[amaybaum]

Active research for #970, separate from SC-36 #978 and Introduction #918. Stacked base/D: 20ca05fe9e7e460de29e08f7a21029042fa45b12 on held draft #982. Current checkpoint: ce978ce5db4165dd1e618e9f44bb67281ac152df, tree f19e8bb1fb89bf12b732f57a3a5084c82a2cdec4.

Accepted finite mathematical core

Independent review accepts the written core at immutable bdcbd32bb55a5464d72b61682721f0b4bfaf446c / tree 700fa72b23aaa37245d136804d0ad62bb5337a21. Its proof/control/results blobs remain unchanged. The exact review, manifest and independent checker are retained under independent-core/; review SHA256 b9a8be21925cb2280fc02ccd6e70195ff21241b62ae9099745aae8dd5da71ab1.

The coherent seed is |+>^k|0>^(n-k). One uniformly random GL(n,2) configuration permutation prepares a uniform k-subspace state. All nested cuts use that same state. Written results give the flat Schmidt spectrum, exact Gaussian-binomial entropy distribution, an independent incidence formula for mean purity, a mean deficit of at most two bits below min(k,n-k,r,n-r), and a simultaneous shared-state cut bound.

Author controls pass 18,837 predicates over 2,658 state/cut cases and 35 larger moments. The independent RREF/amplitude checker passes 14,924 predicates, the same 2,658 cases and 104 larger moments. This is written finite mathematics, not a Lean certificate.

Separate sequential-release companion

Immutable companion 2624d49cffc0794b300517719c879de6b57d395e adds an autonomous clocked-SWAP release window using one fixed coherent sample and a fixed radiation register. Its clock is definite, and the finite permutation recouples later and returns after 2(n+1) steps. Controls pass 4,350 predicates over 1,592 basis configurations and 418 coherent window cases. The coherent-clock counterexample gives radiation purity 3/4. Separate independent review accepts this finite autonomous toy at 2624d49, with its files unchanged at the current head. Report SHA256: 3d3eb16f578f490e8aeb23ea9ab7fab9e2e8b4355ec31c6a6af2297be4d69bec. The independent checker passes 5,726 predicates, 1,592 basis configurations, 418 uniform-state windows and 14 complex nonuniform windows; author-result replay matches.

Checks and scope

The new path-scoped ordinary pull_request-only workflow replays author, independent and release-window exact controls from temporary copies, comparing structured JSON against retained results. Local replay-driver smoke matched all three. The dedicated research replay run 40725910910 passed on this head. Normal verify run 40725910952 is queued. Computational replay and written-proof acceptance remain separate; neither is a Lean certificate or a physical Page-curve result.

This restricted positive-amplitude subspace ensemble is not Haar measure or the full stabilizer ensemble. The mirror Bell-pair tent, repeated-CNOT return, configuration and incoherent-mixture controls retain that distinction. Coherent preparation, ensemble measure, locality, physical scrambling, energy shell, decoupling and gravitational evaporation remain separate inputs. No GR A.8–A.9 restoration, manuscript/coverage promotion, merge, native F/E designation or special dispatch is authorized. The Introduction need not wait for unrelated physical reconstruction.

Evidence: verification/audits/manuscript/page-coherent-recovery-20261028/.

[amaybaum]

Retired without merging (PR-AUDIT-1, #1088). The branch and its commits are kept.

Owner decision (amaybaum, Claude Code session chat, 2026-11-04):

#989 — Entropy profiles | Close unmerged | Approved after handoff to #970 and retention of the #941/NEW-3 pin obligation. Preserve branch ce978ce. Do not merge now.

The governing distinction is that closing a PR transfers responsibility; it does not establish scientific results or make branch-only evidence durable on main.

Closing this PR is administrative. It resolves no scientific question, accepts or withdraws no result, and changes no status.

• Accountable home: Research backlog: advance downgraded and conditional scientific claims from corpus audit #970, handoff. It holds the content, the scope exclusions, the open inputs, and the missing companion independent-review report, which is an obligation and not an accepted result.
• Introduction paper: reconcile sources and integrate scoped theorem recoveries #918 dependency: Introduction paper: reconcile sources and integrate scoped theorem recoveries #918 cites bdcbd32bb55a5464d72b61682721f0b4bfaf446c ([CE]) and 2624d49cffc0794b300517719c879de6b57d395e ([CR]). Neither commit is on main, and both must remain reachable. Retention on main before any dependent Introduction claim lands stays with Introduction full-corpus scientific consistency audit (gate for #918) #941 (item 26 / NEW-3).
• Kept:
  • branch research/page-coherent-entropy-20261028 at ce978ce5db4165dd1e618e9f44bb67281ac152df, and refs/pull/989/head;
  • all 4 commits;
  • this PR's discussion.
• Standing restriction: do not delete the branch. Any landing needs a separate owner decision at an exact SHA.

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