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Editorial corrections: characterization scope (GR, glossary), Breuer–Laine–Piilo citation and backflow direction, ch01 citations, README - #927
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The prerequisites paragraph listed C1–C4 as "necessary as well as sufficient for accessible non-Markovianity". Main's characterization theorem (§3.4) is (ii) ⟺ (iii) with (iii) a per-witness-horizon realization carrying C1, C3 and C4; C2 is deliberately absent from the equivalence, and its necessity for physical hidden sectors is the conditional physical-memory theorem, conditional on the hidden-sector mixing hypothesis (ETH its motivation). The clause now states that equivalence with each direction's witness (readback lemma, §2.3; finite-horizon process dilation, §3.4; both proved in prose, Main:608, :715–717), and the closing sentence drops the "C1–C4" label from "the memory-bearing equivalence". Item (ii) of the same paragraph is untouched (draft #926 edits it). GR.tex regenerated; GR.pdf follows in the final build commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
The "Characterization theorem" entry called it "the framework's central result" and stated it as non-Markovianity iff a realization satisfies "the four conditions C1–C4". Main names S ⟺ D and the universal hidden-memory statement as the core (Main:99), and the characterization is (ii) ⟺ (iii) with (iii) a per-witness-horizon realization carrying C1, C3 and C4, C2 deliberately absent (Main:516; book anchor appendix-b Theorem B.7.6, appendix-c §C.5). The entry now states that equivalence, names what each direction rests on (C4 readback; finite-horizon process dilation), and keeps C2's physical necessity conditional on the mixing hypothesis. It agrees with the glossary's own C1 entry (glossary:25). Mirrored in FULL.md (§A.14); FULL.tex regenerated; FULL.pdf follows in the final build commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…(F21, F22) Attribution (F21). Main:332 attributed "the Breuer-Laine-Piilo criterion" to [3, 4] (Breuer–Petruccione 2002; Rivas–Huelga–Plenio 2010); BLP 2009 had no entry in Main or in the book bibliography. Added as Main [63] (appended; nothing renumbered) and to book/bibliography.md (and its FULL.md copy), from the arXiv record and Crossref: H.-P. Breuer, E.-M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009), doi:10.1103/PhysRevLett.103.210401, arXiv:0908.0238. Main:332 now cites [63]; on the same line the caps emphasis "ANCILLA-ASSISTED" becomes italic (§A.33). ch01:101 / FULL:445 cited BLP as "[9]", which under Main's numbering is Bylicka–Johansson–Acín; it is now the author-year "Breuer, Laine, and Piilo (2009)". Direction (F22). Main:149, Explainer:148 and ch01:101 / FULL:445 stated that divisibility failure (P-indivisibility) is equivalent to information backflow. The corpus establishes one direction: a P-divisible process contracts total-variation distance, so backflow certifies indivisibility (Main:121), and the converse is false — there are P-indivisible pairs with every distance non-increasing (Main:121, translation_probes.py), and system-only backflow is "sufficient evidence of indivisibility, never necessary" (Main:332). Each site now states that direction and that the converse fails. BLP's own claim is described as their abstract states it: backflow as the signature of non-Markovian dynamics. Explainer (superseded) is corrected at :148 only. Other BLP sites checked, unchanged: Explainer:624 (its "cited elsewhere in this framework" now holds), ch18:78 / FULL:4896 and appendix-b:96 / FULL:5883 (consistent with Main:332). Main.tex, Explainer.tex and FULL.tex regenerated; PDFs follow in the final build commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
ch01 carried numeric citations, [2] at :32 and [8] at :85 (with [9] at :101, resolved in the preceding commit), against the author-year book/bibliography.md, where they resolved to nothing. Both date from the chapter's import (334eef0) and follow no current numbering: - [2], "holographic entropy bounds": Main's [2], cited by Main:684 for the same statement — Bao, Carroll and Singh, "The Hilbert space of quantum gravity is locally finite-dimensional", whose argument bounds a region's degrees of freedom by the finite black-hole entropy. It had no book entry; added from the arXiv record and Crossref: Int. J. Mod. Phys. D 26(12), 1743013 (2017), doi:10.1142/S0218271817430131, arXiv:1704.00066. - [8]: introduced (334eef0) as the source of "gravitational-wave measurements at 99.999% agreement", i.e. the GW250114 paper (Main's [8] is Strasberg–Esposito, which does not fit). It is now "(Abac et al. 2025)", the existing book entry, placed at the measurement it supports. Mirrored in FULL.md, including its bibliography copy; FULL.tex regenerated; FULL.pdf follows in the final build commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
