :527) | MI plus parameter independence "would imply" the ceiling | §3.3 | Adds ±1 in every run. |
+| ch02 :188 (+FULL :831) | MI plus parameter independence "would obey" the ceiling; reference sector "cannot itself supply Bell parameter dependence for wings outside each other's graph cone" | §3.3; Corollary | Adds ±1 in every run, and one-step own-wing interventions to the Corollary clause. |
+| ch03 :40 (+FULL :916) | "The reference cubic graph is Bell-local under measurement independence; the adopted branch uses preparation-indexed state-dependent adjacency, with H-Bell conditioning its metric/Ollivier--Ricci compatibility" | Corollary; H-Bell | Bell-locality scoped by one-step own-wing interventions, readouts outside the other wing's graph cone and ±1 in every run; the branch "proposes … under the open hypothesis H-Bell (operational no-signaling and the metric/Ollivier--Ricci continuum limit)". |
+| ch03 :162 (+FULL :1038) | coupling-range separation plus a setting-independent ensemble "factorizes" | §3.3 | Adds one-step own-wing interventions and ±1 in every run. |
+| ch03 :164 (+FULL :1040) | "A finite-range Bell graph plus a setting-independent response-complete ensemble would force" the local class | §3.3 (iii) | "A Bell graph that does not connect the wings before readout, with one-step own-wing setting interventions and a ±1 outcome in every run, plus …". |
+| ch03 :180 (+FULL :1056) | graph separation plus a setting-independent ensemble; "The averaged operational statistics remain no-signaling. H-Bell is the remaining metric/Ollivier--Ricci stability condition …. That condition is now downstream of a harder one." | §3.3; Corollary; §A.30 | Adds one-step own-wing interventions and ±1 in every run; H-Bell sentence as at ch01 :171. |
+| ch03 :182 (+FULL :1058) | "that nonlocality is represented by preparation-indexed state-dependent adjacency" | Corollary (H-Bell open) | "is targeted through … under H-Bell". |
+| ch04 :90 (+FULL :1209) | "finite-range Bell couplings plus a setting-independent pre-setting ensemble imply Bell factorization" | §3.3 (iii) | "Bell couplings that do not connect the wings before readout, one-step own-wing setting interventions and a ±1 outcome in every run, plus …". |
+| ch04 :92 (+FULL :1211) | "its Bell-relevant graph is finite-range at the wings"; reference-graph clause; "with H-Bell now the open metric/Ollivier--Ricci stability condition for the prepared graph family" | §3.3; Corollary; §A.30 | Graph "does not connect the wings before readout", interventions applied at one step, ±1 in every run; one-step own-wing interventions in the Corollary clause; "with H-Bell the open requirement that the prepared graph family preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit". |
+| ch04 :124 (+FULL :1243) | "reaches quantum Bell violation only on the ontically parameter-dependent branch" | either/or | "under measurement independence, only on the ontically parameter-dependent branch". |
+| ch18 :110 (+FULL :4928) | Bell "rules out" an MI and PI completion; "Chapter 1 proves the corresponding Bell ceiling" from coupling-range separation; "The operational distribution remains no-signaling." | §3.3; Corollary | Adds ±1 in every run, and one-step own-wing interventions; "Whether those prepared graphs keep the operational distribution no-signaling and preserve the continuum-curvature limit is the open hypothesis H-Bell." |
+| appendix-c :32 (+FULL :6278) | "local interventions occur before the corresponding cones meet"; "OI therefore cannot combine deterministic response completeness, measurement independence, and ontic parameter independence" | §3.3 (ii), (iii) | Interventions applied at one step, each reading and writing only its own wing, "and each wing's readout lies outside the other wing's graph cone"; ±1 in every run in both sentences. |
+| appendix-c :34 (+FULL :6280) | "keeps a pointwise finite-range cone on one setting-independent pre-setting ensemble is a local hidden-variable model"; "implemented in the SM/GR branch" | §3.3 (iii); Corollary | "with one-step own-wing setting interventions, each wing's readout outside the other wing's graph cone, a ±1 outcome in every run, and one setting-independent pre-setting ensemble"; "targeted … under the open hypothesis H-Bell". |
+| appendix-c :42 (+FULL :6288) | "a parameter-independent deterministic completion would still satisfy CHSH ≤2" | §3.3 (iv), ±1 | "a measurement-independent, parameter-independent deterministic completion recording a ±1 outcome in every run". |
+| glossary :19 (+FULL :6619) | MI plus ontic PI "gives Bell factorization" | §3.3 | Adds ±1 in every run. |
+| glossary :49 (+FULL :6649) | MI plus PI "gives the bound 2; quantum violation therefore uses ontic parameter dependence" | §3.3; either/or | Adds ±1 in every run; "quantum violation under measurement independence therefore uses …". |
+| glossary :147 (+FULL :6747) | "a measurement-independent, parameter-independent deterministic completion, whose Bell bound is 2" | §3.3 | Adds "recording a ±1 outcome in every run". |
+| book/README.md :15 (no FULL mirror) | "H-Bell is the open metric/Ollivier--Ricci stability condition for those prepared graphs" | Corollary | "H-Bell is the open requirement that those prepared graphs preserve operational no-signaling and the metric/Ollivier--Ricci continuum limit." |
+
+## Audit for the outcome-independence error
+
+Every use of "outcome independence", "outcome-independence", "outcome dependence" and "outcome-dependent" in `papers/*.md` and
+`book/*.md` was read in context.
