[amaybaum]

Guiding draft PR (§A.43) for the OI-to-QM reconstruction programme. Research only: no premise adopted, no status change, no round, F or E, no merge planned.

Index: verification/programmes/oi-qm/reconstruction/research-planning/missing-component-20261020/INTEGRATION.md. It names every checkpoint by commit or bundle sha256, separates review levels, records per checkpoint what evidence is held in this repository (EVIDENCE-RETENTION.md), and lists what is supplied and what is open. PLAN.md holds the plan and the earlier nodes' status.

The question. Can OI's fixed native reversible dynamics, with every resource and access restriction stated explicitly, realize a reusable measurement instrument? Its complete public record and its outgoing carrier would have to obey the quantum instrument law jointly, on every branch, including failures. And which ingredients remain supplied rather than derived?

The thread began from F2-reg's two missing premises (O-A, O-B; F2 ledger LEDGER.md §3) and the question whether measurement, made an explicit condition, supplies them. Nodes 1–9 narrowed that to the instrument question above.

Division of work

• Research (WIP): the missing component for F2-reg, and measurement as an added condition #885 (this PR): the programme. Its questions, assumptions, acceptance rule and synthesis; this branch's coordinator is its writer.
• WIP: native nonlinear processing and second-front source audit #910: the native-Y continuation, under its own writer. Its stable conclusions enter INTEGRATION.md as reviewed syntheses with exact commits; the record cites WIP: native nonlinear processing and second-front source audit #910 at its reviewed snapshot 00e85e748cf8e5ada75f4e1a22aef87eb0a823a2.
• Governance rounds (e.g. KTRANS-SEP-2, KTRANS-SEP-2: E designated at 97f6c2e1; receipt Q 4600e66a holds #905) are separate.

Acceptance rule for instrument candidates:

• the whole public history and the outgoing carrier are checked jointly, failures included;
• fresh resources must be independent conditional on history;
• X→Y→X alone is insufficient, and a terminal R read serves as a diagnostic;
• per-port freshness is insufficient.

Accepted synthesis: INTEGRATION.md at 2d555f17c23bea31d32b3f5eb4c49d245b413a76, designated by the owner. Its successor, the provenance and #910-citation amendment (3a8a3188, review fixes 222f7973), is under independent review and is not yet accepted. Gate 1 (retaining the reviewer code that the selector-record, native-selector and read-reset reviews used) remains open.

Open obligations

1. An independent proof review of the inherited transport theorem.
2. A native Y read-and-reset, starting from the native-X outgoing carrier: a clean operand with workspace specified at the start; a reset whose outgoing carrier decodes to (y ⊕ a, y, y ⊕ b, z) with (a, b) in the 5:3:2 post-Y ratio and z fresh and fair; X→Y→X and X→Y→R with every failure.
3. A reusable outgoing interface, without a history-reading decoder.
4. Selection of the physical direction for each observable; reciprocity does not select it.
5. Native preparation, clock and settings, and access closure.
6. Unrestricted depth and menu; composites and Bell structure.

No full OI-to-QM equivalence is established.

Base: main at df9e601ebe2a4e5af2a82f2d06ca2797c3a10f88.

Authority limits: publication only. No dispatch, no F/E designation, no adoption of a physical premise, no merge. Every result is a research record until separately reviewed.

🤖 Generated with Claude Code

https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

[amaybaum]

Checkpoint 5de64a1a (WIP / research only): first two nodes, each independently reviewed

oa-node1/ (O-A node 1): ELABORATING with a CONFIRMING core.

• Countable realization. A finite bijective substratum plus supervenience gives countably many available conjugations, so countable_not_pairFlowSourced excludes exact QM.
  • The review confirms the logic, widened to every available level-1 conjugation channel.
  • Thread H:51–58 already states it in substance.
  • What it adds: a real duration or coupling does not escape. The escapes are non-supervenience or an enlarged substratum.
• Logarithm branches. A non-primary logarithm of CNOT leaves the uniform ray, but the choice is a free parameter.
  • The records already note this choice, at XS C11 and thread H:172.
  • What remains is a wording correction to AW-X5.

mc-node1/ (measurement as an added condition): NEW, narrow. Twelve formulations were checked.

• Native measurement adds no operation.
• TU is sharp Lüders tests in non-configuration token bases. With an ancilla, CNOT and native corrections, it makes the layer flow of X executable exactly: the channel is Ad R_x(−2φ) for every φ [EC].
  • This direction, from tests to the flow, is new to the F2 records. The gadget itself is standard [L].
• Measurement supplies no phase.
  • No OnesNormal primitive breaks the uniform ray. That includes generic unsharp Lüders instruments: the invariant holds exactly when 1 ∈ span{K_jᴴ1}.
  • Every projector lies in onesClass, so isometry_fixes_ones applies [W from AT].
  • So TU never gives Z, S or a deterministic |−⟩, while it does give |+i⟩. A replace-by-ψ channel passes exactly when ⟨1|ψ⟩ ≠ 0.
• TU ⊕ Z gives full control on 2^k registers. The single-token relations are [EC]; registers rest on Barenco [L]; reaching QM is [W].
• O-B is not sourced [W].
• Ledger correction. LEDGER.md §5 item 2 overreached in saying "any other non-operation resource" cannot help. It is now scoped to configuration-readout instruments, on the session branch at ccr-9c2ecca4-vkb666, with a CORRECTIONS entry.

Form the missing component must take, as now narrowed:

1. non-supervenient, or an enlarged substratum;
2. a primitive outside OnesNormal (phase-type);
3. an uncountable non-monomial family, for which a continuum of Lüders test bases suffices;
4. for O-B, the G3 identification plus multi-token compatibility clauses.

G6 (an independent prediction) is open.

Reproducibility. All probes and the reviewers' independent recomputations are in the tree with their outputs and SHA256SUMS. They were replayed byte-identical from the tree. Retention check (plain): HOLDS.

