[amaybaum]

Working-conjecture revision; no new theorem or physical postulate. This draft applies OI's existing Deutschian truth-seeking/hard-to-vary principle to the recursive sub-state findings, rather than treating them as disconnected experimental notes.

Current head: 027ec21a7d0067eec3d0f3d2749952c4c1a11286.
Base D: main at f6989a27815c4d715223eebf2859422c1231e3f8.
Related active evidence (unmerged): issue #1007 / draft PR #1009 (continuous carriers), issue #1010 / draft PR #1011 (recursive carriers and native congruence no-backflow), draft #1003 (gauge-action non-uniqueness).

Intended OI correction in interpretation

• The finite-observer premise is not a theorem that the total hidden substratum is finite. Keep all actual finite-carrier results conditional on their unchanged finite assumptions.
• Treat recursively structured internal carriers and fixed cross-scale dynamics as a serious rival working physical conjecture, not an already-selected ontology or theorem of quantum emergence.
• Incorporate the negative result: simple 2-adic refinement of OI's unchanged integer-linear cubic wave cannot influence fixed low-digit readouts. Reject this shortcut instead of tuning hidden sub-states to rescue claims.
• Make physical adoption hard to vary: require source of physical cross-scale rule and observer interface, reproducible independent discriminant beyond classical three-time memory, gauge action and quantum instrument source gates, finite boundary entropy, and a prediction not used in the construction.
• Preserve F2 quantum operational completion and Wilson-versus-squared YM action selection as OPEN.

Changes

• Root README: targeted correction of the false impression that the OI programme's whole physical carrier is already established finite; brief link to the conjectural carrier and negative constraints.
• verification/programmes/substratum/DEUTSCHIAN-CARRIER-REVISION.md: explicit working-explanation update, status and rejection criteria, exact evidence links and promotion gates.
• verification/ROADMAP.md: one interpretation-boundary paragraph linking the revised working conjecture and its rejection conditions, without changing any queue status or theorem.
• No paper/book/manuscript body, theorem statement, Lean module, archived receipt, CI workflow or release artifact modifications.

This is deliberate project-facing adoption of an explanatory conjecture, not promotion of unreviewed mathematical research to a physically established fact. Manuscript A1 and finite recurrence arguments remain unchanged pending a genuine falsifiable payoff and separately governed corpus propagation.

Governance: draft for independent scientific review and exact-head ordinary CI. No merge/F/E, no special workflow dispatch.

Exact-head author checkpoint

• SHA 6a2b4fd51f7615269104449fe7e2497ddc57f0d0; exact PR diff consists of three files: root README, verification/ROADMAP.md, and verification/programmes/substratum/DEUTSCHIAN-CARRIER-REVISION.md. No manuscript body, frozen proof or physical axiom was changed.
• The project overview now explicitly distinguishes finite observation from finite total substratum (which remains a physical posit in the existing finite-model branch). The roadmap classifies recursive internal states as an active rival working conjecture, not a theorem or sourced physical law.
• The candidate is constrained by the negative 2-adic lift finding: simply allowing finer digits in the unchanged native scalar wave law does not feed new information into fixed low-digit readouts. A working replacement requires actual reversible scale mixing, observer access, an independent falsifiable prediction, the operational QM F2 source gate and YM action selection with independent controls.
• CI: automatic PR run 41067299475 was queued when checked; no exact-head green, independent reviewer verdict or merge attestation. This PR updates the working interpretation only. A1 in Substratum and related manuscript claims remain unchanged until a separate, properly reviewed and corpus-propagated evidence-based revision is warranted.

Cardinality-neutral foundation — precise current change

The project-facing working interpretation now does not assume the actual microscopic state space is finite. It distinguishes:

1. finite visible distinguishability at a specified resolution, conditional on the observer's finite-capacity/boundary premise (mere embeddedness by itself does not force finiteness);
2. finite record alphabets and finite-horizon reversible representatives under the existing S⇔D⇔Qfb theorem; and
3. the finite-total-substratum A1 physical posit required only in already established finite-carrier reconstruction/recurrence branches, not entailed by (1) or (2).

Strict mathematical counterexample: the fixed-skew infinite Cantor tape model from SUBSTATE-2 #1011 has an uncountable carrier, reversible measure-preserving dynamics, only four visible outcome labels, hidden-to-visible coupling and positive three-time conditional memory. Finite observation, reversibility and hidden readback do not logically entail a finite total S. This does not demonstrate that actual physical nature is infinite; every finite observed horizon still has a finite reversible representative.

Concrete publication wording defect found (not silently edited here): Main §1.2 attaches “(Lemma 1)” to the phrase “finite S”, while its own Lemma 1 only establishes finite visible configuration. Explainer similarly slides from visible finiteness to total configuration finiteness in its recurrence explanation. DEUTSCHIAN-CARRIER-REVISION.md records the exact defects and the requirement for a separate minimal manuscript correction, affected mirrors/artifacts, and independent review. The defect is independent of whether the infinite-carrier physical hypothesis survives.