The ch07 summary listed "the Page curve from nested trace-out" without the scrambling condition that ch07:12, ch07 §7.6, ch09:127, glossary:113 and appendix-a G11 attach to it (GR Theorem A.9 is conditional on A.8, hence on H-scramble). It now reads "conditional on the scrambling condition H-scramble", in ch07:12's wording. book/README.md has no mirror in FULL.md and no build product. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Built with sh ./build.sh GR Main Explainer and sh ./build.sh --book (pandoc 3.1.3, xelatex, tools/unicode-fix.tex); no dropped glyphs. The build reproduced the committed .tex byte for byte. Page counts are unchanged (GR 86, Main 90, Explainer 68, book 552). Kept as a separate commit so that a conflict with another PR's generated files is resolved by rebuilding from the merged sources, never by hand-merging PDFs. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…e at GR:567, Main:680, ch04:180 R1. The added equivalence quantified over every finite horizon containing a memory witness; Main's (iii) and the process dilation are stated for finite accessible horizons (Main:496, :516, :520). GR:20 and glossary:39 / FULL:6659 now read "every finite accessible horizon", and the glossary's reverse direction "each accessible witness horizon". R2 and N4 (§A.25). Three more sites stated the characterization as "(ii) ⟺ (iii) under (C1)–(C4)" or as an identification with "embedded observation under C1–C4", putting C2 inside the equivalence against Main:516: - GR:567, in the review's wording: (iii) carries (C1), (C3) and (C4); (C2) lies outside the equivalence, its necessity for physical hidden sectors conditional on the mixing hypothesis (ETH its motivation); - Main:680: "(ii) ⟺ (iii), with (iii) carrying (C1), (C3) and (C4) and (C2) outside it"; - ch04:180 / FULL mirror: "embedded observation under C1, C3 and C4 (…; C2's necessity for physical hidden sectors conditional on the mixing hypothesis)". The paragraph's equilibrium argument (ch04:178) already routes C2's failure through C4's, so it still follows. GR:567's later sentence, that the mixing hypothesis holds and the equivalence applies in our universe, is a separate status claim and is unchanged. N1, N2. GR:20 closing: "the ETH condition for C2 necessity" → "the eigenstate thermalization hypothesis, which motivates the mixing hypothesis behind C2 necessity"; and "the memory-bearing sector those conditions characterize" → "that C1, C3 and C4 characterize". N3. Main:332: the ancilla-assisted witness cites [4] again. Rivas, Huelga and Plenio, PRL 105, 050403 (2010; arXiv:0911.4270), introduce the witness monitoring a system's entanglement with a shielded ancilla (checked in the arXiv text). N5. Abac et al. 2025, bibliography.md and its FULL copy: "Physical Review Letters 135: 111403", checked against Crossref for doi:10.1103/kw5g-d732 (vol. 135, issue 11, art. 111403, 2025-09-10). GR.tex, Main.tex and FULL.tex regenerated; PDFs follow in the next commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Built with sh ./build.sh GR Main and sh ./build.sh --book (pandoc 3.1.3, xelatex, tools/unicode-fix.tex); no dropped glyphs; the build reproduced the committed .tex byte for byte. Page counts unchanged (GR 86, Main 90, book 552). Explainer untouched by the preceding commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
B.7.6 stated the characterization as holding "on each finite horizon"
and displayed it "per finite horizon". Main's (iii) quantifies over
every finite accessible horizon long enough to contain a memory witness
(Main:520), and the process dilation behind (ii) ⟹ (iii) is stated for
a finite accessible horizon (Main:496); nothing else in B.7.6 restricts
the horizon ("accessible" there qualifies only non-Markovianity). Both
the statement and the display now say "finite accessible horizon",
as GR:20 and glossary:39 do after the R1 fix.