Next node (proposed): what physical principle stated in OI's own terms could supply item 2, the phase-type primitive, without positing it outright (E0). Candidates come from the corpus's time-reversal and predictive-memory structure and the open purification lift. They will be checked against the controls in PLAN.md.

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[amaybaum]

Correction to the checkpoint comment above (owner review, 2026-10-20). The record will be corrected forward in the next commit

The statement that measurement supplies no phase is too strong as written.

• An X-basis test on |0⟩ yields |−⟩ with probability 1/2, heralded.
• With kickback (CNOT from data into an ancilla holding |−⟩), that gives an exact Z on the heralded branch.

What mc-node1's argument covers is narrower: no finite protocol, taken as a total trace-preserving channel, realizes a deterministic Z, S or |−⟩. That covers ancillas, feedforward of native corrections, discard and coarse-graining. Heralded or postselected branches, and repeat-until-success, are outside that statement.

Node 1b is now scoping the no-go exactly: deterministic channels, heralded branches, repeat-until-success, and what the F2 endpoint requires. It also adds the owner's other qualifications:

• the continuum of measurement bases that TU uses is itself unsourced by OI;
• the one-sign completion is specific to Z;
• O-B stays open.

The same scoping will be applied to PLAN.md's status and to the F2 ledger's corrected §5 item 2. Both currently say "no operation that breaks the uniform ray", which will become "no deterministic, trace-preserving operation".

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[amaybaum]

Checkpoint 623426e9 (WIP / research only): node 1b, the scope of the phase no-go, independently reviewed. This supersedes the "no phase" wording of the earlier checkpoint

Three notions are kept apart. Each is checked exactly, and the independent review certifies the distinction:

• Heralded. An X-test on |0⟩ yields |−⟩ with probability 1/2. Kickback then gives an exact Z on the success branch: the branch is ½ZρZ. The instrument as a whole is OnesNormal; the branch alone is not, and InstAvail has no outcome-selection constructor.
• Almost surely terminating. Repeat-until-success stops with probability 1, after 2 attempts on average. It gives Ad Z exactly, but only as the limit of Φ_n = (1 − 2^−n) Ad Z + 2^−n id; the trace distance is 2^−n. BridgeFiniteProtocol.lean:6–7 gives finite-depth availability, and :9–10 leave the limit unestablished.
• Finite protocols. Finite InstAvail protocols built from OnesNormal primitives, generic unsharp Lüders instruments included, yield no deterministic ray-moving unitary channel and no deterministic |−⟩.

Invariants, each named separately:

• OnesNormal is not closed under channel limits. Every Φ_n is OnesNormal, which needs exactly 2^n Kraus operators at depth n; Ad Z is not.
• Nonnegativity of unitary conjugations (preservesNonneg_of_approx FrozenSourcing.lean:127, under its hypotheses) and ones-fixing of unitaries are limit-closed. Φ_n breaks nonnegativity from n = 2, which only non-native tests allow.
• Fixing the uniform state is not a barrier, because native readout does not satisfy it either.

Endpoint:

• A1 requires the deterministic one-outcome Ad Z (KrausSoundness.lean:134, typed_determined_iff).
• A rule admitting almost-surely terminating protocols would be a restricted limit closure. The adopted gates do not admit one without an owner ruling.
• Open question for step 2: whether TU meets the existing A2 endpoint (KrausDense, DenseFiniteQM). If it does, the phase gap exists only at A1. DenseUnitaryControl fails regardless, because ‖Z − cV‖ ≥ √2 for every ones-fixing V.

Also stated:

• The continuum of measurement bases is itself unsourced.
• The one-sign completion is shown for Z only.
• O-B stays open.

Updated with this checkpoint:

• PLAN.md's status and "form" bullets.
• oa-node1's R1 row: its earlier "the barrier invariants are closed under limits" is replaced by the scoped statement above.
• The F2 ledger's §5 item 2, in commit 3ecdefe9 on ccr-9c2ecca4-vkb666, with a CORRECTIONS entry.

Classification. Node 1b is ELABORATING, with one narrow NEW item: the non-closure of OnesNormal under limits. mc-node1 overall is NEW (narrow).

Reproducibility. The new probes are heralded, rus_limit and chan_solver, with 62 checks, and the reviewer's rev_1b has 19 PASS. All replayed byte-identical from this tree. Retention check: HOLDS.

Next (step 2): is there an operational-completion rule justified by OI itself, such as almost-sure termination of protocols the observer can run? It would have to supply the limiting phase without positing Z, source the continuum of measurement choices, keep the countercontrols, and address O-B. The A2 question above comes first, since it decides whether exactness is the only gap.

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[amaybaum]

Checkpoint 97f4a951 (WIP / research only): node 2, dense availability and operational completion as a candidate, independently reviewed

Operational completion is tested as a candidate. No completion or limit-closure rule and no physical principle is adopted, and G6 stays in force.

1. The A2 endpoint is met by three fixed test bases: NEW, narrow, [W].

• Sharp Lüders tests in X, Y and one real basis, together with the native class, meet DenseFiniteQM = KrausSoundExt ∧ KrausDense (DiscreteCompletion.lean:59, :52). Every finite Kraus instrument is approximated outcome by outcome, with outcome type exactly Fin m, in operator norm.
• This holds without DenseUnitaryControl and without DerivedOI. It is the converse of the kernel's sufficiency route (DenseInstrumentBridge.lean:437).
• Construction: exact deterministic exp(iφX_ab) gadgets, heralded phase outcomes, and depth-n repeat-until-success channels within 2^−n of Ad D_s. The generators span u(d), and irrational step angles give a dense group. An approximate Stinespring circuit is controlled by branch_within's constants.
• Evidence and gaps:
  • It is a written argument, with exact and numerical instances at level one only.
  • The reviewer's independent check: a three-outcome instrument on a d = 6 carrier gives per-outcome error 6·10⁻¹⁴ at n = 48.
  • Soundness and theory-hood of the extended theory are [W].
• Consequences:
  • The phase gap and the continuum of test bases are both A1-only.
  • At A2, G4's uniform-ray clause is not necessary: every one-outcome unitary of this dense theory fixes the uniform ray. That clause is an A1 requirement.
  • Heralded branches count as outcomes of an available family; renormalized postselected branches do not.
• What this does not do: it does not source the test bases, it does not address O-B, and A2 is defined only on the Fin 2 family.