Hard-to-vary gate unchanged: no ontic cardinality is adopted by fiat. New measurable-carrier physical candidates must source a measure, fixed reversible scale coupling and observer interface and deliver an independently constraining prediction beyond classical memory, while preserving finite-branch theorems and separately testing F2 quantum operational sourcing, Yang–Mills dynamics and boundary entropy.

Governance: all work remains a research/draft working-interpretation change; no A1 rewrite, physics proof promotion or manuscript body modified. Exact-head CI queued at this checkpoint; no independent scientific review or merge.

Separate defect correction tracked: issue #1013 audits the false inference in Main/Explainer and their mirrors; no manuscript was modified in this working-conjecture PR.

Cardinality as observer-relative gauge — current decision

The revised project-facing stance accepts the scoped OI insight that total-state cardinality is not an observable invariant of a specified operational equivalence class, not the stronger claim that all finite/infinite substrata are indistinguishable.

Positive exact argument: any finite reversible model (S,T,μ,π) can be enlarged by an independent normalized hidden fibre D of arbitrary size, using (S×D,T×id,μ×ν,π∘pr_S), without changing even its full all-time passive record laws. Lifted preparations and operations that never access D preserve their own public records. This is an equivalence of differently sized presentations, not a literal gauge bijection on one unchanged space.

Negative exact argument: an infinite Bernoulli shift can have iid visible bits with P(O_L=O_0)=1/2 for every positive L, whereas every fixed finite permutation has some common return L with P(O_L=O_0)=1. Thus unrestricted full-time record equivalence does not identify all finite and infinite carriers; finite-horizon dilation does not give one fixed finite all-time representative.

Existing OI authority: [GR §3.2] already labels deep-sector cardinality is gauge only to O(τ_S/τ_B) under its boundary/slow-backreaction hypotheses; [Substratum §4, Theorem 24(iii)] proves exact channel invariance for independently prepared finite decoupled ancillas. The finite Lean OIBridge.PassiveQuotient has exact hidden-extension and canonical passive quotient results, explicitly distinguishing observer-relative Level G4 from substratum G3. We do not claim those finite Lean proofs cover arbitrary infinite D or unknown interventions.

Finite sanity checks: local exact rational visible-word comparisons passed for inert fibres 1, 2, 3, 7 through horizon 8; 153 finite permutations and 4,282 readout assignments checked the common-period invariant. Separate analytic arguments carry the universal claims. The standalone replay-file push failed in this round, so these checks are not presented as an independently reproducible committed program or exact-head CI certificate.

Unresolved physical bridge: the set of actual observer-accessible protocols, preparations, repeated instruments, composites and their measures must be sourced. If a hidden extension changes any of these complete records, treating its cardinality as gauge is not licensed. Holographic boundary entropy, Bell and YM action-selection claims still have their independent source obligations.

Governance: research-interpretation draft only. Three changed files: README.md, verification/ROADMAP.md, verification/programmes/substratum/DEUTSCHIAN-CARRIER-REVISION.md. No manuscript A1 or finite theorem changed, no main merge or manual workflow dispatch. New head d561b83ea1a95c93b334bb71381cfe0b690cb0bc has no verified all-check green status at this checkpoint; independent review pending.

Observer-relative finiteness — current scoped writer result

The requested physical interpretation is adopted at the working-explanation level: OI is about observer-relative finite information access, rather than a finite total ontology. For each observer with a sourced finite information budget and a fixed finite collection of bounded-horizon deterministic protocols, the complete record map factors through a finite-index history quotient of the full microscopic state space. If protocol p has finite complete-record alphabet W_p, the quotient has at most ∏_p |W_p| classes, regardless of |S|. This is an elementary all-state proof under its stated interface assumptions, not a new fact about actual physical causal horizons.

Mandatory controls that limit this reading:

• No universal finite-area horizon from embeddedness: inertial observers need not have event horizons; GR's finite de Sitter horizon and its finite mode/cell count are named physical/geometric premises, not generic facts of all OI observers. A finite causal diamond and an event horizon are not synonyms.
• No uniform bound across observers: on the infinite binary tape {0,1}^N, observer o_n accesses n bits (2^n finite records), yet the collection o_n over all n distinguishes any two tapes. "Each observer finite" does not imply globally finite S or a common finite bound.
• Finite record words ≠ finitely many exact probability laws: Bernoulli preparations with a binary outcome have continuum-many distinct response probabilities indexed by θ∈[0,1]. A finite-dimensional quantum system similarly has nonorthogonal continua of possible states; information capacity must not be conflated with ontic or exact statistical-state cardinality.
• Finite record quotient need not be autonomous: the states 0 and 7 have the same current bit-3 readout, but under reversible +1 they produce different next bit-3 values. Closure/reuse and complete history must be proved, not assumed.
• Existing gauge scope: total cardinality is only gauge-like relative to complete accessible record/intervention equivalence, as in GR deep-sector boundary limitation, Substratum 24(iii) decoupled ancillas and passive Level-G4 quotient; do not promote it to unrestricted physical G3 or YM gauge equivalence.

