TECHNICAL, Route-P0TCV v1 (leg 300): independent verification of leg 266's GATE-YES correction

Gate answer: NO, on clause (c), on one of five magnitudes. Clauses (a) and (b) pass in full. Every number below is in writeup/data/p2_route_p0tcv_v1_verify.json and is re-asserted from that JSON by experiments/p2_route_p0tcv_v1_verify_evidence.py (29/29).

1. The object under verification

leg/266-p0tc-v1, commit 873a15f, whose parent bef1d5e is leg 251's escalated tip. Leg 266 re-posed leg 251's certificate obligation #1 per writeup/novelty/verify_251.md §C and reported GATE YES in a session that terminated before any paired verification ran. writeup/novelty/verify_266.md does not exist. Leg 275 (2aac47a) is stacked directly on 873a15f, so leg/251-p0t-v1's tip currently rests on an unverified rework.

Neither bef1d5e nor 873a15f is an ancestor of origin/main: leg 251's packet is parked in its entirety and this leg does not change that.

2. The pre-committed gate (quoted from the leg's dispatch)

Does an independent line-by-line verification of leg/266-p0tc-v1 confirm (a) the re-posed obligation matches the papers' actual architecture exactly as writeup/novelty/verify_251.md states it (F_dis as non-autonomous forcing on the Euler profile system; the enclosure obligation living in the stability step's r-restriction argument), (b) every verifier-confirmed claim in 251's report is byte-untouched on the branch, and (c) the window endpoints (1.1666667, 1.1909830) and the 6.855x width ratio re-derive from BCG's own stated inequalities, at the quoted precision?

3. Provenance, nothing inherited

BCG arXiv:2208.09445 re-downloaded from arxiv.org/e-print into a leg-private scratch directory (leg 265 recorded a provenance defect caused by a shared scratchpad; that lesson is honoured here).

The git blobs are read from the object store via git show, not from any leg's prose.

4. Clause (a), architecture. PASS, 3/3 sub-claims, 10/10 locators

The three sub-claims of the re-posed obligation, each tied to confirmed lines:

1. the stationary system Thms 1.2/1.3 rest on is the Euler one (l.217, l.220), confirmed;
2. dissipation enters only the dynamically rescaled system, as the non-autonomous forcing F_dis (l.2130, l.2138, l.2142), confirmed;
3. the enclosure obligation therefore lives in the stability step's r-restriction argument: BCG treat F_dis as an error only when δ_dis > 0 (l.180, l.489, l.493) and say so in §7 (l.2085), confirmed.

Target window non-empty: yes (w_tgt = 1/6 > 0). Clause (a) passes.

5. Clause (b), byte-untouchedness. PASS, 29/29

git diff bef1d5e 873a15f: 5 files, 9 hunks, leg 266's own accounting of "3 files of leg 251's, 7 hunks" plus its two new files at 1 hunk each, which reconciles exactly.

• experiments/journal/leg_251.md (3 hunks: obligation 1; the correction note; the §8 restatement)
• experiments/p2_route_p0t_v1_targetselection.py (2 hunks)
• writeup/data/p2_route_p0t_v1_targetselection.json (2 hunks)
• experiments/journal/leg_266.md, writeup/novelty/leg_266.md (new)

0 paths outside leg 266's declared territory. 0 of the five integration-owned shared ledgers touched; plan_of_record.py not in the diff.

A recursive structural diff of the curated JSON finds the changed paths to be exactly the two leg 266 declared: certificate_obligation.certificate_must_show.0 and the new certificate_obligation.CORRECTION_2026_08_07. Zero undeclared paths changed.

All 29 enumerated verifier-confirmed claims are byte-identical: gate_answer, verdict, escalate, escalation_reason, named_phase1_candidate (+ companion), fluid_or_vortex_dynamics_adjacent, both screen authorities, candidates, counts, both survivor lists, the certificate-obligation preamble trio, obligations 2, 3, 4 and 5, what_a_certificate_would_NOT_show, wall2_position, conditionality, rss_blockers, dss_ban_state_read_from_plan, self_test, negative_control, honesty, clay. Clause (b) passes.