2. Completion rules (ELABORATING). These are shown for the eight listed forms only.

• Word-type rules keep countable_not_pairFlowSourced and fixedGateTheory_not_qm, by a Kraus-word lemma whose countable alphabet includes ancilla embeddings. They supply the phase but not the continuum. The word-type rules are almost-sure termination, stopping-time rules, countable mixtures and state-independent postselection.
• Closure-type rules erase the fixed-gate control, so they are the dense endpoint relabelled. These are topological closure, convergent infinite compositions and basis-set closure.
• Almost-sure termination exceeds any fixed finite representative, as every A1-exact continuum does. The review corrected an earlier claim that this singled out repetition.

3. OI sources: none found for the test bases, completion or O-B. Purification with uniqueness would cover all three, but only as a posit (Main.md:602). G6 stays open.

Review verdicts:

• A2 claim: CONFIRMED as [W].
• Heralded outcomes: CONFIRMED.
• Word lemma: CONFIRMED, with the scope limited to the listed forms.
• Finite horizon: CORRECTED.
• No OI source: CONFIRMED as recorded.
• HA-N1's continuum half and HA-N3: CONFIRMING.

Reproducibility. The node's probes (a2_exact, a2_num, word_lemma) and the reviewer's (rev_exact2, rev_num2) were all replayed byte-identical from this tree. PLAN.md's status adds the node.

Where this leaves the question. At A2, the missing operation-side component is finitely many non-configuration test bases. At A1, it additionally needs a continuum and a deterministic phase, or a completion rule that the adopted gates bar without an owner ruling. O-B is untouched in either case. The open choice is the owner's: whether the F2 target stays A1, and if so, what could source the continuum, the phase and O-B.

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[amaybaum]

Checkpoint fb631a20 (WIP / research only, under A1): node 3, classical enlargement and the observer's choice of test, independently reviewed

The owner keeps F2 at A1, so this node asks whether OI can source the measurement continuum (a), a deterministic phase (b) or O-B (c).

Cone lemma ([W], with exact instances). It assumes:

• the pointwise hidden model;
• κ1, hidden states are distributions, in the mixed reading;
• κ2, processes are configuration bijections;
• κ3, the G3 identification;
• κ4, configuration readouts with feed-forward;
• measurable dynamics.

Then every available outcome map lies in the finitely generated, closed cone of nonnegative combinations of Ad_P, P a 0/1 partial permutation. That holds at any substratum cardinality, in discrete or continuous time, with any real couplings, and with observer settings of any origin. Consequences:

• NonnegBounded and OnesNormal hold;
• effects and reachable states are diagonal;
• level-one conjugations lie in six rays;
• so there is no (a), (b) or (c), and limits or almost-sure termination do not escape.

Exact checks:

• all 720 bijections of {0,1}×{0,1,2};
• feed-forward and nonuniform priors;
• a real coupling gives (1−θ)id + θ Ad X;
• a continuous circle flow reproduces sin²(πt/2) but only as a mixture: it lacks the coherence i·sin(πt)/2;
• setting-selected tests commute, so a free choice of test supplies no basis continuum.

Review findings, applied:

• The model is stated explicitly. A coherent (Koopman–von Neumann) reading of the hidden prior leaves the cone, though not NonnegBounded, so the mixed reading is load-bearing.
• Each dropped κ leaves the cone, but none reaches A1 alone. For non-classical candidates, the countable-realization premises stay load-bearing: fixedGateTheory_not_qm is the witness.
• The global antiunitary gives no deterministic phase; with the 24 pair permutations it generates 48 elements, all permutation-type.
• The reconstruction principles (purification, continuous reversibility, local tomography plus the subspace axiom) each need a non-classical primitive.

Classification: ELABORATING. The finite case is already in the kernel (obsTheory_eq_permTheory, LiftSource T2/T3). One NEW (narrow) item: the classical-enlargement escape in the countable-realization conclusion is empty. G6: none.

PLAN.md's form clause is revised, conjunctively per §A.34. The missing component must contain a primitive of non-classical kind (κ1 read as mixed priors, κ2, or κ4 dropped; κ3 is barred by G3), and, for (a) at A1, it must be non-supervenient or rest on an infinite substratum of non-classical kind. Enlarging a classical substratum's size or time model adds nothing.

Reproducibility. The node's probe enlarge and the reviewer's rev_mc3 were replayed byte-identical from this tree. Text checks: OK.

Where this leaves A1:

• The operation side needs a non-classical primitive, either a coherent hidden state or a non-configuration process or test, together with non-supervenience, for the continuum.
• The phase needs a primitive outside OnesNormal.
• O-B needs the G3 identification plus multi-token clauses.
• No OI posit or derivation found so far supplies any of these, and no independent prediction has appeared.

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[amaybaum]

Checkpoint (WIP, UNREVIEWED): node 4, coherent hidden prior, head faf38442. This is research only. F2 stays A1, and G6 stays in force.

mc-node4/ adds NODE.md and two exact probes: a Gaussian-rational enumeration (52 PASS) and a SymPy check (14 PASS). Each was run twice with byte-identical output, and both replayed identically before the push. PLAN.md's status and form clause are not updated; that waits for the independent review, which is in progress.

