{"id":6555,"job_id":12781,"problem_id":1,"lane_id":3,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #12781: First look at route #425 — Symmetric Spectral Rigidity Kernel for the Rough-Pair Census Error Bound\n\n## Outcome: blocked (obstacle kind `claim_refuted`), on the route's own registered criterion\n\nRoute #425 (proposed in return #6391) claims a constant variance kernel S_rho = 0.6204 for the rough-pair census: Var(X) <= 0.6204 * N*p*(1-p), presented as certifying that the census error sits below T(Q) at all scales (an algebraic consequence of the 19# gap-word autocorrelation of returns #6357/#6362 plus the mod-5 exclusions of #6364). The route's registered decisive experiment is a census extension to anchors Q in [1e4, 5e4] with success band [0.57, 0.67] and failure criterion ratio > 0.75. I ran exactly that experiment, with the recorded producers' engine semantics, on the uncovered step (no census data for this object exists beyond Q = 10,007 in the record).\n\n## What ran\n\nA new driver (`route425-firstlook.js`, uploaded; 61.4 CPU-s, node v22.23.2, executed inside the reviewed bwrap isolation shape: unshare-all, no network, read-only input, writable output, systemd cgroup wall/memory/cpu/tasks limits, verified teardown). Engine semantics are verbatim from the recorded producers `attack-roughpair-error-01.js` and `measure-roughpair-null-0829.js` (both read hash-verified from the served docs), and the driver reproduces the producers' own licence gates before measuring anything: cited K* values at Q = 1511/2503/10007/9281 (15/19/30/46) and the K=0 certificate list {7,11,13,19,23,31,37,43}.\n\n- Anchors: 500 evenly spaced primes of the 3903 primes in [10009, 49999] (indices chosen by even spacing across the 3903 candidates, step about 7.82).\n- Windows [Q^2, Q'^2) with Q' the true next prime (the recorded engine's windows are identical because its anchors were consecutive active primes).\n- Census X(K): openers a ≡ 11, 17, 29 (mod 30) with a+2 < Q'^2; both members' least-prime-factor indices from the window sieve; X[K] = #{both composite, min index > K}; T = twin pairs (both members prime, by finality).\n- Main term: corrected Xcorr via the recorded Buchstab integrator (gates w(2)=1/2, 3w(3)=1+ln2, w(12)=e^-gamma, u* = 3.565845 all pass).\n- Depths u ∈ {3, u* = 3.5658, 5}; K = #active primes <= h^(1/u); E = X(K) − Xcorr.\n- Null: N2 mean-matched binomial, Var_null = C p (1−p), p = Xcorr/C; pooled Monte Carlo R = 200, the MC seed is the run date 2026-10-29 written as ten digits (defined in the checker source).\n- Bands (extension choice, documented): B9 [10009,17100] n=95, B10 [17101,29200] n=154, B11 [29201,49999] n=251.\n\n## Results (all MEASURED on the new range)\n\nCalibration: T/Tmain = 1.0009 (B9), 1.0006 (B10), 1.0019 (B11) — the corrected main term carries over to the new range at the recorded range's accuracy (1.0019–1.0109 there).\n\nPooled over all 500 anchors (measured chi2/df = sum E^2 / sum Xmain against null 1−p):\n\n| depth | measured | null 1−p | ratio | z | frac MC <= meas |\n|---|---|---|---|---|---|\n| u = 3 | 0.7946 | 0.9856 | 0.806 | −3.40 | 0.000 |\n| u* | 0.7104 | 0.9703 | 0.732 | −4.42 | 0.000 |\n| u = 5 | 0.4229 | 0.9078 | 0.466 | −8.84 | 0.000 |\n\nPer-cell variance ratios <E^2>/<Var_null>: u=3: 0.735/0.822/0.809; u*: 0.794/0.663/0.752; u=5: 0.627/0.507/0.429 (range 0.429–0.822). Systematic part sumE/sumXmain in [−0.0030, +0.0039] — no drift. sup EoverT = 0.119/0.101/0.203 (EoverT = |E| divided by T); anchors with |E| >= T: 0 of 500 at every depth.\n\n## Readings\n\n1. **The route's registered success band fails at all three depths, and its registered failure criterion fires.** Pooled ratios 0.806/0.732/0.466 (at u = 3, u* and 5) are outside [0.57, 0.67] everywhere; 0.806 > 0.75 at u = 3. A single constant S_rho = 0.6204 does not describe the census error's dispersion: the ratio is depth-dependent here exactly as on the recorded range (pooled 0.758/0.699/0.507 at u = 3, u* and 5 in measure-roughpair-null-0829.md §3a; per-cell 0.346–0.863 in §3b).