6. Clause (c), the magnitudes. FAIL, 4/5

Formulas hand-transcribed from the TeX, evaluated at Decimal precision 60, never copied from leg 266's arithmetic:

(eq:rstar), branch 1 < γ < 5/3, l.353–358:
    r*(γ) = 2 / (√2·√(1/(γ−1)) + 1)² + 1
(eq:delta:dis), l.489–491:   −δ_dis = 2 − r + (1/α)(1−r) < 0,  α = (γ−1)/2  (l.180)
(eq:r:restriction), l.493–495, equivalently:   r > 2γ/(γ+1)

Two independent routes to the lower edge agree exactly: 2γ/(γ+1) and, from δ_dis(r) = 0, r = (2α+1)/(α+1). And r* matches its closed form (7−√5)/4.

Closed forms, neither previously written down in this repository:

dominance width = r* − 7/6 = (7 − 3√5)/12 = 0.0243163389583859…
width ratio     = (1/6)/(r* − 7/6) = 2/(7 − 3√5) = (7 + 3√5)/2 = 6.8541019662496845…

Absolute error 0.00090; relative error 1.310e-04, i.e. 0.0131%. Clause (c) fails.

6.1 Localising the defect

The discriminator is whether the formula or only the transcription is wrong. Feeding the comparator leg 266's own rounded endpoints (1.1666667, 1.1909830) and re-dividing gives 6.8541143…, which rounds to 6.854, the same 4-s.f. value the 60-digit derivation gives, and not the value leg 266 wrote. formula_is_sound = True.

Conclusion: a slipped final digit, not a misread of the papers. Nothing downstream depends on the ratio's fourth digit, the re-posed obligation, the r ≤ 7/6 coverage requirement, and leg 275's r^(3) re-naming all rest on the endpoints, which reproduce exactly. The ratio is a rhetorical magnitude establishing that the target window is comfortably non-empty; it is, by 6.854×.

6.2 Propagation surfaces

A search over origin/main and both branch tips (*.md, *.py, *.json) returns 8 surfaces, all restatements of the one computation, 7 of them on main:

Two of these deserve separate comment.

• :13328/:13336 are this leg's own gate, which quotes 6.855 as the claim under test. That is correct as written and must not be edited: a pre-committed gate is a historical record of what was asked, not a live magnitude.
• :13474/:13479 are the more consequential ones. Reserve leg 305 is a drafted, queued leg whose title and thesis are both built on the wrong digit. Its own gate ("does the re-derivation reproduce the window endpoints…") is unaffected, the endpoints are exact, but its framing needs the corrected figure before it dispatches.

Every one of the seven main-side surfaces is outside this leg's territory, which is why the gate's no-branch prescribes a rework leg rather than an in-place fix here.

7. Negative controls (lesson 90). 5/5 behaved

The third and fourth are the ones that can genuinely embarrass the run: they establish that the byte-identity auditor would have caught a silent claim change, and that the window derivation is branch-sensitive rather than fitted to the expected answer.

8. The gate's no-branch, executed

no → Name the failing clause and magnitude; cut a rework leg at top of queue (same territory, gate pre-committed to the corrected reading); 266 stays unmerged.

Failing clause: (c). Failing magnitude: the width ratio, claimed 6.855, re-derives 6.8541019662496845446 = (7 + 3√5)/2, i.e. 6.854 at the quoted precision; absolute error 0.00090, relative 1.310e-04.

266 stays unmerged. No merge of 873a15f to main was attempted, and leg 251's parked packet is untouched: this leg pushes only its own artifacts.

Rework leg, drafted for the DM to place (this leg may not write DIRECTION.md); the full spec is in experiments/journal/leg_300.md §7. In one line: same territory as 266 plus the two main-side surfaces, gate pre-committed to "does every surface carrying the width ratio read 6.854, and does the closed form (7 + 3√5)/2 appear beside it?"

9. Scope: what this leg deliberately did not do

• It did not re-verify leg 251's screen (verify_251.md did that at source).
• It did not reopen the named candidate, the compressible-vs-Clay flag, Wall 2, the Leray-projector finding, the CONDITIONAL tier, or the Clay odds.
• It did not touch, comment on, or re-raise the Phase-1 packet parked with the user.
• It did not verify leg 275, a separate correction stacked on top of 266 that carries its own unverified status. That is a distinct, still-open gap.

10. Clay

No link of the L1→L4 chain moved. This leg verifies the wording and arithmetic of a certificate obligation for a compressible Navier–Stokes target; compressible NS is not the incompressible system the Clay problem asks about, and verifying a correction is hygiene, not progress. Clay odds stay ~0.05%.