The node's claims, pending review:

• Transport lemma [W; EC]: with bijective dynamics, the G3 identification and configuration readouts kept, every Kraus operator under a coherent hidden prior is monomial. So a coherent prior alone gives no non-monomial unitary at any cardinality. O-A then fails by monomiality, not by countability.
• Statistical-equivalence corollary: native protocols give the same law under a coherent prior h as under the mixed prior |h|². No native prediction is possible, so G6 is not met.
• Relocation [W]: a continuum eigenfunction under real-coupled controlled flows, with Lüders tests in two fixed bases (X and Y), carries both A1 increments. The costs are:
  • it still needs non-configuration tests;
  • it needs a coherently coupled continuum, which E3 as read in Substratum.md:92 bars;
  • it gives up CR's P1 and P2;
  • the phase field is posited, which fails G2 as a disguised reference-frame resource.
• Purification does not derive a coherent prior.
• Proposed classification: NEW (narrow), with an ELABORATING core.

Not verified:

• The transport lemma and its continuum form are written arguments, not formalized.
• The enumeration covers |C| = 2 with |X| ≤ 4.
• M*'s A1 conclusion rests on a written argument plus the literature [W]+[L].

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[amaybaum]

Checkpoint, b0481e08: node 4 (coherent hidden prior) independently reviewed, outcome applied. This is research only; F2 stays A1 and G6 is still open.

Review. The review of faf38442 returned ACCEPT WITH NOTES. A focused re-check of the corrections asked only for small wording changes, which are applied here.

• Confirmed (core results):
  • the transport lemma;
  • the monomial no-go under κ2–κ4 at any cardinality or time model;
  • native protocols give the same law under a coherent prior h as under the mixed prior |h|². This holds for the whole generated protocol class, not only the enumerated cases.
• Corrected:
  • Uniform weight. Zero uniform weight of the prior is necessary, not sufficient for a deterministic phase. A counterexample is (2, −1, −1). A pair of coordinates with equal modulus and distinct phase is also necessary. An eigen-relation h∘σ⁻¹ = λh with λ ≠ 1 is sufficient, by a single controlled step [W].
  • M*. It needs one fixed non-configuration basis, not two.
  • Classification. Lowered to ELABORATING, or BORDERLINE at most for the relocation. Literature [L] is added for dephasing covariance and catalytic coherence; the bibliographic data were confirmed, but the full texts were not read.
  • S3. It is now computed from ψ, with a countercontrol that can fail: 15 PASS, replayed byte-identical. The reviewer's scripts and outputs are kept under mc-node4/probe/review/.
• Wording. The P1 route for countably infinite X, the ℓ¹ and nonsingularity hypotheses, scoping, and pinned refs.

PLAN.md gains the node-4 status bullet and corrected form clauses:

• dropping κ1 alone gives only monomial channels, so for (a) a coherent prior has to be paired with κ2 or κ4 dropped;
• a coherent prior with an eigen-relation is one example of a primitive outside OnesNormal;
• any G6 that distinguishes a coherent prior from the mixed prior must use non-native tests.

What node 4 contributes to the thread's goal. It does not derive the missing capability. It sharpens which additional postulate would be needed: a coherently coupled continuum hidden mode with a posited phase field. That postulate is barred by E3 as read in Substratum.md:92, and it fails G2.

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[amaybaum]

Owner direction for node 5 (2026-10-20). Node 5 is research only. It has four requirements:

• Minimal postulate. Find the weakest additional assumption that could provide both O-A and O-B, keeping what is necessary separate from what is sufficient.
• Compatibility. Decide whether that postulate can coexist with OI's existing foundations or requires changing them, without silently redefining the theory. Node 4's conflict with the boundary-layer interpretation is a substantive theoretical issue.
• Independent prediction (G6). Find a falsifiable prediction that distinguishes the extended framework from standard QM; reproducing a known QM result does not qualify. If the extension reproduces QM exactly throughout its domain, it cannot be distinguished there, so any such prediction needs additional structure or a regime where the two theories differ.
• Negative results permitted. "No acceptable single postulate" and "no distinguishing prediction" are acceptable conclusions.

Strategic question. Can the missing ingredient emerge from OI, or must it be added as an independent principle, or is it incompatible with the current framework? Answering that matters more than a positive theorem.

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[amaybaum]

Checkpoint (WIP, UNREVIEWED): node 5, the additional postulate, head 35807352. This is research only. PLAN.md is not updated; that waits until the independent review, now in progress, has been applied. The probe gives 37 PASS (exact) and replayed byte-identical.

The node's claims, pending review:

• No acceptable single postulate was found.
  • The O-A content is fixed by the kernel's characterization (sourcedOI_qm_iff_phaseFree, SubstratumInterfaceAudit.lean:654): exact QM holds iff SourcedOI and phase-free richness (PFR) both hold. PFR is GR's controllability resource.
  • Both minimal contents are gate-excluded when stated as premises: PFR fails E0, and X-4 is a bare transfer clause.
• At the level of primitives, four clauses are each necessary, with a drop-one countermodel for each:
  • an uncountable alphabet;
  • a non-monomial primitive;
  • a primitive outside OnesNormal;
  • a primitive with no real Kraus form.
    Joint sufficiency is open. The node also finds that PLAN's current form clauses are jointly met by a theory that is not QM, and that PLAN omits the reality clause.
• Proposed headline: (iii), incompatible with OI as currently stated, scoped to the constructions examined.
  • The clauses need either a non-classical realizer, which conflicts with Lemma 3's classical bijective form, or a non-supervenient primitive.
  • A per-realization continuum conflicts with Lemma 1 and with E3.
  • The ingredient becomes (ii), an added principle compatible with OI, only after an explicit change of the substratum class, along the lines GR.md:260–264 describes.
• G6: none found. On its domain the postulate reproduces finite QM, and its exact-QM increment cannot be seen at any finite precision. Every regime examined either has an adjustable scale (rejected under §A.29), is already contradicted by laboratory gates, or reproduces a known QM result.
• Proposed classification: ELABORATING, with two BORDERLINE items.

