[amaybaum]

Status: DRAFT research evidence, not a manuscript correction or merge candidate

Tracked finding: #979. This independent unit is separated from SC-44 #980 under the scientific-contradiction closure rule.

Exact four-state pure-Python reproducer: verification/audits/manuscript/intro-corpus-audit-20261026/tracks/SC45-generator-soundness/verify_four_state.py. It confirms with rational arithmetic that an arbitrary state relabelling can change the rooted one-step transition matrix for a fixed visible/hidden partition. It checks a positive hidden-only relabelling control and the contrasting, transport-of-the-observer-interface interpretation. Also enumerates the 24 full-state relabellings to detect counterexamples.

The manuscript Theorem 24(i) currently claims arbitrary relabellings preserve the full observational equivalence; that is not established and is false on the fixed-interface reading. A separate check of Theorem 24(iv)'s graph-invariant/full-observable conflation is required.

No source theorem text is changed here yet. Freeze the actual observable carrier and permitted relabellings; write and independently review a precisely scoped replacement; propagate all affected source/corpus sites and re-run checks. Do not use this draft as acceptance of the four-generator completeness claim. No merge authorized.

[amaybaum]

The writer prepared a separate reconciliation preview with SC-44 #980: #982 at 053130e6, stacked on SC-44. It imports this PR's Theorem 24 fixed-interface proof and counterexample verbatim and preserves the SC-45 checker/README, while retaining SC-44 Proposition 24.2 and correcting the local hierarchy/synthesis dependency. This is not a merger of the research units or a substitute for independent review; the preview keeps Theorem 24 at GAP and the full gauge classification open.

[amaybaum]

Independent scientific review — REVISE (owner-relayed, exact head 6aff07d452c0f298012d6bc2cd30772161c865fa)

Provenance: The owner's independently obtained SC-45 review, summarized here faithfully. Reviewer-supplied exact replacement text is not present in this conversation or existing PR thread; wording below is not represented as its verbatim patch.

Positive findings

• The exact four-state example refutes arbitrary full-state conjugation as an invariance of a fixed observation/readout interface. The reviewer checked the coherent channel, not just populations. Equality when the readout itself is transported is passive coordinate invariance, not evidence of physical equivalence.
• A single hidden permutation σ independent of the visible fibre preserves the full coherent channel family; zero failures across the enumerated (2,2), (2,3), (3,2) cases. Exact decoupled enlargement preserves the coherent channel in 160 reviewed cases.
• Completeness depends on the observable carrier. On fixed-interface coherent-channel equivalence, Pair C has equal channels at every time but is not reached by restricted hidden-only relabelling (i) or decoupled enlargement (iii); the balanced-word-trace invariant is a candidate chain-level proof (review reported a paper argument). This refutes the proposed generators for that specific equivalence (not all-partitions). On population-only equivalence, a hidden relabelling (v,h)↦(v,σ_v(h)) preserves the rooted T_{ij}(t) only with the appropriate caveat: check all times and fixed hidden prior rather than assuming a one-step statement extends to iterates. Pair C may be absorbed under this broader generator reading. Across all partitions, the classification remains open.

Blocking findings and repairs

1. No stand-alone landing. Deleting the definition of ∼ and G_sub leaves many uses and the old Lemma 24.1, completeness and direct generator citations. Both source and canonical ledger row overlap SC-44. Integrate in #982, not this PR alone.
2. Restore sound claims rather than downgrade them: a population-level relabelling with visible-fibre-dependent σ_v for the appropriate observable/time scope; exactly decoupled enlargement with arbitrary normalized ancillary state and well-defined infinite-dimensional trace-class cases; the unconditional q-insensitive structural results of SM §2.7 separately from the hypothesized equality of transition probabilities across q; and established Theorems 1–6 structural graph content under their exact hypotheses, not full coherent-channel equality.
3. Correct other dependences: the old 'π=T is generator (i)' is false if T changes visible layers; same-channel dilations need not differ by hidden unitary (ST3_pairC); the old definition, conclusion, amplitude-scale remark, source citations, and Complexity/Computation/ch14/FULL/Explainer mirrors need explicit disposition.
4. Gate failures: architecture check flags unqualified 'families exhaust' at approx. Substratum lines 251 and 269; regenerated .tex/.pdf are stale. Mathlib bridge failed on the reviewed head, reason to diagnose independently.
5. Checker quality: 2/6 mutants did not fire; positive control tested only populations and missed fibre-dependent coherent-channel distinctions; transported-readout test is a tautology; assert the reported 16/8 count rather than printing it only. Normal and optimized Python and meaningful mutant controls required.

Decision: REVISE. Preserve the exact proven positive theorems; explicitly label fixed-interface generator non-exhaustiveness and all-partitions open without conflation. The complete reviewer-authored replacement paragraphs should be attached separately if supplied. No source edit, verification claim, merge or F/E designation is implied by this review post.

[amaybaum]

Writer handover. At the owner's instruction (2026-10-31), this session is now the single writer for this PR. Other sessions should not push to its branch.

• Starting head: 6aff07d452c0f298012d6bc2cd30772161c865fa.
• Next step: a status and review-state check. The next unit will be stated here before any work begins.

No merge, special dispatch, F/E designation or manuscript change.

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[amaybaum]

Closing without merge: superseded as an integration vehicle (owner decision, 2026-10-31).

Its fixed-interface Theorem 24 correction and the SC-45 track reached main through #982, #994, #1005 and #1019. main's verify_four_state.py is a stronger rewrite: it uses require, has mutant kills, asserts the 16/8 count and adds coherent-channel controls. This PR also conflicts with main.

The review obligations that remain are carried to #979:

• generator completeness and the Pair C witness;
• the observable-carrier and all-partitions scope;
• the downstream generator-reading sites, including Structure.md:53's "arbitrary cardinality".

Retirement does not mean those questions are solved. The branch, commits, reproducer and review history are kept.

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