Route-COBV v1: CLAY_OBLIGATIONS.md checked clause by clause against its own sources

Leg 384. Verification class. CEILING: TIER 2. No link of the L1 → L4 chain moved; CLAY_OBLIGATIONS.md §6's two no-method obligations stay OPEN; Clay stays ~0.05%.

• Runner: experiments/p2_route_cobv_v1.py
• Curated data: writeup/data/p2_route_cobv_v1.json
• Evidence / figure: experiments/p2_route_cobv_v1_evidence.py → fig105 (writeup/figures/fig105_route_cobv_v1.png), rebuilt from the JSON alone
• Document under audit: CLAY_OBLIGATIONS.md, sha256 f47a73ac27903d79f63435ba8f4726245059e0c09f931e15cb9c0ed7a2923bde (read only, never edited by this leg
• Landed edit under test: a962e4a (merged in d65419c)
• Source of truth for item (i): writeup/data/p2_route_cloc_v1.json (leg 381, 7aecf78)) read, never written

1. The pre-committed gate, and its answer

Does every checked clause either verify against its primary source / landed record, or get reported with the exact discrepancy verbatim? yes → The obligations document graduates from DRAFT-UNVERIFIED clause by clause, on integration's edit. no → A source is unreachable: bank the refusal as a refusal; an unverifiable clause is recorded as exactly that.

The gate answers YES. 23 checks ran; 17 MATCH, 6 MISMATCH, 0 UNVERIFIED; the unverifiable_clauses list is empty. The Clay Institute's rules were reachable (HTTP 200 on both the rules page (79 319 bytes) and the 2018-revision PDF (43 263 bytes, sha256 9b5003745c0ae7268dc7769f83e1c61eaca674f28631f1df2cd8400976640b2a)) so the no branch never engaged and no refusal needed banking.

Reproducibility note. Re-running the fetch reproduces every verdict, every count and the document digest exactly, but the rules page's HTML byte-digest changes between fetches (cache-busting markup); its extracted text is invariant at 4 040 characters, and the PDF's digest above is stable. The PDF digest is therefore the load-bearing one, and the JSON's self_hash, which covers the volatile page digest, is deliberately not quoted as a fixed value anywhere in this write-up.

2. The instrument control: proving the counts are measurements

A leg this cycle found a fabricated zero in its own instrument, a variable initialised to 0.0 and never written. A mismatch count has exactly that failure shape, so every one of the 23 checks carries its own targeted plant, by name, and the plants run in both directions:

• a MATCH is only reported for a check whose corrupt-plant made it read MISMATCH;
• a MISMATCH is only reported for a check whose repair-plant made it read MATCH.

23 controls run, 23 fired, 0 failed. Three plants did not fire on the first attempt and each exposed a real defect in the checker rather than in the document: I10's plant failed because the banked rows step 2 decades, not 1, so the naive first difference was double the per-decade increment and the "cube of" branch could never trigger; that repair turned I10 from a false MATCH into a genuine finding. The other two (I5, III2) failed because a raw str.replace could not cross a markdown line wrap and a PDF non-breaking space respectively. A green light that could not go red was, in each case, the bug.

Two normalisation facts made the mechanical read possible at all: pdftotext -layout emits U+00A0 between every word of the rules PDF, and the document's clauses wrap across markdown > blockquote markers, so norm() strips both before matching.

3. Item (i): the landed block against leg 381's check_D verdicts

15 checks (I1–I15). 12 MATCH, 3 MISMATCH. Confirmed mechanically: the excision of with f ≡ 0 (0 occurrences remain in the target paragraph); the 4 CONFIRMED / 1 CORRECTED / 1 REFUTED counts, recomputed from the JSON's six ledger rows and equal to the document's stated counts; the (b)→(C) labelling fix; the not-a-shortcut clause; §4's VERIFIED AS A SPECIFICATION — leg 381 (7aecf78), gate YES header with its three numbered amendments; the §4-stays-OPEN-until-DTOL rule; §7 marked STILL UNCHECKED; §8 ask #1 recorded SATISFIED; and (D) named-but-not-authorised.

