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OI-BH-1: audit Hawking information, Page curve, and gravity implications - #917

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@amaybaum amaybaum commented Oct 25, 2026 •

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OI-BH-1: a bounded black-hole information audit based on book/ch07-gravity.md §7.6 and papers/GR.md Appendix A. It is exploratory research. It changes no manuscript and no existing proof module, and it makes no claim about physical black holes.

  • Head: 84aca6b06cc23976e4e95c896fcc0fff988f01e4.
  • Merge: not authorized.

Packages

There are two finite audit packages under verification/programmes/black-hole-information/.

bh01_access_v1: an exact classical access model. The tested finite classes are all bijections of small configuration spaces and named families, not the substratum dynamics. In them:

  • bijectivity neither implies nor is necessary for recovery from accessible records;
  • with bijectivity, complete endpoint access suffices;
  • an inaccessible endpoint set K bounds the loss by P_succ ≥ 1/|K|.

Item F is an audit observation, not a model claim. By GR's own formulas, the Appendix A.7 premise τ_evap ≪ τ_B^D fails at 30 M_sun; that premise is still in main at GR:811.

bh02_scramble_v1.

  • Permutation unitaries on configuration bases create no entanglement from configuration states, across bipartitions aligned with configuration coordinates.
  • Page-like values arise only from superpositions the analyst supplies.
  • t_P/t_evap = 1 − 2^{−3/2} holds conditional on β = 1, a constant mass-loss coefficient and S ∝ M². With Page's β ≈ 1.4847 it is 0.538 (Page 2013, Eqs. (2), (8)).

What it does not show

There is no statement about physical black holes, Hawking radiation, scrambling times, islands or the generalized second law. The physical inputs used are attributed to their sources: Page 2013's β in bh02 C7, and GR Appendix A.7's evaporation law in bh01 item F.

BH-03 and BH-05 to BH-07 are planned in PROGRAMME.md and have not been run.

The MANUSCRIPT-AUDIT.md files are proposals against the text at 809fac52. #920 has since corrected that text on main (merge c37700ad), independently of this PR, so the proposals must be re-checked against main before any use.

Review and landing audit

Each package keeps its separate-agent internal reviews in review/:

  • bh01_access_v1/review/:
    • the review of 587d4196;
    • the written re-checks of 95458016 and df2ea6f5, with their summaries (redactions recorded).
  • bh02_scramble_v1/review/REVIEW.md: the review of 1739f4e0 and the re-checks of 91e2230a, 1f1aec6f and ce7937d2.

A separate-agent internal landing audit of f6698781 was READY WITH NITS, and its re-checks of 606c98d8 and 84aca6b0 accept, with the description fixes applied here. It confirmed:

  • claim separation;
  • non-vacuous controls (bh01 mutants re-run, 12/12 caught; bh02 targeted mutants reproduced, full campaign recorded at 91e2230a);
  • byte-identical replays and every SHA256SUMS entry;
  • a clean merge with main;
  • the cheap gate steps:
    • legacy-records: 303 intact;
    • V3 self-test and corpus;
    • 52 receipts hold.

Its nits are fixed in 606c98d8:

  • reviews retained;
  • manuscript-audit headers;
  • Page time stated at β = 1;
  • programme status;
  • the C7 attribution to Page 2013;
  • replay recipes.

The re-check nits are fixed in 84aca6b0: the written re-checks retained, the redaction record completed, and a provenance entry added. Across 606c98d8 and 84aca6b0, only the /C7/verdict leaf of bh02 result.json changes, and bh01's outputs are unchanged. Replays are byte-identical under -I -B and -I -B -O, and the targeted mutants reproduce.

Landing

Land with an ordinary merge commit, as #920 was. The packages cite plan, review and preregistration commits that exist only on this branch, and a squash or rebase would leave them unreachable from main.

Related: #920 (merged; corrected ch07 §7.6 and GR Appendix A without using this PR), #918.

🤖 Generated with Claude Code

https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb

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Writer handoff for #917.

At the owner's direction, the Claude session that writes #910–#912 is now the sole writer of this branch (research/oi-bh-information-audit). The existing draft is preserved as is: head 809fac52cdf207d24eccc63c734996bcb9d073a0, one commit adding verification/programmes/black-hole-information/PROGRAMME.md. Any other writer should stop modifying this branch; if a competing push appears, this session stops rather than racing it.