Mirrored in FULL.md; FULL.tex regenerated; FULL.pdf follows in the next
commit.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Built with sh ./build.sh --book (pandoc 3.1.3, xelatex, tools/unicode-fix.tex); no dropped glyphs; the build reproduced the committed FULL.tex byte for byte. 552 pages, unchanged. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
…efined" The same equivalence as R1 (GR:20, glossary:39, B.7.6) was quantified over every finite horizon at its shorthand sites. Main's (iii) is over finite accessible horizons (Main:520), and the process dilation is stated for a finite accessible horizon (Main:496). None of these sites restricts the horizon in its own sentence. In their own register: - Substratum:111: "⟺ C1/C3/C4 per finite horizon" → "per finite accessible horizon"; - Substratum:126; appendix-b:22 and :406 with their FULL mirrors: "realization per horizon" → "realization per accessible horizon" (Main:608's own wording); - Explainer:378: "on each finite horizon" → "on each finite accessible horizon"; the paragraph's other wording is unchanged; - Explainer:358: "(per finite horizon)" → "(per finite accessible horizon)"; Explainer:1026: "per horizon" → "per accessible horizon". These two state the same equivalence and were found by the re-grep. appendix-b:454 / FULL:6241: "In the redefined form of [Main §3.4]" → "In the form of [Main §3.4]" (§A.30: no self-narration). Substratum.tex, Explainer.tex and FULL.tex regenerated; PDFs follow in the next commit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Built with sh ./build.sh Substratum Explainer and sh ./build.sh --book (pandoc 3.1.3, xelatex, tools/unicode-fix.tex); no dropped glyphs; the build reproduced the committed .tex byte for byte. Page counts unchanged (Substratum 52, Explainer 68, book 552). Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
Reconciliation of #927 after #926 landed. First parent b7cda8d (#927 head), second parent c1cade8 (main). Conflicts and resolution: - papers/GR.md:20 (text): both PRs edit this one line, in disjoint spans. Resolved by keeping both: #927's item (i) clause, its R1/N1/N2 edits and its closing-sentence edits, and #926's canonical-measure insertion in item (ii). Checked mechanically: the merged line minus #926's insertion equals #927's line, and the merged line minus #927's spans equals main's line. - papers/GR.tex, GR.pdf, Explainer.tex, Explainer.pdf, book/The-Incompleteness-of-Observation-FULL.tex, FULL.pdf (generated): not hand-merged; regenerated from the merged sources with sh ./build.sh GR Main Explainer Substratum and sh ./build.sh --book. Main and Substratum rebuilt to identical .tex and PDF text; their committed PDFs are kept, since only build metadata differed. Auto-merged without conflict, checked: book/README.md, FULL.md, appendix-c-objections.md, ch01-observation.md, ch07-gravity.md, papers/Explainer.md. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb
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Independent review: ACCEPT at
b7cda8d2. The reconciliationd6fde588was checked: ACCEPT. Merge: authorized by the owner at exact headd6fde588, as a normal merge commit.This PR makes the owner-approved editorial and bibliographic corrections recorded by the novelty audit (#918,
novelty-v5/AUDIT.md§4, F21–F25 and F27). It adds no theorem, assumption or novelty claim, and changes no scientific classification.d6fde58803ff7409e23a6a267a67cf43631fb172, tree3a872f7e.mainc1cade86(Manuscript consistency: canonical-measure scope, Explainer C₄ and two-branch status, Explainer document status #926) into the reviewed headb7cda8d2.maingives exactly this tree.Corrections
The characterization's proved scope. Accessible non-Markovianity holds exactly when every finite accessible horizon containing a memory witness admits a deterministic realization with C1, C3 and C4.
Breuer–Laine–Piilo.
ch01 citations. The numeric citations become author-year: Bao–Carroll–Singh 2017, and Abac et al. 2025 (PRL 135, 111403).
book/README.md:64. The Page curve summary is now conditional on H-scramble.Voice. "redefined" is removed at Theorem B.7.6.
Review
bb14ab0cb7cda8d2d6fde588(reconciliation with #926)The reconciliation check of
d6fde588established:.texfiles rebuild byte-identically, the stamps match, and the PDF text is identical.main's: GR 86, Main 90, Explainer 69, Substratum 52, book 553.legacy_records_checkreports 303 records intact.CI at
d6fde588: 25 pass, 1 skipped.Recorded, not changed (outside the approved scope)
Related: #918, #925 (merged), #926 (merged).
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https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb