Written answers to the second review, October 1, 2026

Disposition of the same-family self-review (REPORT.md, commit b8a7569)

Applied 2026-10-01, 20:55 to 21:3x EDT (America/New_York), by the same session after the report was committed. Every item is CORRECT (applied), WRONG (not applied, with the reason), or NOTED. The report's text stands as delivered; its addendum below the verdict records the Astra re-check.

MAJOR

#	Finding	Verdict	What was done
1	The abstract states the margin 2 - a >= 2h/(B - 1) without its B > 1 + h condition; for 1 < B < 1 + h the formula exceeds 2 and the inequality is the reverse of the truth (a > 2 - 2h/(B - 1) for constant strain, by the barrier-from-below argument; confirmed by integration)	CORRECT, applied	abstract: "whenever the running supremum B ... exceeds 1 + h ... and with a <= 0 otherwise"; "the margin, where B > 1 + h, is proportional to h"; Section 1 paragraph 3 conditioned the same way; Remark 3.5 says "where B > 1 + h"; the attempt's remark 3 and the paper README carry the same condition and the reason the formula fails below it
2	Lemma 4.2 claims S_n = 0 and X N_s constant for X >= X_v; the proof (z-independent pressure, heat form of E) covers X >= X_b, and on [X_v, X_b) the canonical pressure integrates across the annulus swirl	CORRECT, applied	statement: "hence, for X >= X_b, a function of (r, t) alone. Then for X >= X_b ..."; proof opens "For X >= X_b ..." with a parenthesis saying nothing is claimed on [X_v, X_b); the attempt's relaxed form and its proof say X_b
3	The Rayleigh and Ludwieg reading of the cone (Duraiswami p. 21, with d log Gamma / d log X = 1 - a/2; p. 22; p. 25) and the characteristic curve D eta + d U = 0 set by the sign of U(X, 0) (p. 6) are presented as the paper's own	CORRECT, applied	Remark 3.6 credits the reading to Duraiswami pp. 21-22 with the circulation slope; Section 1's "Two features" paragraph credits the curve to p. 6 and says Lemma 3.1 is what it becomes on the dividing plane; Section 6's Duraiswami sentence lists both; the attempt's section 0, remarks 1 and 4, and section 4 carry the same credits; the abstract is unchanged (the credit lives in the text)

MINOR

#	Finding	Verdict	What was done
4	X_0 = sup{X < X_1 : a(X) <= a_*} can be the supremum of an empty set when a_* = 0	CORRECT, applied	(X_0, X_1] is now the maximal interval ending at X_1 on which a > a_*, X_0 >= 0; X_0 = 0 forces a_* = 0 because a(0+) = 0; same in the attempt, with the old wording noted
5	"(w - 1)(1 - a/2) < B - 1 <= h" is not strict at B = 1, w = 1	CORRECT, applied	"<=" in the paper and the attempt (the conclusion rests on -(1 - a/2) a < 0, as the parenthetical said)
6	Theorem 3.2(4): when a(X_a, 0) <= 0 the clause of Proposition 4.10(ii) that fails is a(X_a, eta) > 0, and v_s is undefined	CORRECT, applied	statement names the two cases; the proof's (4) names them; the attempt's section 0, Theorem I(4) and its proof name them
7	Lemma 3.1's smoothness and phi > 0 are Theorem 4.6(i), not (ii)	CORRECT, applied	Theorem 3.2(4) reads "Theorem 4.6(i), (ii) and (13)"; the proof cites (i); same in the attempt
8	"using (13) on the whole segment the average runs over" is not what gives W(X, 0) = 1 - w	CORRECT, applied	replaced by the reason (the 2 D eta A_X(U) term carries the factor eta); same in the attempt
9	"a nonnegative zeroth-order coefficient" in the abstract: the displayed second form has -hX/2	CORRECT, applied	"whose zeroth-order term has the sign that forbids an interior maximum"
10	"no energy source at the inner edge of the annulus" overreaches; the theorem is about the point (X_a, 0)	CORRECT, applied	"at the dividing-plane point of the inner edge"; the attempt's section 0 says "at that point"
11	Remark 3.5: "the margin near the axis is 2h/3" is the bound, not the margin	CORRECT, applied	"the bound (15) on the margin is 2h/3 < 1/150 near the axis (the margin itself is close to 2 there, since a -> 0 at the axis)"; same in the attempt
12	The Duraiswami quotation on p. 20 drops "The leading profile of the OpenAI 2026"	CORRECT, applied	quoted as written, in the paper and in the attempt's remark 8
13	"assert no uniform limit as j -> 0" reverses Lei and Ren's "no uniform limit as j -> 0 is asserted"; their p. 109 sentence is the closest statement to the barrier	CORRECT, applied	"do not assert a uniform limit as j -> 0 [p. 108]"; the p. 109 sentence quoted in Section 6; the attempt's receipt row records it
14	"that the construction's critics have asked about" has no source	CORRECT, applied	clause dropped ("instances of a loss of uniformity as h -> 0")
15	"and nothing about the Clay alternatives" is itself a Clay mention, against the house rule for this paper	CORRECT, applied	clause deleted; "nothing about the unforced problem" stays
16	"two inequalities on p_s": (4.21) is stated in the cone coordinates (P_c, J_c, v_s)	CORRECT, applied	"the manuscript's two inequalities (4.21) on the cone coordinates (P_c, J_c, v_s), which are p_s resolved in the shear frame together with v_s"
17	Lei and Ren's arXiv title has "Part I:"	CORRECT, applied	bibliography matches arXiv
18	paper/common/README.md lacks this paper in its set table and says "two of the mathematics papers"	CORRECT, applied	row added (marked as an owner-facing sample, not public); "three"; pattern item 5 reworded for a paper written after the night of 2026-09-28/29
19	Remark 3.4 could locate where j_0 > 0 enters the manuscript's existence argument	CORRECT, applied as a hedged observation	one sentence added: Proposition B.2's contraction is set up around the datum phi_0 of (B.3), defined for j_0 = 0 as well; j_0 > 0 is used in Section B.1 (Z^* > 0 at the zero of H^*) and in Proposition B.3's exit alternative (B.19); "we have not checked the existence argument at j_0 = 0 and claim nothing about it"
20a	A bare run of the checker rewrites the committed receipt with a fresh timestamp	CORRECT, applied	--json now defaults to None (print only); the receipt is regenerated with --json checks/midplane_barrier.json; docstring, attempt section 6, paper README and the paper's verification record say so; the receipt was regenerated once with the new B1_note field (53 flags unchanged)
20b	At h = 0, w = 1 + X/2 the sampled sup_a prints as 2.0 while a_below_2 is read from the sign of D_X H	CORRECT, applied	the paper's verification record item 2 and the attempt's section 6 say how a < 2 is read; the receipt carries B1_note
20c	main.aux, main.out untracked in the paper directory	CORRECT, applied	.gitignore added, copied from paper/unfolded-zeros/

Also applied, from the report's header and the house pattern: the attribution block names both reviews in one clause each (the self-review first, as a fresh instance of the same model line, with its date; the cross-vendor review by GPT-6 Astra with its four findings) and keeps "No human mathematician has reviewed this paper"; the verification record says the same-family reviewer reran the checker and the arena; "the reviewer" became "both reviewers" where both did the check.

The Astra items re-checked against the paper (REPORT.md addendum)

Every item of docs/research/2026-10-01-ns-open-map/reviews/astra/DISPOSITION.md that bears on the paper (A1-A9, B1-B6, C1-C3, D1-D4) was read against the paper's text. All are applied. Three were applied incompletely, and all three are closed by the edits above:

Astra item	What was incomplete	Closed by
A4 (the margin WRONG as an unrestricted formula; the valid statement is piecewise)	applied to Theorem 3.2(3) but the abstract and Section 1 kept the unconditioned formula	item 1
A5 (the inner-edge contradiction with a case split; never write v_s at a = 0)	applied to Theorem 3.2(2) and (4) for Theorem 4.6(iii), but the Proposition 4.10(ii) clause still named v_s(X_a, eta) > 2 + c_ex in the a <= 0 case	item 6
B3 ("Beyond X_b, use the heat exterior ... X N_s = K throughout that exterior")	the paper's Lemma 4.2 wrote X_v for the range	item 2

The F items (Astra's response to Claude's review of its attempts) concern reviews/claude/REVIEW-astra.md, not the paper; a grep confirms the three wording repairs landed there. reviews/astra/REVIEW.md and reviews/astra/LAST-MESSAGE.md differ only by a trailing newline.

Outcome: no open item. The paper carries both reviews; the research record carries the repairs where they bear; the pair of reviews the house pattern asks for is complete.

Consistency pass, 2026-10-01 (fresh Claude Opus 5.5 agent, directed by the Claude Fable 5.1 outreach thread; the heading said 2026-10-02, the UTC date, until the final review of 2026-10-02 caught it: the pass ran and was committed on 2026-10-01 in Eastern time, 7c3931b at 23:27 EDT)

Scope: the five checks of the brief and nothing else, namely (1) the abstract and Section 1 against the results they summarize, (2) every quotation verbatim against its source, (3) every page, equation and result number attributed to a source, (4) the attribution block against paper/common/README.md, and (5) US English, no em dash, no statement of the Clay alternatives; the sources are the five PDFs of the bibliography (the OpenAI manuscript at the pinned SHA-256), read with pdftotext -layout and PyMuPDF, and the quotations were also matched word for word against the cited page by a scratch script, with symbols, first-letter case and punctuation checked by eye.

#	check	item checked	source and page	command or method	finding	verdict	what was done
1	3	printed page numbers of the OpenAI manuscript	openai-ns.pdf, 166 pp.	pdftotext -layout -f N -l N, running head read on PDF pp. 1, 2, 6, 20, 26, 74, 108, 127, 144, 146, 166	printed number equals PDF page on every sampled page	NO FINDING	none
2	3	printed page numbers of Duraiswami	duraiswami-2609.17642.pdf, 31 pp.	same, folios on pp. 1, 2, 3, 5, 6, 11, 20, 21, 22, 26, 31	equal	NO FINDING	none
3	3	printed page numbers of Lei and Ren	leiren-2609.35406v2.pdf, 245 pp.	same, folios on pp. 1-3, 5, 6, 11, 20-22, 26, 74, 107-109, 127, 141, 144, 146, 149, 151, 245	equal	NO FINDING	none
4	3	printed page numbers of Constantin, Ignatova and Vicol	civ-2609.20803v2.pdf, 34 pp.	same, running heads on pp. 2, 6, 11, 20, 22, 26, 34	equal	NO FINDING	none
5	3	printed page numbers of Liu	liu-2609.14292v1.pdf, 32 pp.	same, folios on pp. 1-3, 5, 6, 11, 20-22, 26, 32	equal	NO FINDING	none
6	1	abstract: "On a stress-free core whose dividing plane carries no axial velocity"	Lemma 3.1	read against the hypotheses	the lemma needs the first equation of (4.13) on [0, X_a] and U(X, 0) = 0; a stress-free core gives the first	NO FINDING	none
7	1	abstract: "a linear second-order equation whose zeroth-order term has the sign that forbids an interior maximum"	(14), the equation of Lemma 3.1	read	the zeroth-order coefficient is -hX/2 <= 0 for every h >= 0	NO FINDING	none
8	1	abstract: "strictly increasing"; "the swirl shear ... stays below 2 there"	Theorem 3.2(1)	read	D_X H > 0 and a < 2 on 0 < X <= X_a, strict as stated	NO FINDING	none
9	1	abstract: "2-a >= 2h/(B-1) whenever the running supremum B ... exceeds 1+h ... and with a <= 0 otherwise"	Theorem 3.2(3) and (15)	case by case against A_*(B)	B > 1+h strict; B <= 1+h gives a <= 0; both inequalities nonstrict, as in (15)	NO FINDING	none
10	1	abstract: "the sign of Rayleigh's centrifugal criterion that forbids growth, with Ludwieg's axial-shear term inactive"	Theorem 3.2(1)-(2); Remark 3.6	read	a < 2 and b_s = 0 on the plane	NO FINDING	none
11	1	abstract: "no energy source at the dividing-plane point of the inner edge"; "clause (iii) ... fails at that point"	Theorem 3.2(4)	read, both signs of a(X_a, 0)	the point is (X_a, 0); clause (iii) fails in both cases (the bound on a, or the bound on v_s - 2)	NO FINDING	none
12	1	abstract: "The sign holds for every h >= 0 in the equation; the margin, where B > 1+h, is proportional to h"	Remark 3.5	read	same quantifier and same condition	NO FINDING	none