Out of scope, recorded as such, not as verified: the DTOL numbers in §4 amendment 1 (0.8686, 3.35, 0.434) and §8 ask #1's SATISFIED ruling are not present in p2_route_cloc_v1.json. They lie outside this leg's declared comparison source and are banked as unchecked here.

I8, the quoted verification tolerance is the single best row

The document (line 128): "repaired it with the truncated law … verified to 2.6e-5". 2.6e-5 is the abs_error of the α = 0.8 row alone (2.577133230399764e-05). The JSON's own max_abs_error over its four banked rows is 0.0256893924479335 at α = 1.4: larger by a factor 988.05. At α = 1, which is the exponent §4 is actually about, the error is 0.000264923221459137. Panel B of fig105 draws all four rows against both lines.

I10, 326.875 per decade is the increment of the cube, not of the norm

The document (line 158): "the critical L³ tail grows 326.875 per decade of window, constant to 7.4e-10". The JSON's own reading says "the cube of the critical-norm tail grows by a constant amount per decade". 326.87521405120924 is the per-decade increment of tail_L3_cubed (653.7456, 1307.496, 1961.2465, 2614.9969, 3268.7473); the L³ norm itself runs 8.679 → 14.841 across the same five banked rows. The three words "the cube of" were dropped in transcription. The document's qualitative conclusion is unaffected (the tail is still log-divergent and still never small) but the number as printed is not the number of the quantity it is attached to. Panel C.

I15, reverse direction: a JSON verdict the document does not carry

Running the comparison the other way (every JSON ledger row → is it reflected in the document?) found one. On the reviewer's clause "decaying faster than any polynomial", leg 381 banked CONFIRMED AND STRENGTHENED: Fefferman's condition (4) bounds every derivative, |∂ₓ^α u°(x)| ≤ C_{αK}(1+|x|)^{−K} for any α and K, and the JSON says in terms that the reviewer's phrase understates it. The landed document says only that decay "stands as stated", folding a strengthening into a plain confirmation.

4. Item (ii): §2's four screen rows, machine-read

All four MATCH. Nothing here was transcribed: solver/dssp_screen.py was imported and executed read-only, and the cited legs' JSONs were parsed.

Provenance finding on row 1 (recorded on a MATCHing check, not a mismatch). The row cites "legs 253, 341". Leg 341's record carries the claim verbatim. No writeup/data/*.json declares leg 253, so that half of the citation has no machine-readable landed record; the operative encoding is solver/dssp_screen.py (legs 357/359/362).

5. Item (iii): §7 against the Clay Institute's published rules

Four checks, 1 MATCH, 3 MISMATCH. The two-year clause (III2) is correct: the rules require "at least two (2) years have elapsed since publication of the Proposed Solution in a Qualifying Outlet".

• III1: "refereed journal" is narrower than the rules. Section 6(a)(i) says "a refereed mathematics publication of worldwide repute meeting the conditions in Section 6(e)", and Section 6(a)(ii) gives a second qualifying route the document does not mention: "a publication meeting a relaxed set of conditions approved by the BOD following a recommendation from the SAB". Section 6(e) lists four characteristics whose absence disqualifies an outlet, including "inclusion in the list of publications maintained by MathSciNet".
• III3: two load-bearing words dropped. The rules (Section 4(c), repeated at 7(a)(i)) say "general acceptance in the global mathematics community, as determined in the sole discretion of CMI". Acceptance is not a community fact the repository could observe; it is a CMI determination. Section 7(a)(i)(4) enumerates what CMI may consider.
• III4: §7 lists three conditions; the rules impose four. Missing is Section 4(d): "the Proposed Solution has satisfactorily answered the questions raised by the Problem's official description, as determined in the sole discretion of CMI", sharpened by 5(d). Also absent, and of planning relevance: 5(e) "CMI will not accept Proposed Solutions submitted directly to CMI"; and, directly relevant to route 4, 5(b), which states that for the Navier–Stokes Problem "a resolution in either direction will be evaluated by the standard evaluation procedure set forth in Section 7", so the breakdown direction this repository pursues is explicitly in scope.