Planned work, local only until reviewed and separately authorized for push:

  • BH-01: information recovery from emitted records under a fixed observer-access class, with one positive model and one reversible counterexample.
  • BH-02: exact finite comparison of permutation-only and quantum scrambling models, with the Page-curve control and the supplied-ensemble distinction stated explicitly.

Each round commits its plan before computation and gets an independent review. No push, manuscript change, new physical postulate or merge is authorized by this notice.


Generated by Claude Code

Plan only, committed before any computation: definitions (finite
reversible map, nested V/B/D and moving-partition layouts, access
schedule, cumulative and snapshot records, operational equivalence),
claims A-E, endpoint-decoupling arithmetic item F, decision rule,
controls K1-K6 with mutants, invariant-to-checkpoint table and scope.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…Page-time plan

Plan only; no computation yet. Decision rules, controls with targeted
mutants, invariant-to-checkpoint table.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…ipt audit

checks.py enumerates S_8, all maps on {0,1}^2, GL(4,2) and structured
swap/CNOT/leak families with exact Fractions; controls K1-K5 green,
K6 (byte-identical under -O) measured by mutants.py, 10 of 10 mutants
caught. All preregistered claims A-E hold within scope: bijectivity
alone does not imply recovery from accessible records; with
bijectivity, complete endpoint access gives exact recovery and an
inaccessible endpoint set K gives P_succ >= 1/|K| (tight). Item F:
GR A.7's stated decoupling tau_evap << tau_B^D is reversed by at
least 1e57 at 30 M_sun. MANUSCRIPT-AUDIT.md lists dependent sentences
of book ch07 section 7.6 and the chapter overview with wording
proposals only; no manuscript file is changed.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
git archive omits verification/programmes (export-ignore in
.gitattributes), so the recipe now extracts each file with git show.
SHA256SUMS regenerated for the changed REPORT.md.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…nd report

C1 proved: permutation dynamics on configuration states never entangles.
C2 proved: entanglement under any permutation is capped by the initial
state's configuration-basis entropy. C3: supplied superpositions reach
Page-like values. C6: H-scramble fails in the configuration setting; the
Page value enters only through the posited Haar ensemble; shell-factor
gap certified off half filling. C7: 0.646 conditional on constant
mass-loss coefficient and beta=1 accounting; Page's beta gives 0.5381.
All 15 mutants caught.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Wording proposals only; no manuscript edit. Covers ch07 7.6 and overview,
GR Appendix A.7 and corpus restatements with their FULL.md mirrors.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…rols)

Post-review changes; PLAN.md unchanged, every preregistered verdict and
the item F status unchanged.
- REPORT.md: R1-R4 restated as sufficient guarantees (R1 rewritten to
  be a condition); C3 stated under W-autonomy; claim A qualified by C2
  (zero advantage needs |K| >= |M|); necessity diagnostics (36416 /
  36368 / 36032 / 14496); programme tags; item F shows / does not show;
  assumption-watch note on GR A.5/A.7; scope additions.
- MANUSCRIPT-AUDIT.md: classes re-keyed; L12, L139 not supported by
  bijectivity alone; L155 proposal withdrawn (unfalsifiable as stated);
  ch09 L108, ch09 L127 mirror, ch18 L130, ch18 L158, ch19 L334 added.
- checks.py: reworded generated verdict; post-review diagnostics;
  item F pi interval tightened, upper bounds rounded up, Page-time
  bound; controls K7 (item F reference value, cubic scaling) and K8
  (non-vacuous monotonicity test).
- mutants.py: K7 and K8 mutants; 12 of 12 caught.
- result.json, mutants-output.json, PROVENANCE.json, SHA256SUMS
  regenerated; result.json byte-identical under -O.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
amaybaum pushed a commit that referenced this pull request Oct 25, 2026
…paper records