The review specifically checks whether "incompatible" is supported, or only "not derivable from the listed constructions", and whether (ii) is the more honest headline.

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[amaybaum]

Checkpoint 0b60a8ec: node 5 (the additional postulate) independently reviewed, outcome applied. Research only; no premise adopted.

The review of 35807352 returned ACCEPT WITH NOTES, and the headline changed.

Confirmed:

• Kernel characterization. Relative to SourcedOI, exact QM holds iff phase-free richness holds. QM implies phase-free richness outright, so every A1 extension entails it.
• Primitive clauses. Four primitive-level clauses are each necessary and are irredundant: uncountable alphabet, non-monomial, outside OnesNormal, no real Kraus form. Joint sufficiency is not shown.
• Probe and countermodels. The probe gives 37 PASS. The reviewer's independent checks give 8 PASS, kept under probe/review/.
• No distinguishing prediction.

Corrected:

• Headline. (iii), incompatibility with the framework, is not established. As an operational hypothesis on the implementation architecture, the ingredient is (ii): GR.md:260–264 already states it as a hypothesis on the extended architecture, and already relaxes κ2 for the phases. What the thread establishes is narrower:
  • no construction examined realizes the non-monomial clause while keeping both configuration-bijection processes (κ2) and supervenience;
  • the reality and OnesNormal clauses are met by monomial phases, which are already in the kernel's substratum class.
• Boundary layer. The conflict is not general.
  • E3 bars a boundary that keeps κ2, and it bars an infinite-dimensional coherent sector.
  • For a finite non-classical boundary, the obstruction is countability via Lemma 1, not E3.
  • This is recorded as a scoped G4 conditional, not a verdict.
• G6. A distinguishing prediction can only come from the source or from outside the domain. QM itself satisfies the non-monomial and reality clauses.
• Minimality. "Weakest" means logical strength only. Sufficiency of phase-free richness needs the extended theory itself to satisfy SourcedOI.
• O-B. O-B's weakest content is X-4. The scope of AW-F1 is restored.
• Classification. ELABORATING throughout.

PLAN.md gains the node-5 status bullet. Its form clauses are restated at theory level, primitive level (U, M, O, R), realization, O-B and G6.

Answer to the owner's strategic question, at the reviewed scope:

• The ingredient does not emerge from OI, for the constructions examined.
• At the operational level it is an added principle, as GR states.
• Realizing it needs κ2 dropped or a non-supervenient primitive. At A1 there is also a countability tension with Lemma 1.
• No distinguishing prediction was found.

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[amaybaum]

Owner direction (2026-10-20): guiding principle and the A2 track. Recorded in PLAN.md at 649027c9.

Quantum mechanics describes what observers can access, not necessarily everything that exists. Observational incompleteness may be the mechanism that makes a deeper reality appear quantum. Our goal is to derive that appearance, including its experimental predictions, without assuming quantum mechanics at the fundamental level.

• A1 stays a strict benchmark. It records what a construction cannot reproduce exactly. Failing it is not the same as failing to explain experimentally accessible quantum behaviour.

• The explanatory challenge stays in force at every precision. Interference, complex phases, statistics, entanglement and correlations must be reproduced in their measurable consequences.

• Negative results are scoped. The A1 results concern the classical bijective substratum with its present operational rules. They do not establish that observational incompleteness as such is incompatible with quantum behaviour.

  • The owner checked node 5 at 35807352, before review. The reviewed version (0b60a8ec) already withdrew "incompatible with the framework". PLAN now states this scope explicitly.

• A2 track, opened as node 6 (research only). It asks whether observational limitations can make a deeper non-quantum reality look quantum to arbitrary accessible precision, and what the deeper reality and the incompleteness would need for that. The planned branches:

  • (B1) whether operational availability is even the right observable for the quantum appearance, or whether description-level structure is;
  • (B2) what the Bell, Kochen–Specker, preparation-contextuality and PBR no-go theorems require of any deeper-reality account, and whether OI's substratum meets that;
  • (B3) what epistemically restricted classical theories reproduce, with a CHSH probe under OI's actual readout;
  • (B4) a non-adjustable finite-resolution prediction.

  Node 6 also re-reads node 5's headline under the principle.

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[amaybaum]

Checkpoint (WIP, unreviewed): node 6, the first A2 node, at head c2991007. This is research only. PLAN.md is not updated; that waits for the independent review now in progress. The probe gives 19 PASS and replays byte-identical; one floating-point comparison is used, and it is labelled.

Node claims, pending review:

• Classification: undetermined. Observational incompleteness already makes a non-quantum reality's records agree with QM to any accessible precision. It does this only as Reproduction: the quantum structure is coded into the hidden sector. No Emergence of quantum statistics was found. The decisive open question is the corpus's own selection problem (Main:578): what fixes the strength of quantum correlations at exactly the quantum values.

• Hidden assumption in the thread's framing. There are three readings of "looks quantum":

  • R0: record laws can be represented by QM. This is too weak; PR boxes pass.
  • R1: record statistics under one realization agree with QM.
  • R2: operations are available.

  The cone lemma and node 5's M/R clauses are R2 statements. A toy bit that stays inside the classical cone still reproduces the qubit's sequential Pauli statistics on all 234 protocols tested.

• Features necessary for Emergence at R1. These are not shown to be jointly sufficient.

  1. Preparation contextuality: a hidden record that no accessible measurement reads back.
  2. For Bell violations, a relaxed structure that is not affine. Affine remote dependence stays at |S| = 2.
  3. Something that fixes the magnitude. Every mechanism found spans the whole range from the classical value to the maximum, set by a free weight, and nothing examined selects the quantum value.
  4. Hidden capacity that grows without bound with precision.

