[amaybaum]

#941 Units 3–4. One narrowly scoped Introduction correction PR, as the owner rulings allow:

• #941 c.6677500012 (amaybaum, Claude Code session chat, 2026-11-06T05:11:33Z): R-15, X-2, Har04;
• #1031 c.6678672357 (amaybaum, Claude Code session chat, 2026-11-06T06:26:04Z): revise to include S9-I7, preserve the other three corrections, and integrate against the updated main.

Writer: writer-941. Draft. Do not merge automatically. Merging needs exact-head review, green CI and an owner merge decision.

Head: dd79b705fab22963676330cbb5685d6702a3c415. History, in order:

1. 41d70e799565a4a0f072914e793575e65052d701: the R-15, X-2 and Har04 edits, single parent 424f28b1e7b1201e9a13bd0e608e1b0e4ad9f93b (the first-reviewed head).
2. 3dc6e4f35af93e65ab538bb80877d0b76c4a419e: merge of updated main (git merge --no-ff origin/main), with parents 41d70e79 and 374b2ef3d0af1f3233a1d6bc74bee3c32683e3c0 (Merge #941 Unit 2: SC17/SC31/SC33 provenance narrowings, README 29-declaration inventory, closure ledger #1159). It merged cleanly, with no rebase, amend or force-push.
   • #941 Unit 2: SC17/SC31/SC33 provenance narrowings, README 29-declaration inventory, closure ledger #1159 changed README.md, papers/introduction_repro/README.md and four files under verification/audits/manuscript/intro-corpus-audit-20261026/.
   • It changed no papers/Introduction.* file: main's Introduction blobs are still .md e85f6699, .tex 99d1775c and .pdf 80091191.
3. dd79b705fab22963676330cbb5685d6702a3c415: the S9-I7 edit plus a single rebuild of .tex and .pdf, parent 3dc6e4f3.

Diff against main (374b2ef3): only papers/Introduction.md, .tex and .pdf, all generated from the same source revision. There are no Main, companion, book, FULL or Explainer edits.

The four edits below each map to one ledger row and one owner-ruling item. The R-15, X-2 and S9-I7 changes are each traced to reviewed evidence.

1. R-15 (= X-1 = #918 rF-10). Ruling item 4: "Approve restoring the previously reviewed, narrower Doukas wording."

Intro L93

-… [RHP14, Thm 2.4; BD16]; Doukas states the same argument concurrently [Dou26, Prop. 1].
+… [RHP14, Thm 2.4; BD16]; Doukas states the contraction argument concurrently, as a no-revival obstruction to Markovian realizers [Dou26, Prop. 1].

That is +7 words, which matches the ledger.

Reviewed evidence on main. The sentence is the landed text of the #918 Introduction landing, f5efa7a0813218b580272f7fd80a6b0c87eb6657 (Merge #1124), which is reachable from main. git show f5efa7a0:papers/Introduction.md | sed -n 172p contains:

… and Doukas states the contraction argument concurrently, as a no-revival obstruction to Markovian realizers [Dou26, Prop. 1].

The reviewed correction was #918 round finding rF-10, which is FINDINGS R-15. Its proposed text for this site is the same string, citation bracket included:

Proposed. Doukas states the contraction argument concurrently, as a no-revival obstruction to Markovian realizers [Dou26, Prop. 1]

The current L93 wording, "the same argument", is rF-10's pre-correction wording, and it came back in the rewrite.

How the citation bracket is handled. I restored the reviewed clause verbatim, with [Dou26, Prop. 1] kept after "realizers". That is the bracket's position at f5efa7a0:172 and in rF-10's proposed text. A byte check confirms the new L93 contains exactly the landed clause, grep -F with one match in each.

• Dropping the locator would make the attribution less precise than the reviewed text.
• Moving it, for example directly after "Doukas", would produce wording no one has reviewed.

Keeping the bracket as landed makes the edit a pure restoration, and the +7 count holds: 9 → 16 words, bracket unchanged. The clause's role is also the same as at f5efa7a0. It follows the contraction step ("the standard contraction criterion for divisibility [RHP14, Thm 2.4; BD16]"). It attributes the contraction argument, not the overlap-and-return theorem, which is what rF-10 corrected.

First-hand source check (this PR). I read Dou26 = arXiv:2602.22095v3 (19 Oct 2026, matching reference entry L231) on 2026-11-06 at 05:30Z.