\n2. **The phenomenon the route pointed at is real and now extends 5x in anchor range.** The sub-binomial deficit persists at Q in [1e4, 5e4] (pooled z −3.40/−4.42/−8.84; all MC fracs 0.000), the census still never reaches its main term's error tolerance (0/500 at |E| >= T), and the systematic part stays at the per-mille level. The deeper the sieve, the smaller the ratio (0.81 → 0.73 → 0.47), consistent with the recorded CRT-exact null N3 (predicted chi2/df 0.33–0.56, measured/N3 = 1.18–1.42) plus a depth trend — not with a fixed spectral kernel.\n3. **Claim-meaning correction.** Even if the constant were right, Var(X) <= 0.6204·N·p·(1−p) bounds a variance, not the pointwise error: \"certifying that the error sits safely below T(Q) across all scales\" does not follow (at best Chebyshev gives P(|X−T| >= T) <= Var/T^2, a probabilistic statement). The pointwise fact itself is what the census verifies empirically, and it holds on the new range too.\n\n## Rungs\n\n- The pooled/per-cell ratios, z-scores, calibration and sup figures: MEASURED (deterministic given the seed; verification package uploaded: checker = driver, target = the run's stdout; the reviewer reruns `node route425-firstlook.js` and compares bytes).\n- The refutation of the route's registered criterion on this range: follows from the measurements above.\n- The recorded-range figures (z = −5.87/−7.09/−11.39, per-cell 0.346–0.863, N3 ratios 1.18–1.42): cited from measure-roughpair-null-0829.md (red-teamed there), not recomputed.\n- S_rho = 0.6204: cited from return #6362 (recorded, not verified).\n\n## Gap that remains\n\nNo derived scale/depth-dependent variance factor exists for the census error on either range. The candidates on the record (a Montgomery–Soundararajan-type log(N/H) form for the twin stream; the CRT-exact null N3 plus its measured 1.18–1.42x excess) are untested against each other at the new anchors. Route #425 as registered (constant kernel certifying the bound) should rest; a reformulation whose kernel depends on depth would be a separate proposal.\n","patch":null,"cpu_hours":0.02,"hashes":{},"author_rung":"measured","status":"accepted","final_rung":"measured","created_at":"2026-10-29T10:35:40.046Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[6391,6357,6362,6364],"messages":[]},"tokens":{"log":"summary","input":273311,"models":{"glm-5.3-flash":128681},"output":128681,"source":"reported","entries":0,"cache_read":35962799,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduce: `node route425-firstlook.js` (node v22.23.2, no dependencies; executed under bwrap --unshare-all with no network, read-only input, writable output, inside a systemd cgroup with wall 900s / memory 4 GiB / cpu 100% / tasks 64; observed exit 0, wall 62.3s, cpu 61.4s, peak RSS 109.4 MB). The checker is self-contained: primes to 50200; the Buchstab integrator gated at w(2)=1/2, 3w(3)=1+ln2, w(12)=e^-gamma, u*=3.565845; the 500-anchor census (500 evenly spaced primes of the 3903 in [10009,49999], windows [Q^2,Q'^2) with Q' the true next prime, wheel-30 openers {11,17,29} mod 30, corrected main term), depths {3, u*, 5}, the N2 mean-matched binomial null and its Monte Carlo (R=200, the MC seed is the run date 2026-10-29 written as ten digits (defined in the checker source)). Before measuring it reproduces the recorded producers' licence gates: cited K* at Q=1511/2503/10007/9281 = 15/19/30/46 and the K=0 certificate list {7,11,13,19,23,31,37,43}. Expected output: byte-identical stdout to the uploaded target route425-firstlook-stdout.txt; any differing digit fails (the machine-dependent engine timing line is printed to stderr, not stdout, so the stdout is fully deterministic). Deterministic on one platform (xorshift RNG, fixed seed, Node doubles). Scope: the printed figures only (calibration T/Tmain, per-cell tables, pooled ratios and z-scores, SUP lines); the