Addresses the focused review of 96b2a75. Each audit file now opens with a
status block (unreviewed; no verdict in it is an established result; its
relation to the auditor's report, with that report's sha256), so a reader
reaching it directly sees its status. README.md states that #917 was read
at 809fac5 (not on main), attributes the Equivalence.lean docstring to the
class RevReal, records two errata in EXPLAINER-AUDIT.md (its tools/ paths
mean explainer-tools/; the Explainer has 41 displays, not 42), gives the
scripts' expected argument, and lists the unresolved literature and scope
questions. SHA256SUMS is regenerated.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Post-review round 2; PLAN.md unchanged; every preregistered verdict
and the item F status unchanged.
- checks.py: the W-autonomous C3 counts get their own post-review
  verdict field and generated line, marked as not bearing on the C3
  verdict (which stays the preregistered product-map check).
- REPORT.md: R3 noted as more than C1/C2 need; turnover-window mass
  fraction stated as a computed upper bound (< 1.9e-58).
- MANUSCRIPT-AUDIT.md: ch19 L334 reclassified as holds under unstated
  conditions (H-scramble); L12 proposal points to item F.
- result.json, mutants-output.json (12 of 12 caught), PROVENANCE.json,
  SHA256SUMS regenerated; result.json byte-identical under -O.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Addresses review F1-F9 of 1739f4e: shell-dependent direction with an
exact diagonal-shell counterexample (H_m - 1 > S_Page), new K-shell and
K-diag controls with mutants, CC5 state below the Page-like band,
attribution and classification fixes in REPORT and the audit, analytic
-1/2 limit, report numbers read from result.json, assumption-watch note.
PLAN.md and amendments unchanged; 17 mutants caught.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…hell total check

Second-review nits on 91e2230: every use of the Page 2013 figures in the
audit is marked as quoted from the abstract with the full text unverified,
and proposals using them stay pending; C7 verdict wording follows. K-shell
checks sum(counts) == comb(n,w) == D. Targeted mutants rerun (M-canonical,
M-page2013, M-ode), all caught.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
A misspelled name or an empty selection now prints VOID and exits 2
before any run, so a targeted run cannot report a vacuous pass. Full
and valid targeted runs print unchanged output.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…only labels

Page 2013 has been read in full: beta Eq. (2) p.6, t* Eq. (8) p.11, 40.25%
p.12, 1/(1+beta) = tau_12 Eq. (14) p.19. Audit tags become citations;
item 1 and 5 wording fixed (0.538 is at constant alpha; the entropy
clause limited to emission into empty space, Page 2005 Eqs. (5)-(10)).
C7 verdict cites Eq. (8). M-page2013 rerun and caught.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Combines the independently reviewed BH-01 access-model chain (head
df2ea6f) and BH-02 scrambling chain (head ce7937d), both on 809fac5.
The two packages occupy disjoint directories; no conflicts.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Scoped landing audit of f669878 (READY WITH NITS):
- Reviews retained (§A.42): bh01_access_v1/review/ (REVIEW.md verbatim;
  re-checks of 9545801 and df2ea6f delivered as messages, one local
  path redacted in each, recorded with before/after digests in
  review/README.md) and bh02_scramble_v1/review/REVIEW.md (verbatim, with
  its three re-checks). bh01 REPORT.md's review numbers now cite it.
- MANUSCRIPT-AUDIT.md (both): the proposals concern the 809fac5 text;
  ch07 7.6 and GR App. A were since corrected on main (c37700a), so they
  must be re-checked against main before use. report.py: "GR:837 (at
  809fac5)".
- bh01 REPORT.md: t_P stated at beta = 1 at both sites.
- PROGRAMME.md: status names the two reviewed packages; BH-03 and BH-05
  to BH-07 not run.
- bh02 C7 verdict: "in Page 2013, beta itself is computed from the
  species' greybody factors" (literature attribution). result.json:
  only /C7/verdict changes; replay identical under -I -B and -I -B -O;
  targeted mutants M-canonical, M-page2013, M-ode reproduce
  mutants-targeted-output.txt; report.py reproduces REPORT.md.
- Replay recipes name f669878 or any later commit containing the
  directory; the full-campaign line notes it was recorded at 91e2230.
- bh01 result.json replays unchanged. SHA256SUMS regenerated in both
  packages, now covering review/.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Re-check of 606c98d (READY WITH NITS):
- R1: bh01 review/ retains the reviewer's written re-checks of 9545801
  and df2ea6f verbatim (-full.md). The summary messages are kept, with
  the local path now replaced by "[local path removed]/" and the
  redaction recorded at every site (lines 1 and 42; line 27), with
  before and after digests, in review/README.md.
- R2: bh02 PROVENANCE.json gains post_review_5 (the /C7/verdict change,
  the superseded result.json digest ee26de70) and generated_on_parent
  f669878; review/README.md states REVIEW.md is verbatim and that the
  literature-reading notes and their review are not retained.
SHA256SUMS regenerated in both packages. bh02 checks.py and report.py
replay byte-identically.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
@amaybaum
amaybaum marked this pull request as ready for review October 25, 2026 18:41
@amaybaum
amaybaum merged commit ebf98d8 into main Oct 25, 2026
26 checks passed
@amaybaum
amaybaum deleted the research/oi-bh-information-audit branch October 25, 2026 18:42
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