13	1	abstract: the moment obstruction holds "on every horizontal slice" and "excludes every reflection-symmetric profile"	Proposition 4.1	read	every eta in [-1, 1]; hypothesis Theorem 4.6(v)	NO FINDING	none
14	1	abstract: "for h > 0, the vanishing of the coefficient of the r^{-1} axial stress tail alone forces the identity"	Proposition 4.3 and its proof	read	h > 0 matches; the hypothesis U odd is not repeated, but the clause sits in the reflection-symmetric sentence, and the proof's own parenthetical shows oddness is not used to force M_inf = 0 and so S_inf = 0	NO FINDING	none
15	1	Section 1, paragraph 1: the manuscript's result and its scalings	manuscript pp. 1-2 (abstract, Theorem 1.1) and p. 4	pdftotext and grep	"every positive viscosity", "starts from rest", "uniformly bounded kinetic energy"; tau^{1/2}, tau^{1/2-h} with 0 < h < 1/100, and tau^{-1/2-h} are on p. 4, inside the cited pp. 4-5	NO FINDING	none
16	1	Section 1, paragraph 2: "U^* = 4 eta + j_0 with 0 < j_0 <= .05"	(B.1), p. 144	PyMuPDF text	"Choose 0 < j0 <= .05 small"; strictness matches	NO FINDING	none
17	1	Section 1, paragraph 3: Theorem 3.2 restated (strict increase; a < 2; the margin when B > 1+h; a <= 0 when B <= 1+h; v_s = a < 2 wherever defined; the two bounds of Theorem 4.6(iii) "cannot both hold there")	Theorem 3.2(1)-(4)	case by case	matches	NO FINDING	none
18	1	Section 1 paragraph 3, Section 2.2, Theorem 3.2(4) and README item 2: lambda_0^2 called "the growth rate", and "the growth rate is 2F_0^2(a-2) < 0"	manuscript p. 74 (the unnumbered display above (7.1) defines lambda_0^2 = -2F_0N_theta(2F_0N_theta + abs(g_0)) > 0 and says "take lambda_0 > 0"; the next sentence gives lambda_0^2 = 2aF_0^2(1 - 2/v_s)); p. 22 (lambda is "the positive reference growth rate"); Duraiswami p. 22 ("the rate is lambda_0 = F sqrt(2a(1 - 2/v_s))")	PyMuPDF text of the three pages	location confirmed, and 2F_0^2(a - 2) < 0 for 0 < a < 2 confirmed from the p. 74 formula; but the rate is lambda_0, so the text gave the rate itself a negative value where the truth is lambda_0^2 < 0, no real rate	CORRECT, applied	"squared growth rate" in Section 1 (twice), in Theorem 3.2(4) and in README item 2; Section 2.2 now reads "the square of the reference growth rate lambda_0 of a pulse, displayed just above equation (7.1), is"
19	1	Section 1, paragraph 4: "the margin by which the symmetric core misses the Rayleigh threshold is proportional to h"	Remark 3.5; Theorem 3.2(3)	case by case	no B > 1+h condition; for B <= 1+h the bound is a <= 0 (margin at least 2), not proportional to h	CORRECT, applied	"but where B > 1+h the margin ... is proportional to h", as in the abstract and Remark 3.5
20	1	Section 1, paragraph 4: "needs only that u_z vanish on the dividing plane"; H_c "vanishes on that plane exactly when U does"	proof of Lemma 3.1; Remark 3.3	read	matches	NO FINDING	none
21	1	Section 1, paragraph 5: the scope sentence (one hypothesis; Theorem 4.6 as imposed; the summed background; the unforced problem)	Remark 3.7	read	matches	NO FINDING	none
22	1 (found in passing, outside the abstract and Section 1)	Section 5 item 2, "the constant-strain margins approach 2h/(w-1) from below", and the Figure 1 caption, "approached from below"	Theorem 3.2(3); Remark 3.5; scripts/make_figures.py (the right panel plots 2 - a)	the figure's integrator rerun in the scratchpad at w = 4	the margin falls from about 2 to its bound and stays above it: h = 1/100, minimum 0.006905 > 2h/3 = 0.006667; h = 1/10, 0.068969 > 0.066667; Remark 3.5's "1.99310 against the bound 1.99333" is the same fact seen from a	CORRECT, applied	"from above" in both places