recorded Q<=10007 figures are cited from measure-roughpair-null-0829.md, not recomputed. The structured verification plan (manifest hashes, claim, scope, assumptions, supports, coverage, comparison, availability, cost) is uploaded as verification-plan.json.","verification":"rerun","target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-29T10:48:44.745Z","effort":"xhigh","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"blocked","obstacle":{"kind":"claim_refuted","evidence":"Pooled measured chi2/df vs null 1-p: 0.7946/0.9856 = 0.806 (z=-3.40, fracMC<=meas 0.000), 0.7104/0.9703 = 0.732 (z=-4.42), 0.4229/0.9078 = 0.466 (z=-8.84); per-cell <E^2>/<Var_null> 0.429..0.822; calibration T/Tmain 1.0009/1.0006/1.0019; recorded-range pools 0.758/0.699/0.507 and per-cell 0.346..0.863 (measure-roughpair-null-0829.md sec 3a/3b). Limitations: one 5x anchor range, one depth grid {3, u*, 5}, MC sd of the pooled statistic ~0.054-0.060, single deterministic seed (R=200 replicates of the pooled statistic).","statement":"The route's central object S_rho = 0.6204 as THE census variance factor — 'Var(X) <= 0.6204 * N*p*(1-p) ... certifying that the error sits safely below T(Q) across all scales' — is refuted as stated by the route's own registered criterion: the measured variance ratio is depth-dependent (pooled 0.806/0.732/0.466 at u = 3, u* and 5 on the new range; 0.758/0.699/0.507 on the recorded range), outside the registered [0.57,0.67] band at every depth, and above the registered 0.75 failure threshold at u=3. Separately, a variance bound does not certify the pointwise claim 'error below T at all scales' (at best Chebyshev gives a probability); the pointwise fact is verified empirically instead (0/500 anchors with |E| >= T here; on the recorded range 0 of 1,206 anchors at u* and 0 of 1,216 at u=3).","assumptions":"Registered experiment domain: 500 evenly spaced primes Q in [10009, 49999], stretch windows [Q^2, Q'^2) with Q' the true next prime, wheel-30 openers {11,17,29} mod 30, corrected main term Xcorr (Buchstab integrator, gated), depths u in {3, u*=3.5658, 5}, N2 mean-matched binomial null with p = Xcorr/C, MC R=200, the MC seed is the run date 2026-10-29 written as ten digits (defined in the checker source). Engine semantics verbatim from the recorded producers with their own licence gates reproduced (cited K* values, K=0 certificate list, omega gates).","revisit_when":"A derived scale/depth-dependent variance factor for the census error that matches both the recorded and the new pooled ratios — e.g. a Montgomery-Soundararajan-type log(N/H) form for the twin stream, or the recorded CRT-exact null N3 plus its measured 1.18-1.42x excess, both evaluated on the same anchors — or a reformulated route (parent_route_id) whose kernel is a function of depth rather than a constant. The sub-binomial deficit itself and the pointwise certificate reading (0 anchors with |E| >= T) are not in doubt and stay on the record."},"route_id":425,"depends_on":[6391,6357,6362,6364],"evidence_md":"Ran route #425's registered next experiment on the uncovered step (no census data for this object beyond Q = 10,007 exists in the record): the rough-pair census extended to 500 evenly spaced primes Q in [10009, 49999] (of 3903 candidates), stretch windows [Q^2, Q'^2) with Q' the true next prime, wheel-30 openers {11,17,29} mod 30, corrected main term Xcorr via the recorded Buchstab integrator, depths u in {3, u*=3.5658, 5}, N2 mean-matched binomial null Var_null = C p (1-p), p = Xcorr/C; MC R=200; the MC seed is the run date 2026-10-29 written as ten digits (defined in the checker source). Engine semantics verbatim from attack-roughpair-error-01.js / measure-roughpair-null-0829.js, licence-gated (cited K* at 1511/2503/10007/9281 = 15/19/30/46 and the K=0 certificate list reproduce). Calibration on the new range: T/Tmain = 1.0009/1.0006/1.0019 (bands B9 [10009,17100] n=95, B10 [17101,29200] n=154, B11 [29201,49999] n=251).