• §4.2.1, "A distinguishability-revival obstruction", pp. 19–20, Proposition 1 (No distinguishability revival): "Markov compatibility implies D(t) ≤ D(u), s ≤ u ≤ t ≤ T … Thus any increase in D(t) rules out a Markovian realizer on the same configuration space."
• Its proof is the ℓ1 contraction of a stochastic matrix, Eqs. (80)–(82).
• The section has no overlap, return or finite-recurrence argument.

So the restored wording, "the contraction argument … as a no-revival obstruction to Markovian realizers", is supported as stated.

2. X-2 (= R-20 prior leg = R-35 bound = S9-A2 Introduction side). Ruling item 9: "Approve the narrow correction, but first independently verify the prior conditions. If missing, add only the supported uniform-message qualifier."

Intro L163

-Reading everything at the end recovers the message, and hiding it completely requires the unread registers …
+Reading everything at the end recovers the message, and, for a uniformly distributed message, hiding it completely requires the unread registers …

That is +5 words, and nothing else in the sentence changes.

Reviewed evidence on main. The paragraph cites [BHa], which is verification/programmes/black-hole-information/bh01_access_v1/REPORT.md at 424f28b1.

• REPORT.md:42–44: "Zero accessible advantage (P_succ = 1/|M|) requires the inaccessible endpoint set to have at least |M| joint values: by C2, a bijective instance with |K| < |M| has P_succ >= 1/|K| > 1/|M|"
• REPORT.md:92: "P_succ = (1/(|M| N)) sum_y max_m c_m(y)". The 1/|M| weight is the uniform message prior, with equal-size supports |X_m| = N (:91).
• REPORT.md:297 (Scope): "Uniform message prior with equal-size supports."

The cited source therefore proves the "joint values ≥ possible messages" floor only for a uniformly distributed message, and L163 stated it with no prior. The qualifier narrows the sentence to what [BHa] proves. Its wording is R-35's own ("for a uniformly distributed message").

Prior condition independently verified (Unit 4 check, before the edit).

• The independent proof review S9-A2 gives an exact counterexample without the qualifier: prior (1/2, 1/4, 1/4), |M| = 3, |K| = 2, P_succ = 1/2, equal to the maximum prior. The same review states that the uniform-message qualifier is a correct and sufficient fix.
• The independent Units 3–4 check reproduced this with an exact rational enumeration over all bijections of {0,1}² and {0,1}³ with one register unread:
  • 376 zero-advantage instances (n = 2) and 66,816 (n = 3) with |K| < |supp M| under non-uniform priors;
  • 0 such instances under a uniform prior;
  • a violation detector that fires, so the check is not vacuous.
• Under the "learn nothing" (independence) reading, the statement holds for every prior, but that argument is not in [BHa]. [BHa] supports the sentence only for a uniform message, so only the qualifier is added.

Placement. The qualifier goes between "and" and "hiding", not before "Reading". The recovery clause is C1, which REPORT.md:52–54 states for every encoding and prior. No mirror of this sentence exists anywhere in the corpus (see the re-grep below).

3. Har04 (ledger OD-8 Har04 row). Ruling item 8: "Require a first-hand source check for any substantive claim attributed directly to Har04. Otherwise, explicitly qualify the attribution as secondary."

Intro L133

-Montina reports Hardy's result that the number of underlying states cannot be finite [Mon08; Har04].
+Montina reports Hardy's result that the number of underlying states cannot be finite [Mon08, citing Har04].

The reference entry [Har04] (L241) is kept, and "citing Har04" still cites it.

First-hand check: Har04 itself is unreachable.

• Crossref matches L241: L. Hardy, Stud. Hist. Philos. Mod. Phys. 35(2), 267–276 (2004), DOI 10.1016/j.shpsb.2003.12.001.
• ScienceDirect returned 403. Unpaywall reports is_oa: false and has_repository_copy: false, and OpenAlex reports closed. No arXiv copy was found.
• No content of Har04 was read or inferred, so the attribution is qualified as secondary.

First-hand check: Montina's report is supported. Source: Mon08 = arXiv:0711.4770v2, Phys. Rev. A 77, 022104 (2008), matching L259. Re-read for this PR.

• p. 2, Sec. I: "similar questions were discussed by L. Hardy [10]. He proved that the number of ontic states can not be finite …"
• p. 9, Sec. V: "As previous proven by Hardy [10], this mapping of quantum state does not work, since the number of ontic states has to be infinite."
• Ref. [10] is "L. Hardy, Studies in History and Philosophy of Modern Physics 35, 267 (2004)", which is Har04.