23	2	abstract quotation 1, "slightly asymmetric"	manuscript p. 5	word-sequence match on the cited page; symbols, case and punctuation by eye	verbatim	NO FINDING	none
24	2	abstract quotation 2, "with a small upward bias and nonzero velocity at z=0"	p. 5	same	verbatim	NO FINDING	none
25	2	abstract quotation 3, "this transport would vanish at z=0"	p. 5	same	verbatim	NO FINDING	none
26	2	abstract quotation 4, "symmetry would also impose u_z(r,0,t)=0, leaving no radial shear of the axial velocity to compensate"	p. 5	same	words verbatim, but the source sentence opens "Symmetry", capitalized	CORRECT, applied (made verbatim)	the opening quotation mark moved past the word: and symmetry "would also impose ..."
27	2	Section 1 block quotation (four sentences)	p. 5	same	verbatim, symbols included	NO FINDING	none
28	2	Section 1, Duraiswami: "a profile with U odd in eta has U(X,0)=0, so S(inf,0) = -int E(X,0)^2/2 dX"	Duraiswami p. 20	same	words verbatim, but the integral's limits 0 and infinity were dropped inside the quotation	CORRECT, applied (made verbatim)	limits restored, -\int_0^\infty E(X,0)^2/2\,dX
29	2	Section 1, Lei and Ren: "The positive shift j separates ... contribution there"	Lei and Ren p. 108 (cited pp. 107-109)	same	verbatim	NO FINDING	none
30	2	Section 2.2: "required by the viscous waves"	manuscript p. 31	same	verbatim	NO FINDING	none
31	2	Section 2.3: the Theorem 4.6(ii) quotation	p. 33	same	verbatim	NO FINDING	none
32	2	Section 2.3: the Theorem 4.6(iii) quotation	p. 33	same	verbatim	NO FINDING	none
33	2	Section 2.3, item (v): "for some fixed X_v in (X_a, X_b), U=V_0=0 throughout [X_v, inf)."	p. 33	same	words verbatim, but the source goes on ", including the outer collar [Xv, Xb].", so the period inside the closing mark was not the source's	CORRECT, applied (made verbatim)	the period moved after the citation, the paper's own pattern for a quotation followed by a citation
34	2	Section 2.3: Proposition 4.10(ii), "at its inner endpoint, a(X_a, eta) > 0 and v_s(X_a, eta) > 2 + c_ex for a constant c_ex > 0"	p. 37	same	words verbatim, but the source opens "At", capitalized	CORRECT, applied (made verbatim)	"at its inner endpoint" moved outside the quotation
35	2	Remark 3.6: "the pulses grow only" followed by "if angular velocity decreases sufficiently rapidly with radius"	p. 6	same	words verbatim (the source opens "If"); the source gives a sufficient mechanism and adds "In the full flow, axial shear also contributes to the amplification", so "only" reversed the implication attributed to "the manuscript's words"	CORRECT, applied (made verbatim)	"only" deleted and "if" moved outside the quotation
36	2	Section 4, Duraiswami: "The leading profile of the OpenAI 2026 construction ... axial through-flow"	Duraiswami p. 20	same	verbatim	NO FINDING	none
37	2	Section 6, Lei and Ren: "If the shift were zero, ... at the same point"	Lei and Ren p. 109	same	verbatim	NO FINDING	none
38	2	the paper's own phrases in quotation marks: "The sign of Rayleigh's criterion" (Section 1), "no tail" (Section 4), "new" (Section 6)	none, not attributed	read	mentions of the paper's own wording, outside check 2	NO FINDING	none
39	3	"(4.1), p. 24", closing the sentence that also defines D_X	manuscript pp. 24-25	equation labels located at line ends page by page; PyMuPDF text	(4.1) prints on p. 24, but D_X f = X d_X f is defined on p. 25	CORRECT, applied	[(4.1), p. 24; p. 25]
40	3	"(4.3)-(4.4), p. 25", closing the sentence "phi smooth and positive; ... F = phi/C, not E"	pp. 25, 26, 33	same	(4.3), (4.4) and the smooth F are on p. 25; phi > 0 is stated on p. 26 (before (4.8)) and in Theorem 4.6(i)	CORRECT, applied	[(4.3)-(4.4), p. 25; p. 26]