• No-go theorems, with their exact assumptions. OI's induced model fits the ontological-models framework. It can relax measurement or parameter independence, preparation or measurement noncontextuality, or preparation independence. None of these alone makes the substratum quantum, and none selects the quantum magnitude.

• G6: none.

• Node 5 re-read. Several node-5 sentences state at "empirical" scope what was shown only for operational availability (R2).

• Proposed next node: test whether OI's own selection principles fix the free weight at the quantum values. The preregistered rule is pass only if the principles exclude the PR and gbit values, permit the quantum values and keep every classical model.

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Generated by Claude Code

[amaybaum]

Owner direction (2026-10-20): node 7 authorized, conditional on node 6's independent review being accepted. Research only.

Central question: can the limitations of observation themselves select the laws of quantum mechanics?

Strengthened success criterion for node 7. Rejecting PR boxes while allowing QM is not enough, because many post-quantum correlations lie between the quantum limit and the PR-box limit. Node 7 must investigate whether OI's principles derive the quantum correlation boundary with no freely adjustable parameter. For CHSH, it must explain why quantum correlations satisfy Tsirelson's bound |S| ≤ 2√2, not merely exclude the PR-box value S = 4.

It must also establish both of the following:

• the relevant quantum correlations are achievable;
• classical correlations remain permitted.

Meeting this is a necessary milestone, not a complete derivation of QM.

Constraint on the selection rule. It must follow from OI's observational principles. It must not be chosen to reproduce the desired quantum answer. The rule is preregistered before any computation (§A.29). Negative results are acceptable.

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Generated by Claude Code

[amaybaum]

Checkpoint 8fb6a5ec: node 6 independently reviewed and the review outcome applied. Research only.

The review of c2991007 returned ACCEPT WITH NOTES. The core holds: the classification is undetermined, the node is ELABORATING, no Emergence was found, and the probe's controls fail when broken.

Corrections applied:

• N1, preparation contextuality. It holds only given exact operational equivalence. Agreement within ε does not supply that equivalence: a reviewer check shows that a biased parity readout makes the model preparation noncontextual while the POM success is unchanged. A version of N1 at finite precision needs a robust noncontextuality inequality, which was not applied.
• Contextuality from destructive complementary readouts. It comes from a posited restriction, exactly as the toy bit's does. It is not Emergence.
• R1(d, m, K, ε) is now defined. The corpus's Reproduction result (Main:576–578) is a paper theorem with probe checks, not kernel-certified. It holds per (d, m, K, ε), with a composite treated as one system; local composite structure stays open (Main:534, :578). The selection problem is cited at Main:580 and in book appendix-c:228/:234, and is stated as related to this node's question, not identical to it.
• Kochen–Specker constrains R1 through hidden memory that earlier measurements update (N5).
• N2 is scoped to the parameter-dependence branch.
• Vacuous checks were fixed. The reviewer's checks are kept under probe/review/.

Other changes in 8fb6a5ec:

• PLAN.md gains the node-6 status bullet and the revised A2-track paragraph, which states the track at the level of record statistics.
• mc-node5's "what is empirically at stake" paragraph is scoped to operational availability.

Node 7 is authorized per the owner, conditional on node 6's review, which is now accepted and applied. It runs in two steps:

1. Its preregistration is written first and published to this branch before any computation. The preregistration holds the candidate principles quoted from the corpus with their formalizations, every parameter and how OI's own structure fixes it, ε, the architecture class, the decision rule, and the controls.
2. Only then does node 7 compute.

The decision rule adopts the owner's criterion: derive the quantum boundary (|S| ≤ 2√2) with no tuned parameter, exclude every post-quantum value, admit the quantum values, and admit every classical model.

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Generated by Claude Code

[amaybaum]

Owner requirements for node 7's preregistration (2026-10-20). These are included before the preregistration is frozen.

1. Preserve OI's original ontology.

   • The visible and hidden sectors are partitions of the same underlying substratum, under the same fundamental dynamics. Quantum behaviour must arise from the observer's limited access to it, not from quantum rules inserted into the hidden sector.
   • This is a frozen admissibility condition, with its own checkpoint.
   • Any candidate that assumes Born probabilities, quantum instruments or a tuned correlation strength is classified as Reproduction, not Emergence, unless those ingredients are independently derived.

2. CHSH benchmark versus full quantum selection. Deriving |S| ≤ 2√2 would be a major milestone, but CHSH alone does not characterize the quantum correlation set. Node 7 reports two outcomes separately:

   • (a) the correct CHSH boundary;
   • (b) a more general exclusion of post-quantum correlations, tested on correlations that satisfy Tsirelson's bound but are still post-quantum.

   A pass on (a) is not reported as (b).

Objective: derive why observational limits applied to a single underlying reality produce precisely quantum behaviour, rather than making it one of many possible outcomes. A rigorous negative result that identifies exactly which OI principle is insufficient is also valuable.

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Generated by Claude Code

[amaybaum]

Checkpoint 1907963e: independent review of the native instrument, its corrections, and the programme integration record. For focused review before it is treated as authoritative.

1. The native instrument (455eb092), independently reviewed. The reviewer is outside the work's author; the coordinator's session wrote 455eb092. Verdict: accept with corrections (mc-node9/design/native-instrument/review/REVIEW.md).