Artifacts: new verification/programmes/substratum/OBSERVER-RELATIVE-FINITENESS.md (proof, assumptions and countercontrols), bounded_observer_controls.py (finite regression source), and minimal links/phrasing in the README, ROADMAP and Deutschian working-revision note. Exactly five changed paths, no paper/book/manuscript theorem or A1 physical premise edited. An independent exact arithmetic implementation passed 30 bounded checks; the pushed Python script has not yet been executed and certified on the exact PR head. The general mathematical counterexamples are analytic and do not depend on treating finite tests as proofs.

Outstanding physics: a finite boundary-information budget must be sourced for any specified class of real embedded observers; the measurable observer/intervention interface and an independent prediction are open. This does not discharge F2 quantum operational sourcing, C4, Bell/no-signaling, area-law entropy premises or Yang–Mills action selection. Research only, no F/E designation, manuscript promotion, workflow dispatch or merge. CI on latest c86e0a33f783cbc294f92d2f12e3d267c1387c1c: 41073243133 queued at checkpoint. Independent math/scientific review pending.

Observer-relative finiteness — latest explanatory revision

Working hypothesis adopted: what can be justified generally is observer-relative finite information access, conditional on each observer's finite capacity, resolution and protocol budget. The total substratum's state cardinality stays open and gauge-like only relative to an established operational equivalence. Relative finiteness is not a theorem that every observer has a finite-area event horizon, that the exact operational preparation state space is finite, or that finite record classes constitute one autonomous reversible physical system.

Conditional finite-index theorem (elementary written proof): for any microscopic carrier S (arbitrary cardinality), a finite permitted menu of fully specified deterministic complete-record protocols with finite output-word sets W_p on a bounded time window partitions S into at most ∏_p |W_p| history classes. This is a finite observer-specific record quotient. It does not imply |S|<∞, and the equivalence need not be dynamically closed. For stochastic response laws or unrestricted preparations, the exact operational class may still be infinite.

Countercontrols: a family of prefix observers on an infinite tape each sees finitely many strings, but collectively separates all tapes and has no uniform bound; a single binary Bernoulli measurement admits continuum-many distinct response laws as the preparation θ varies; two states agreeing on the present bit-3 observation can be distinguished after one reversible increment (0→1 vs 7→8). An infinite full-record process need not share one finite reversible all-time representative. None of these contradict the conditional finite-horizon correspondence or the finite-model A1 reconstruction.

Horizon qualification: OI's GR finite de Sitter boundary area / finite-mode counting has named physical assumptions; not all embedded observers have finite-area event horizons. Positive cell size and finite internal settings are separate necessary premises. A causal diamond is not synonymous with a cosmological event horizon.

New files: verification/programmes/substratum/OBSERVER-RELATIVE-FINITENESS.md (formalization and proof/control scope), bounded_observer_controls.py, and OBSERVER-RELATIVE-FINITENESS-RESULTS.json; corresponding small links/scoping clarification in README, ROADMAP and Deutschian working-carrier revision. Exactly six changed files, no manuscripts, A1 edits, or altered finite theorems.

Verification: local Python normal/-O executions both returned zero and emitted byte-identical output. Git blobs of committed source and results match executed local bytes; 30 independently checked integer arithmetic controls also passed. This establishes finite regression only. Automatic exact-head CI run 41073727624 was queued when checked; independent physics/math review and total physical finiteness hypothesis verification remain open. No F/E, manual workflow dispatch, release or merge.

[amaybaum]

Closing without merge, on the owner's approval in chat on 2026-11-04 (#1015 c.6624266088).

Carried to #1007. Its unique content is recorded at #1007 c.6624321475:

• the finite-index theorem;
• the prefix-observer, Bernoulli and non-closure countercontrols;
• the horizon qualification;
• the inert-enlargement and Bernoulli all-time controls;
• the finite regressions.

Dropped:

• The README edits. docs: distinguish bounded observer access from finite total substratum #1036 is the single README:6 correction.
• The verification/ROADMAP.md hunk. That file is frozen.

Preserved. The branch research/oi-deutschian-carrier-framing-20261030, the head 027ec21a, every commit and the full discussion remain intact.

Closing this PR changes no scientific status and adopts no claim.

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