41	3	"(4.6)-(4.7), p. 26"	pp. 25-26	same	(4.6), the radial average, prints at the foot of p. 25	CORRECT, applied	[(4.6), p. 25; (4.7), p. 26]
42	3	(4.2) and Lemma 4.1, p. 25; (4.8), (4.9)-(4.10), the axis fact l = 1 + XF_X/F and the q^{2h} viscosity ratio, p. 26; (4.11), (4.13), (4.14) and Proposition 4.2, p. 27; (4.15), (4.16), Lemma 4.3 and the integration by parts, p. 28; (4.20) and the moment-tail paragraph, p. 30; (4.21), p. 31; Theorem 4.6, pp. 32-34, with (i), (ii), (iii), (v), (4.25) and (4.28)-(4.29) on p. 33; Lemma A.8, p. 141	manuscript	same	every label and statement is on the cited page	NO FINDING	none
43	3	Proposition 4.10(ii), p. 37	pp. 36-37	same	the proposition opens on p. 36 and clause (ii) is on p. 37	NO FINDING	none
44	3	the display above (7.1), p. 74	p. 74	same	resolves (row 18)	NO FINDING (the wording is fixed under row 18)	none
45	3	Appendix B: (B.1) and Section B.1, p. 144; (B.3), p. 145; Proposition B.2, p. 146; Proposition B.3, p. 148, with (B.19), p. 149, and its two alternatives, pp. 149-150; (B.21), p. 149; (B.25), p. 151	pp. 144-151	same	all resolve; (B.25) reads D_X p_{1,r} = X S_{q,r}/L - l_r p_{1,r}; (B.21) bounds the transport term below by .95 Lambda L chi - C sigma_*/Lambda, so Remark 3.6's "of size Lambda L" holds up to the fixed factor chi at eta = 0	NO FINDING	none
46	3	Remark 3.4: "the datum phi_0 of (B.3)"	p. 145, (B.3); p. 146, (B.12)	same	(B.3) defines the azimuthal datum phi^* = exp(Lambda int_0^eta zeta^*) and xi_0 = Lambda zeta^*; there is no phi_0 in it, and Proposition B.2 writes phi = phi^* Phi	CORRECT, applied	"the datum phi^* of (B.3)"
47	3	Remark 3.4: "the existence of an actual symmetric solution ... is what its Proposition B.2 provides for its own datum with j_0 > 0"	p. 146	read	Proposition B.2 provides a solution for the Section B.1 datum with j_0 > 0, which is not symmetric	CORRECT, applied	"the existence of an actual solution ... and is not proved here for the symmetric datum j_0 = 0"
48	3	Remark 3.4: "the manuscript's own axis data at j_0 = 0 (U^* = 4 eta, phi^* = 1, an even pressure datum)"	pp. 144-145	read	U^* = 4 eta is (B.1) at j_0 = 0, but the manuscript's azimuthal datum is the phi^* of (B.3), not 1	CORRECT, applied	"the manuscript's axial datum at j_0 = 0, U^* = 4 eta, together with phi^* = 1 and an even pressure datum"
49	3	Duraiswami p. 6 (characteristics emanate from the curve D eta + dU = 0, the sign of U(X, 0) deciding which way information leaves the plane); pp. 20-22 (the moment obstruction, p. 20; the cone failure and the Rayleigh and Ludwieg reading with d log Gamma / d log X = 1 - a/2, p. 21; the growth condition, p. 22); the abstract's p. 20; Section 6's pp. 6, 20-22	Duraiswami	PyMuPDF text	all resolve	NO FINDING	none
50	3	Remark 3.7: "Duraiswami's observation that the cone fails on the whole annulus of his computed profiles [p. 21]"	Duraiswami p. 21	read	p. 21: the cone "fails on every matched profile", which is admissible "on at most 7% of the annulus"; on his construction-style annulus it "holds in the quiet stages", and on the power-law stage "the admissible cone holds outright"; that is not failure on the whole annulus	CORRECT, applied	"the cone condition fails on every smooth profile he computed", the wording of Section 1
51	3	Lei and Ren pp. 107-109; (8.9)-(8.10); p. 108, "no uniform limit as j to 0 is asserted"; p. 109	Lei and Ren	PyMuPDF text; table of contents	(8.6)-(8.8) on p. 107; (8.9), (8.10), the "no uniform limit" sentence and the first quotation on p. 108; the second quotation on p. 109; all in Section 8, which starts on p. 105	NO FINDING	none