Why this form. The Introduction's brackets use [Key, locator] and [Key; Key], so "[Mon08; Har04]" presented Har04 as a co-equal direct source. "[Mon08, citing Har04]" keeps Mon08, the source that was checked, as the cited source, puts the secondary qualifier in the locator slot, and leaves the prose ("Montina reports …") unchanged.

• The alternative "[Har04, as reported in Mon08]", which OD-8 described, leads with the unchecked source.
• The "citing" form has corpus precedent: papers/Juno.md:59 "[18, §7.1, citing Mason et al.]".
• papers/oi_lattice_code/citation_check.py passes with 0 broken citations.

4. S9-I7 (leg 3, t ≪ t_R). Ruling #1031 c.6678672357 §2: "replacing the categorical assertion that observable timescales are short relative to recurrence with a qualified may be statement. Do not claim that has been derived or controlled." "Use the minimum correction, preserving the explanation that delayed memory may be observationally inaccessible."

Intro L97. The text was verified on the updated main (374b2ef3) before editing.

-… not necessarily of anything an observer will see: the stretches of time an observer can examine are short compared with the recurrence time of a large world, and memory can first appear after all of them [Main §2.3, Scope]. …
+… not necessarily of anything an observer will see: the stretches of time an observer can examine may be short compared with the recurrence time of a large world, and memory can first appear after all of them [Main §2.3, Scope]. …

The change is "are" → "may be", +1 word. Nothing else in the sentence or paragraph changes.

Ledger row and finding. The row is S9-I7, an independent proof review finding (proofs/README.md:62 in the audit records): "t ≪ t_R is not controlled". The independent Units 3–4 consistency check found legs 1 and 2 supported, but leg 3 not supported at L97:

• L97 stated the uncontrolled premise as fact.
• Read universally, it is false. A world of any size with the involutive rule φ(v,h) = (h,v) has recurrence time 2.

Reviewed evidence on main.

• papers/Main.md:141 states the timescale separation as a requirement, not a result: "(C4) and condition (ii) of §3.4 require an accessible order, $k\tau_S \ll t_R$".
• papers/Main.md:447's "exponentially large" is stated only for Hamiltonian flow under its own assumptions.
• book/ch01-observation.md:121 and its FULL mirror use the modal form: "the recurrence time $N$ can be astronomically large".

The Introduction's categorical "are short" was therefore stronger than its cited support [Main §2.3, Scope]. The qualified form matches what Main provides.

Why "may be". It is the owner's wording, and it reads correctly in context. The sentence still explains why the failure need not be "of anything an observer will see": memory can first appear after every examinable stretch whenever those stretches are short. The paragraph's conclusion needs only that possibility, so the explanation the ruling says to preserve is intact.

The consistency check had proposed "can be". I used the ruling's "may be", since both are within the one-to-two-word limit and the ruling names that form. The edit asserts no derivation or control of the separation. The register scan confirms no "derived" or "controlled" wording was added at L97.

Mirrors. None. "recurrence time of a large world", "stretches of time an observer can examine", "memory can first appear" and "not necessarily of anything an observer" occur only at Intro L97 and its .tex.

• The other corpus hits for "short compared with" are unrelated claims: Intro L177, Medicine, Substratum, and book Lemma B.7.4 / ch16.
• The book's recurrence statements (ch01:121, ch18:176, FULL:465, :4989) are already modal ("can be"), so they agree with the edit.

S9-I2 and S9-I8 are not touched, as ruling §2 requires.

No-change rows recorded (sources from the independent Units 3–4 check)

• R-16 (L93, RHP14/BD16). Ruling item 5: keep the current wording unless a first-hand check establishes a material citation defect. The check found none.
  • RHP14 (arXiv:1405.0303v2), Thm 2.4, p. 8, is the contraction iff. L93 uses only the "only if" direction and claims no equivalence, so §A.34 is not engaged.
  • BD16 (arXiv:1408.7062v3), p. 5, Prop. 1 and Cor. 1, are divisibility ⇔ information-decreasing, which is accurate support for "the standard contraction criterion for divisibility".
  • The dropped locator "[BD16, Prop. 1 and Cor. 1]" makes the citation less precise but not wrong. No change, and the locator is not restored.
• O-26 (L191, concept DOI). Ruling item 7: one fresh read-only resolution required.
  • Resolved 2026-11-06T05:24:59Z: doi.org/10.5281/zenodo.19060318 → zenodo.org/records/23608753, with version 3.1.4, published 2026-10-24, version DOI 10.5281/zenodo.23608753 and conceptdoi 10.5281/zenodo.19060318.
  • This matches Audit: the Introduction against the full core OI corpus (gate for #918) #942 c.6434035598 and README.md:143 on main ("concept DOI 10.5281/zenodo.19060318, which resolves to the latest version").
  • The Introduction makes no release-specific claim. No change.

