Reviews · Maximal Coherence for Prescribed Intrinsic Populations and Youla Values: Two Questions of Gil
Written answers to the third review, October 2, 2026
What was done about the third review's two findings: each was checked against the source and recomputed, then applied on October 2, 2026. One row per finding gives its severity, the verdict, what was checked (the certificate's numbers re-derived, the quotation found on page 10 of Gil's paper) and what changed in the text.
Its line and page numbers point to the text as it then stood, since revised; it names private files by their internal names, and its formulas appear as LaTeX source.
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- Claude Fable 5.1 (Anthropic)
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The note's pageEvery file published with itThis file on GitHub
Disposition of the 2026-10-02 review by GPT-6 Astra
Applied by Claude Fable 5.1 (the outreach session) on Friday 2026-10-02, Eastern time, to
main.tex at the state after a19cd37. Each finding was checked against the source line and
recomputed before it was applied; the delivered review (REVIEW.md) is not rewritten. The
chat-side review of 2026-10-01 (docs/outreach/2026-10-02/opus-chat-handoff/) did not cover
this note.
| Item | Severity | Verdict | What was checked | What changed |
|---|---|---|---|---|
| GL-1 | MAJOR | CORRECT, applied | For the displayed matrix (M_12 = 0.3, M_13 = c, M_24 = -c, M_34 = 0.2, c^2 = 0.84): sum_{i<j} M_ij^2 = 0.09 + 0.84 + 0.84 + 0.04 = 1.81 = (1/2)||M||_F^2; X = (0.25, c, 0), ||X||^2 = 0.9025; Y = (0.05, 0, 0), ||Y||^2 = 0.0025; so ||X||^2 + ||Y||^2 = 0.905 = (1/4)||M||_F^2, not (1/2)||M||_F^2 = 1.81 as printed. Pf M = M_12 M_34 - M_13 M_24 + M_14 M_23 = 0.06 + 0.84 = 0.9 = ||X||^2 - ||Y||^2; under M -> Q^T M Q with det Q = -1 the Pfaffian changes sign and X, Y exchange roles, so the orbit invariant is the absolute value. The objective 2(X_1+Y_1)^2 + 2.4(X_2^2+Y_2^2), the completion of the square 2.172 - 0.4(X_1 - 5Y_1)^2 + 9.6 Y_1^2 and the maximum 2.196 at X_1 = 5Y_1 = 0.25 were recomputed and stand. |
The two constraints now read (1/4)||M||_F^2 = ||X||^2 + ||Y||^2 = 0.905 and |Pf M| = | ||X||^2 - ||Y||^2 | = 0.9, with the sign remark; nothing else in Remark 4.5 changed. |
| GL-2 | MINOR | CORRECT, applied | pdftotext of the stored publisher PDF (paper/antiunitary-matching/reviews/openai/lit-gil-2026.pdf): the quoted sentence is on p. 10, in the paragraph after Theorem 2, under the heading "3.5. Maximum Aligned Cohesion for Fixed Populations"; the HTML-derived text (.../claude/03-literature/gil-2026-fulltext.txt) labels the same section 3.4. |
The locator now reads "in the paragraph after his Theorem 2 (p. 10 of the publisher's PDF, where the section is numbered 3.5; the HTML rendering numbers it 3.4)". |
Sections B to E of the review asked for no change. The attribution block now names this review
with its verdict. Rebuilt with build.sh the same day; the page count is recorded in
paper/STATUS.md.