+
+- **Main :700.** The only instance of the error. Corrected above.
+- **ch04 :90 (+FULL :1209).** "does not obtain quantum Bell violation from outcome-independence failure in an indivisible
+  stochastic law". This is correct and is kept.
+- **ch03 :162 (+FULL :1038).** "cannot use graph locality, screening, outcome dependence, or indivisibility to explain the quantum
+  violation". This is correct and is kept.
+- **ch04 :98 (+FULL :1217).** "in the adopted branch it is ontic parameter dependence, not mere stochastic outcome dependence".
+  This is correct and is kept.
+- **Main :714, Substratum :483, ch04 :146 (+FULL :1265), GR :599.** These use "outcome-independent rule" for identifying
+  fundamental open-system processes. That is unrelated to Bell.
+- **GR :248.** This uses "outcome-dependent continuation" in an operational protocol. That is unrelated to Bell.
+- **Explainer.** It has no outcome-independence placement. Its Bell sites are SC-17's.
+
+## Sites checked and left unchanged
+
+- **Main :770.** It names the adopted branch, measurement independence retained and ontic parameter dependence, and states no
+  ceiling.
+- **Main §3.3 (:356–:425).** This is the anchor.
+- **Main :352.** "the intervention side is settled as a characterization" is outside this unit's Bell lines and is left as it is.
+- **ch03 :186, ch05 :95** (SC-17), **Main :176, :706** (SC-28) and **Main :268, :510, :584, :608, :610** (SC-29) are not
+  touched.
+- **ch02 :188.** The H-Bell gloss, "the compatibility of the local lattice sector with the ontically parameter-dependent Bell
+  completion", names no wrong condition, and the text is left as it is.
+
+Deferred to a companion unit (not touched here):
+
+- "That condition is now downstream of a harder one" at Main :410 (the Corollary paragraph), Explainer :340 and Methodology :339.
+- Explainer, Methodology, Structure and Substratum Bell wording of the same class: "finite-range Bell" (Methodology, Substratum),
+  "remain(s) no-signaling" (Explainer, Methodology, Substratum) and the H-Bell "stability condition" glosses (Explainer, SM,
+  Substratum).
+
+## Re-grep (`papers/Main.md`, `book/*.md`; line counts)
+
+| Phrase | Count | Where |
+|---|---|---|
+| "outcome independence violation" | 0 | |
+| "is now separate", "H-Bell now", "not yet claimed", "should not be turned" | 0 each | |
+| "implements through preparation", "realized in the SM/GR", "realized in the specific SM/GR", "implemented in the SM/GR", "represented by preparation-indexed" | 0 each | |
+| "finite-range Bell", "pointwise finite-range", "finite-range at the wings" | 0 each | |
+| "remains no-signaling", "stability condition for" | 0 each | |
+| "now downstream of a harder one" | 1 | Main :410, deferred |
+| "is downstream of a harder one" | 4 | ch01 :171, ch03 :180 and FULL |
+| "outcome-independence failure" | 2 | ch04 :90 and FULL; correct use |
+| "outcome dependence" | 4 | ch03 :162, ch04 :98 and FULL; correct uses |
+| "therefore requires ontic parameter dependence" | 1 | Main :558, scoped to the adopted branch |
+| "\pm1$ outcome" | 46 | Main 8, chapters, appendix-c and glossary 19, FULL 19 |
+| "applied at one step" | 20 | Main 4, chapters and appendix-c 8, FULL 8 |
+| "one-step own-wing" | 15 | Main 1, chapters and appendix-c 7, FULL 7 |
+| "open hypothesis H-Bell" | 9 | Main 1, chapters and appendix-c 4, FULL 4 |
+| "open requirement that" | 7 | book/README, ch01, ch03, ch04, FULL 3 |
+
+Each chapter line changed here appears verbatim in FULL (`mirror_check`: 0 chapter lines absent).
+
+The Introduction (`papers/Introduction.md` on `draft/oi-introductory-paper-20261025` at `3e600003`, read only) states the
+ceiling with all four hypotheses and ±1 in every run (L254). It states the either/or and the adopted branch (L258), and H-Bell as
+no-signaling plus the gravitational continuum limit (L258, L260). It makes no outcome-independence placement. The L306 entry
+"the Bell ceiling" is proved on paper.
+
+Regenerated: Main and the book (`.tex` and `.pdf`). Main stays at 96 pages and the book goes from 558 to 559, from the added text; no glyph was dropped.
diff --git a/verification/coverage/LEDGER.json b/verification/coverage/LEDGER.json
index 7510b34eb..a5083c945 100644
--- a/verification/coverage/LEDGER.json
+++ b/verification/coverage/LEDGER.json
@@ -380,7 +380,7 @@
       "line": 82,
       "kind": "Theorem",
       "label": "statement",
-      "fingerprint": "70572f0b3e1aa833",
+      "fingerprint": "2748dd752bdd9f03",
       "area": "oi-foundations",
       "assumptions": "see the constituent rows",
       "checks": [],