§A.42 item 8: off-main references in this PR

Reference	Claim it is attached to	Classification
#941 c.6677500012 (owner rulings)	authorization for the three edits	provenance (authorization; no manuscript claim uses it)
#941 c.6643207092 (PDF build conditions)	rebuild procedure	provenance
#918 round finding rF-10 and FINDINGS R-15 (commit 16fc745d, not on main)	R-15 wording	provenance. The restored wording is on main at f5efa7a0:172, and the attribution it makes is supported by the external Dou26 v3 Prop. 1, which I re-read first-hand above. Neither the claim nor its support uses the off-main file.
FINDINGS R-35 and proofs/bha-c1-c3/REVIEW.md S9-A2 (commit 16fc745d, not on main)	X-2 qualifier	provenance. The narrowed sentence is supported by REPORT.md:42–44, :92 and :297 on main. The counterexample shows why the qualifier is needed, but the sentence as edited does not use it.
Independent Units 3–4 literature check and its probe (session scratchpad, not on main)	X-2 verification, Har04 and Montina reads, R-16, O-26	provenance. Each claim edited here is supported by on-main content or by a public external source quoted above.
#1031 c.6678672357 (owner ruling)	authorization for S9-I7 and for the merge of main	provenance (authorization)
Independent Units 3–4 consistency check, S9-I7 row (session scratchpad, not on main)	S9-I7 edit	provenance. The narrowed L97 sentence is supported by papers/Main.md:141 on main, which states the separation as a requirement. The check's counterexample shows why the qualifier is needed, but the sentence as edited does not use it.
S9-I7 finding, proofs/README.md:62 (proof-review records, commit 16fc745d, not on main)	S9-I7 edit	provenance. The edit weakens a claim, and the weaker claim rests on Main.md:141 on main.
FINDINGS OD-8 (commit 16fc745d)	Har04 citation form	provenance
#942 c.6434035598	O-26 no-change	provenance. The concept DOI is also stated in README.md:143 on main, and it was re-resolved.
External: Dou26 (arXiv:2602.22095v3), Mon08 (arXiv:0711.4770v2), RHP14 (arXiv:1405.0303v2), BD16 (arXiv:1408.7062v3), Crossref record of Har04	the attributions at L93 and L133	public published literature, cited in the manuscript's own reference list

No reference is classified "support off main", so no gap remains.

Corpus-wide re-grep (§A.25, §A.14)

I grepped all tracked papers/*.{md,tex}, book/*.md (chapters and The-Incompleteness-of-Observation-FULL.md) and every other tracked file outside verification/.

• Search terms: "Doukas states", "same argument concurrently", "no-revival obstruction", "Mon08; Har04", "Har04", "Hardy's result", "number of underlying states cannot be finite", "as many joint values", "Reading everything at the end", "hiding it completely", "recovers the message", "uniformly distributed message".
• Paraphrase sweep: Doukas|Dou26|Montina|Har04|ontological excess|perfect secret sharing|Shamir|joint values|uniform(ly distributed)? message|drawn uniformly.
• Results.
  • All four edited sentences occur only in papers/Introduction.md (L93, L97, L133, L163) and its generated .tex. The L97 terms are listed in section 4.
  • There is no book chapter or FULL mirror, and no tracked Explainer file exists outside verification/.
  • Non-target uses: papers/Main.md:218, :228 and :836 (with Main.tex) cite Doukas [22] for different claims (correspondence scope, phase uniqueness), so they are left unchanged.
  • Stale occurrences of "same argument concurrently", "[Mon08; Har04]" or "can examine are short" in .md and .tex: 0.
• §A.32/§A.33 added-line scan. I scanned the four added lines against main (each a whole paragraph) for the meta-commentary, reader-instruction, history-phrase and label-restating families, and for mid-sentence ALL-CAPS outside acronyms: 0 hits. I also checked for added "derived" or "controlled" wording. The only match is the existing L163 text "none is derived from the substratum's dynamics", which is not new wording. tools/voice_check.py passes.