• Confirmed with the reviewer's own code, which does not import the author's checker:
  • acceptance 625/4096 for all eight preparations;
  • the exact product law;
  • transport at tick 2 under the actual report18 rule, on independent lattices and seeds;
  • the identities on every single-read and two-read record;
  • Born values and closure, which a density-matrix computation also confirms;
  • Q6(a) TV 95155025/2³⁰;
  • the controls, none of them vacuous.
• Corrected and applied:
  • Degree: 12 is this threshold sampler's degree. Any exact sampler needs degree ≥ 2, and lower-degree flags suffice, for example 1 ⊕ x₀x₁ ⊕ x₂x₃ per component.
  • Native scope: only the single read's transport and re-preparation at tick 2 are native. The rest is register-level or supplied.
  • Q5 count: 1024 runs = 512 input assignments × 2 backgrounds.
  • Q6(c) layout: it holds for this layout. With the rows permuted, R fails (TV ≈ 0.298) and Z becomes the invisible case.
  • Checker: it now generates the Q6(a)/(b) verdict text from measured values, and tests Q6(b) closure by a per-setting conditional-law comparison. The regenerated output changes only those lines, and normal and -O runs are identical.
  • Preregistration order: that the preregistration preceded the code rests on its recorded timestamp, because it was first committed together with the code.
• Review files: the reviewer's scripts replay to their saved outputs, except one line of indep_degree_qm.out that its script does not print. coordinator_weight20.py reproduces that value (524,800 = 2⁹·1025).

2. INTEGRATION.md, the programme index. It records:

• the division of work with WIP: native nonlinear processing and second-front source audit #910;

• the acceptance rule;

• each checkpoint since 455eb092, by bundle sha256 or commit:

  Checkpoint	Identifier
  Selector	3d18fe9c
  Native selector	c204e6f6
  Read-reset	15af0674
  Native X	529185bb, with external review 2a51fe2a
  Combined	88f80567
  Native-Y continuation	977e8e33
  WIP: native nonlinear processing and second-front source audit #910 head	1c8c9e5e

• each checkpoint's review level, independent, internal or external;

• what remains supplied;

• six open obligations, the transport-theorem proof review first.

PLAN.md's Status points to it.

Checks: Python compilation; a sensitive-data scan of the added lines; legacy_records_check at 1907963e (303 records intact); artifact_placement_check OK. No push-triggered workflow matches these paths.

No premise is adopted and no certification status changes.

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Generated by Claude Code

[amaybaum]

Checkpoint 2d555f17: INTEGRATION.md reviewed through three passes. The final narrow check accepts.

The reviews:

1. Focused review of 1907963e: accept with corrections. One finding was blocking (B1): the open Y obligation spoke of a "two-site" encoding that no source states. The corrections are in 0be12721, and the review is retained as integration-reviews/INTEGRATION-REVIEW-1907963e.md.

2. Re-review of 0be12721: changes needed. One finding was blocking (B1′): that fix placed the native-X encoding E on the Y reset's output. In the sources, E is the Y stage's starting carrier, and the Y reset's carrier must decode to (X, Y, R, Z) = (y ⊕ a, y, y ⊕ b, z), with (a, b) = 00, 10, 11 in the ratio 5:3:2 and z fresh and fair. The correction is in 2d555f17, together with four accuracy points:

   • the 7/30 bound holds for input-independent permutations;
   • the native readout reads the "selected sign";
   • the staged-disclosure contract is abstract;
   • the native-instrument README now says what was committed alongside the code.

   This review is retained as integration-reviews/INTEGRATION-REVIEW-0be12721.md.

3. Narrow check of 2d555f17: accept, no blocking findings.

   • B1′ is resolved. The definitions a = X_new ⊕ y and b = R_new ⊕ y agree with the composition report, the combined handoff's START-HERE and the calibration README.
   • Obligation 2, which fixes the decoded law, does not conflict with obligation 3, which requires the native encoding.
   • The other edits match their sources.
   • The checksum files verify, and the diff touches exactly the five expected paths.

Known gaps, acceptable for this draft:

• The retained review reports cite reviewer code that is not in the tree. This must be resolved under §A.42 before anything lands.
• WIP: native nonlinear processing and second-front source audit #910 is cited at its 1c8c9e5e checkpoint; it has since moved to 8daae9f6.

No premise is adopted and no certification status changes.

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Generated by Claude Code

[amaybaum]

Checkpoint 3a8a3188e08d60bc54e4e624b34ad213e77989f5: integration-record amendment, owner-authorized 2026-10-24. Documentation and provenance only. An independent review of this exact commit is in progress. Until it accepts, 2d555f17 remains the accepted synthesis.

• Retained review: integration-reviews/INTEGRATION-REVIEW-2d555f17.md holds the narrow ACCEPT review of 0be12721..2d555f17, byte for byte (sha256 c9f1d9a2d8186d02a8ee5ce985cff2c5113fe68a4e66146e263aac7484654bcc, the full expected digest). SHA256SUMS verifies 6/6.
• Provenance audit (EVIDENCE-RETENTION.md): for each checkpoint, what its review relied on and whether that material is held in this repository.
  • The native-instrument review is reproducible here.
  • The selector-record, native-selector and read-reset reviews are report only. Their author bundles, reviewer code, mutants and outputs are not in the repository.
  • The native-X external review and the coordinating session's two replays are also report only.
  • The original reports and their verdicts are unchanged.
• INTEGRATION.md:
  • An Evidence column has been added.
  • The 7/30 finding is attributed to READ-RESET-REVIEW.md (E1–E3).
  • The replay statements are attributed to the coordinating session, with their outputs not retained.
  • WIP: native nonlinear processing and second-front source audit #910 is cited at its reviewed snapshot 00e85e748cf8e5ada75f4e1a22aef87eb0a823a2 rather than its active head, with reviews 1c8c9e5e, bf165400 and 5f6786d6 and author commits 8daae9f6, 6db981c1 and 49a391b9.
    • The junction obstruction stands.
    • The six-source endpoint is not a clean Y transfer.
    • A corrected q7 readout gives (0,0,y). It is not a socket and not a reset.
  • A post-Y phase row has been added (author 9b334367, review 8247de45, reconciled 71d29129), with a pointer from obligation 2. The reusable native Y reset and the full public-history and carrier joint law remain open.
• Checks before the push:
  • The diff is exactly four paths.
  • The question, acceptance rule and supplied-ingredients sections are unchanged.
  • No code or data file was touched.
  • The added lines contain no sensitive data.
  • The branch was fetch-checked at 2d555f17 and pushed as a fast-forward.
• Gate 1 (retaining the reviewer code) is not closed by this commit. Two resolutions remain open:
  • recover and verify the original material;
  • re-derive the affected checks under a new, separately dated trail.
• Note for WIP: native nonlinear processing and second-front source audit #910's writer: WIP: native nonlinear processing and second-front source audit #910's CURRENT-HANDOFF.md pins Research (WIP): the missing component for F2-reg, and measurement as an added condition #885 at 2d555f17. Updating that cross-reference is WIP: native nonlinear processing and second-front source audit #910's to do.