52	3	Constantin, Ignatova and Vicol, Remark 2.6 and footnote 9, p. 11	CIV p. 11	PyMuPDF text	Remark 2.6 assumes u_z(0, t_0) != 0; footnote 9 gives u_z(0, t) = j_0 (-t)^{-1/2-h}, which is j_0 tau^{-A}; both on p. 11	NO FINDING	none
53	3	Liu, cited without a page: his conditional families "do not touch the symmetric case"	Liu, Theorem 3.1(i) and p. 19	grep and PyMuPDF text	his designs take G = 4 + j_0 with j_0 > 0, and an auxiliary core at gamma = 0 is used "only for this parity estimate, not as a completed exit" (p. 19); consistent	NO FINDING	none
54	3	items in the brief that main.tex does not cite: the manuscript's Lemma A.1 (stated p. 126, proof p. 127), Duraiswami pp. 1-2, Lei and Ren Section 2.5 (p. 16)	sources	grep of main.tex	nothing in the paper to resolve	NO FINDING	none
55	4	pattern items 1 and 2 (who wrote and who directed, and what each did; where the questions came from)	paper/common/README.md	read	present	NO FINDING	none
56	4	pattern item 3: both reviews named by model and vendor, a verdict in one clause each, every finding applied	README pattern; REPORT.md ("0 BLOCKING"; "Proved: yes"); this file (3 MAJOR; 17 MINOR, items 4-20)	read and count	the self-review is named (a fresh instance of Claude Fable 5.1, 2026-10-01, Anthropic by the block's first sentence) with the clause "found no blocking error, three major items ... and seventeen minor ones"; the cross-vendor review is named (GPT-6 Astra, OpenAI, Codex CLI) with "found the barrier theorem correct, ..."; the counts match; the tally form is the set's practice (the unfolded-zeros block states its self-review the same way)	NO FINDING	none
57	4	pattern item 4	main.tex	grep	"No human mathematician has reviewed this paper." verbatim	NO FINDING	none
58	4	pattern item 5: the place in the set, and no paper called "the first"	main.tex; the README's set table	grep for "first"	"the only manuscript so far from the harness's second problem lane, written two days after the three manuscripts of 2026-09-28/29"; "first" occurs only in "ranked that question first" and "the first draft"	NO FINDING	none
59	4	pattern item 5: "written without reading the others"	no record this pass can read	none	the block states independence from the symmetric-core literature instead; whether the writing session read the three earlier manuscripts is not established by any file available here, so nothing was added	NOT CHECKABLE	none
60	5	British spellings	main.tex	Python scan for -our, -tre, -lled and -lling, -ise and -yse, -ogue, defence, licence, and the brief's list	the only hits are "characteristic(s)", "otherwise", "piecewise" and "rises"; "gray" in the caption is US	NO FINDING	none
61	5	em dashes	main.tex	grep for U+2014 and for three hyphens; scan for any non-ASCII character	none; main.tex is pure ASCII	NO FINDING	none
62	5	the Clay alternatives, the Millennium problem, the unforced problem	main.tex	grep for Clay, Millenn, alternative, unforced, (A), (B), (C)	only "nothing about the unforced problem", which the rule allows; the other hits are the math A_*(B) and "exit alternative (B.19)"	NO FINDING	none

Build: bash paper/ns-dividing-plane/build.sh exited 0 with "Built main.pdf", and main.pdf has 12 pages (the TeX log of the same source built with --keep-logs in the scratchpad reads "Output written on main.xdv (12 pages, 96268 bytes)"); its two warnings, an overfull box of 0.36717pt at line 141 and an underfull box of badness 2277 at lines 288-289, are those of the committed version built the same way, so no warning is new.