6. Proposed corrections, routed to integration

This leg is a verifier: it reports gaps and repairs none. CLAY_OBLIGATIONS.md was not edited. The exact text below is proposed for integration to land; line numbers are against the audited sha256.

(a) I8: line 128. Replace repaired it with the truncated law ... verified to2.6e-5. with:

repaired it with the truncated law E_ρ(t) ≍ ρ^{3−2α}(T*−t)^{α−1}, verified across four exponents to a worst-case absolute error of 2.57e-2 (at α = 1.4); at α = 1, the exponent §4 is about, the error is 2.65e-4.

(b) I10: lines 158–159. Replace the criticalL³tail grows **326.875 per decade of window, constant to 7.4e-10** with:

the cube of the critical L³ tail grows 326.875 per decade of window, constant to 7.4e-10 (the norm itself running 8.679 → 14.841 across the banked 2→10 decades

(c) I15) lines 38–40. Replace the CONFIRMED bullet with:

• CONFIRMED, verbatim: bounded energy is Fefferman's condition (7), and it is the condition §4 and §5 are about. Smoothness and divergence-free stand as stated. Decay is confirmed and strengthened: condition (4) bounds every derivative, |∂ₓ^α u°(x)| ≤ C_{αK}(1+|x|)^{−K} for any α and K, so "faster-than-polynomial decay" understates what the statement requires.

(d) II1: line 86. Replace λ ≫ 1 is outside the hypothesis (legs 253, 341).` with:

λ ≫ 1 is outside the hypothesis (leg 341's landed record; encoded operatively in solver/dssp_screen.py by legs 357/359/362, leg 253 is cited from narrative only and has no landed JSON).

(e) III1/III3/III4: replace §7's opening paragraph and its STILL UNCHECKED blockquote (lines 209–216) with:

The Millennium Prize rules (CMI, 2018 revision) impose four conditions in their Section 4, not three:

1. Publication in a qualifying outlet: Section 6(a)(i), "a refereed mathematics publication of worldwide repute meeting the conditions in Section 6(e)"; Section 6(a)(ii) admits a second route, "a publication meeting a relaxed set of conditions approved by the BOD following a recommendation from the SAB". Section 6(e)'s conditions include "inclusion in the list of publications maintained by MathSciNet".
2. At least two (2) years elapsed since publication in a qualifying outlet.
3. General acceptance in the global mathematics community, as determined in the sole discretion of CMI, Section 4(c). It is a CMI determination, not a community fact; Section 7(a)(i)(4) enumerates what CMI may consider.
4. The Proposed Solution has satisfactorily answered the questions raised by the Problem's official description, as determined in the sole discretion of CMI: Section 4(d), sharpened by Section 5(d).

Two further facts of planning relevance: Section 5(e) ("CMI will not accept Proposed Solutions submitted directly to CMI"; and Section 5(b)) for the Navier–Stokes Problem "a resolution in either direction will be evaluated by the standard evaluation procedure set forth in Section 7", so the breakdown direction this repository pursues is explicitly in scope. These are listed so that "the obligations are discharged" is never read as "the problem is solved", and because the two-year clock is a planning fact.

CHECKED AGAINST THE PUBLISHED RULES: leg 384, HTTP 200 (millennium_prize_rules_0.pdf, sha256 9b500374…). §7's own "check before relying on it" is discharged.

7. What can graduate from DRAFT-UNVERIFIED

On the gate's yes branch, clause by clause, on integration's edit: every item (i) clause except the three named above; all four of §2's screen rows (row 1 with the citation note); and §7's three prize-rules clauses once (e) lands. The document's STATUS: DRAFT, UNVERIFIED header is integration's to change, not this leg's.

8. What this leg did not do

No outreach of any kind. No edit to CLAY_OBLIGATIONS.md, to p2_route_cloc_v1.json, or to any solver module. No repair of any discrepancy. No claim of movement toward Clay: no link of L1 → L4 moved, §6's two no-method obligations remain OPEN, and Clay stays ~0.05%.