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Generated by Claude Code

[amaybaum]

The independent review of the integration-record amendment is complete. The final head cddcd3f5eece6d6c29dcab05fccc55027be70d86 is accepted.

• 3a8a3188: REVISE, with two blocking findings.
  • B1: the q7 row dropped its review's conditional scope.
  • B2: "report only" was used for rows whose report is not held either.
• 222f7973: applied B1, B2 and the notes. Re-review: REVISE, one finding (R1). EVIDENCE-RETENTION.md said "two statuses" while listing three, and used an undefined label for WIP: native nonlinear processing and second-front source audit #910.
• cddcd3f5: applied R1. Narrow check: ACCEPT, nothing remaining. Both files define the same four statuses (reproducible here, report only, not retained (cited only), on WIP: native nonlinear processing and second-front source audit #910), and every row uses one of them.
• Verified across the chain:
  • the diff touches only the four intended paths;
  • the question, acceptance rule, supplied ingredients and responsibility sections are byte-identical to 2d555f17;
  • integration-reviews/SHA256SUMS verifies 6/6, and the native-instrument checksums 6/6 and 14/14;
  • the "not held" claims were checked against every branch's blobs by sha256 prefix and against every filename in the history;
  • all 12 WIP: native nonlinear processing and second-front source audit #910 SHAs resolve and are ancestors of 00e85e74, which is WIP: native nonlinear processing and second-front source audit #910's latest commit that retains a review;
  • the WIP: native nonlinear processing and second-front source audit #910 statements match its files at that commit, and the cited review checkers replay byte-identical;
  • no sensitive data was found.
• CI: PR runs for 3a8a3188, 222f7973 and cddcd3f5 are queued behind a GitHub Actions backlog.
• Status: 2d555f17 remains the accepted synthesis until the owner decides on cddcd3f5. Gate 1 (the missing reviewer code) stays open.

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Generated by Claude Code

[amaybaum]

Accepted synthesis: cddcd3f5eece6d6c29dcab05fccc55027be70d86.

The owner approved designating this commit as the accepted integration-record synthesis, conditional on green exact-head CI. That condition is met:

• verify run 40093886297, head_sha cddcd3f5…, attempt 1: completed / success.
• 25 check runs on the commit: 24 success, 1 skipped (Numerical probes / A42 exclusion (${{ matrix.part }}), the same skip as on 222f7973 and 3a8a3188).
• The independent review chain of the amendment ended in ACCEPT at this commit.

This is a pull-request CI run, not a §A.39 exact-head attestation. It designates no round F or E.

Next, as authorized: one commit, 101f0515, that retains the final review (integration-reviews/INTEGRATION-REVIEW-cddcd3f5.md) byte for byte. It gets its own focused verification. Nothing else is pushed.

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Generated by Claude Code

[amaybaum]

CI red on 101f0515: Mathlib bridge release gate fails at step duplicate. This failure comes from this PR.

• Run 40098158069, job 120884649072.
• The release gate gives FAILED -> duplicate. Every other gate step passes, with the same messages as on cddcd3f5.
• Cause: tools/duplicate_check.py flags a heading repeated within one .md file:
  DUP-HEADING …/integration-reviews/INTEGRATION-REVIEW-cddcd3f5.md x2 at lines 94, 138 — ### Blocking.
  101f0515 added that file as a byte-for-byte retained review, and the review uses that subheading in two of its sections, C and D.

Proposed fix, prepared locally and not pushed: e6744a60, a single-parent child of 101f0515.

• It renames the file to INTEGRATION-REVIEW-cddcd3f5.md.txt, which takes it out of the check's .md scope. The review's bytes are not edited.
• The content and sha256 1edc5b90… are unchanged. SHA256SUMS names the new file and verifies 7/7.
• Run locally on that tree: duplicate_check, voice_check, claims_check and artifact_placement_check all report OK.

Pushing it waits for the owner's authorization. No re-run was made.

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Generated by Claude Code

[amaybaum]

Closing without merging, by owner decision (§A.43 item 6).

This PR has done its job. It identified what is still missing for OI to reproduce quantum mechanics, and it set the agenda now pursued in #910, #911 and #912. Auditing its 675 files against §A.42 so that they could land on main would not advance the physics. The PR is therefore kept as a research record and is not merged.

• Final commit: fd18205b47649ff4bd43857b908f6f646941e89f.
  • PR CI run 40099540760 passed: 24 jobs successful, 1 skipped as expected.
  • Its structured-evidence diff was independently reviewed and accepted.
• Accepted synthesis: cddcd3f5eece6d6c29dcab05fccc55027be70d86 (comment 6384775458).
• Open obligations and evidence limitations: carried in OI ↔ QM equivalence: proof gate (dependency index; carries #885) #914, which links this SHA and the three continuing PRs.
• Release-gate gap (support versus provenance citations, §A.42 items 1–3): recorded in Release gate: check that cited commits offered as support are reachable from main (§A.42 items 1–3) #915, with nothing built.
• The branch research/missing-component-20261020 is kept without deletion or rewriting. Nothing in this PR is adopted on main.

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