Rebuild (c.6643207092 conditions; AGENTS.md build recipe)

• Command: sh ./build.sh Introduction, which runs pandoc with --include-in-header=tools/unicode-fix.tex for both the .tex and the .pdf.
• Toolchain: pandoc 3.1.3; XeTeX 3.141592653-2.6-0.999995 (TeX Live 2023/Debian); xdvipdfmx 20220710. This is the canonical toolchain recorded in c.6643207092; lmodern.sty is present, so no shim was used and the PDF is not provisional.
• .md, .tex and .pdf come from one source revision. The .tex footer reads % source-sha256: 9be0977202f1aa885ee2e4a817b074950003d61a2dcb8ef93ddbc34c0ee8a43a, which equals sha256sum papers/Introduction.md at head, and tools/staleness_check.py passes.
• The .tex diff against main (374b2ef3) is confined to the four edited paragraphs (re-wrapped) plus that footer line. One rebuild at dd79b705 covers all four edits.
• PDF metrics:

Metric	This build	main PDF
Pages	16	16
Median characters per page	2963.5	2964.0
Min / max characters per page	322 / 3591	322 / 3591
Missing character warnings (separate verbose build log)	0	—

• The extracted text of the committed PDF contains all four new strings.
• A word-level diff of the extracted text against the main PDF shows the four edits plus layout reflow only: page-number positions, one line-end hyphen ("classical-dimension") in the L133 paragraph, and one page break.
• A second independent build is text-identical. The PDF bytes differ only in creation metadata, so a matching page count is not offered as proof of identical output.

Checks run locally (no Lean build, no dispatch)

All of the following passed at head dd79b705 (and earlier at 41d70e79):

• release-gate steps toolchain, staleness, voice, voice-scope, ci-gate-presence, artifact-placement, manifest-drift, claims, duplicate, mirror, citation (109 citations, 0 broken), architecture, dependency-label --strict, coverage, lean-manuscript (census), baseline-label;
• legacy-records (303 records intact);
• v3_verifier --self-test, --corpus and --receipts (53 receipts hold);
• citation-roles.

Not run: lean-axioms, which needs a Lean build and runs in CI.

Push-triggered workflows were inspected before each push. None fires on this branch. The path filters match neither papers/ nor the merged #1159 paths (README.md, papers/introduction_repro/, verification/audits/manuscript/intro-corpus-audit-20261026/), #1159 changed no workflow, and verify.yml and hidden-sector-replay.yml trigger on push only for main. The draft PR runs the ordinary verify.yml pull-request CI. That run tests a synthetic merge and is not an exact-head attestation.

Not done (outside authority)

No merge, no workflow dispatch, no Issue state change, and no edit beyond the four above. S9-I7 is to be recorded as corrected only after this revised text passes review (ruling §2).

https://claude.ai/code/session_011zDyUSyEszk3JJx83uXKKq

---

Generated by Claude Code

[amaybaum]

Independent exact-head review: ACCEPT

Reviewed head dd79b705fab22963676330cbb5685d6702a3c415 against main 374b2ef3d0af1f3233a1d6bc74bee3c32683e3c0 under the owner ruling. The reviewer was a separate model agent that wrote neither the PR nor the earlier source. No material findings.

• Against previously reviewed 41d70e79, the sole source change is the S9-I7 qualification at L97. Main.md L141 treats accessible time order as a requirement. The revised Introduction says the accessible timescales may be short relative to recurrence, preserving the delayed-memory explanation.
• The Markdown diff against current main has only the four authorized changes. R-15 restores the previously landed clause at f5efa7a0 L172. X-2 matches the uniform-prior condition in BH-01 REPORT.md L42–44, L52–54, L91–92 and L297. Har04 is explicitly secondary via Montina. R-15 and Har04 retain the prior reviewed wording. The reviewer independently checked that preservation and did not have access to the primary full texts for a new literature review.
• The reviewer ran the canonical sh ./build.sh Introduction in scratch from byte-checked inputs using Pandoc 3.1.3, XeTeX 2023 and lmodern. No missing glyphs were reported. The rebuilt TeX is byte-identical, and the rebuilt and committed PDFs have identical layout text and identical raster images for all 16 pages at 72 dpi. These are PDF content and rendering checks.
• PR verify run 42174761022 passed: 25 successful jobs and one skipped matrix placeholder.

The revised head is ready for a separate owner merge decision, subject to final head/base and CI guards.