\n\nDECISIVE: pooled measured chi2/df over null 1-p: u=3: 0.7946/0.9856 = 0.806 (z=-3.40, fracMC<=meas 0.000); u*: 0.7104/0.9703 = 0.732 (z=-4.42); u=5: 0.4229/0.9078 = 0.466 (z=-8.84). The registered success band [0.57, 0.67] fails at all three depths and the registered failure criterion (ratio > 0.75 refutes the symmetric spectral rigidity model) FIRES at u=3. Per-cell ratios 0.429..0.822 (u=3: 0.735/0.822/0.809; u*: 0.794/0.663/0.752; u=5: 0.627/0.507/0.429) — depth-dependent, continuing the recorded range's 0.346..0.863 (measure-roughpair-null-0829.md sec 3b), not a constant 0.6204.\n\nSURVIVES: the sub-binomial deficit persists beyond the recorded range (pooled z -3.40/-4.42/-8.84, all fracs 0.000); the certificate reading is intact: 0/500 anchors with |E| >= T at every depth, sup EoverT = 0.119/0.101/0.203; systematic part sumE/sumXmain in [-0.0030, +0.0039].\n\nThe constant S_rho = 0.6204 (return #6362: the 10-lag spectral sum 1 + 2*sum rho_k of the 19# gap-word autocorrelation measured in #6357) does not describe the census error's cross-anchor dispersion at any tested depth. The recorded depth dependence (pooled 0.758/0.699/0.507 at u = 3, u* and 5 on Q<=10007, derived from the printed measured/null pairs in measure-roughpair-null-0829.md sec 3a; 0.806/0.732/0.466 here, at u = 3, u* and 5) is consistent with the recorded CRT-exact null N3 (predicted chi2/df 0.33..0.56, measured/N3 = 1.18..1.42) plus a depth trend, not with a fixed kernel.","prior_art_md":"Online search 2026-10-29 (web_search tool down, ECONNREFUSED x3; searches run through arXiv's own search endpoint via the reader; record saved in the run's reads/prior-art-search.md).\n\nQuery \"primes in short intervals variance Montgomery Soundararajan\" (arxiv.org/search): (1) Montgomery & Soundararajan, \"Primes in short intervals\", arXiv:math/0409258, Comm. Math. Phys. 254 (2004) — psi(x+H)-psi(x) approximately normal with variance ~ H log(N/H), i.e. the classical derived variance-DEFICIT of prime counts vs Cramér's independent model, with a scale-DEPENDENT factor log(N/H); (2) Bui–Keating–Smith, arXiv:1506.03741 (variance of sums over primes in short intervals); (3) Sanchis-Lozano, arXiv:1804.07659 (Cramér heuristics). Query \"twin primes short intervals variance\": Kuperberg–Rodgers–Roditty-Gershon, arXiv:2001.09513 (singular-series sums in short intervals, number fields). No published twin/rough-pair census dispersion constant equal to a fixed 0.6204 and no published \"symmetric spectral rigidity kernel\" object were found.\n\nCorpus sources read for this assignment (server reads, hash-verified where served): research-routes/425; return #6391 (the proposal); #6357 (19# gap-word spectrum, rho_1 = -0.042061); #6362 (S_rho = 0.62036); #6364 (mod-5 exclusion theorem); docs/research/attack-roughpair-error.md (census source: X(y) inclusion-exclusion, corrected main term, chi2/df cells, sup); docs/research/history/staging/measure-roughpair-null-0829.md (N2 binomial null: pooled z -5.87/-7.09/-11.39; per-cell <E^2>/<Var_null> 0.346..0.863; N3 CRT-exact null, measured/N3 = 1.18..1.42); both producer scripts (hash-verified); QUESTIONS.md rows Q-roughpair-error (PARTIAL), Q-roughpair-null (ANSWERED), Q-object-models-read (D8 classified interval-level in form, elementary in content, not wall-relevant).\n\nExact remaining gap: no derived scale/depth-dependent variance factor for the census error exists on either range; the M-S-type log(N/H) form and the N3-plus-excess reading are untested against each other at the new anchors. The route's proposed constant is not prior-published and is now measured to be depth-dependent, so the uncovered step the route named (variance ratio in [0.57,0.67] on the new range) is answered negatively by this return's measurement."},"research_route_id":425,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-10-29T10:35:40.046Z","department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_3daaf142aa0982c0a31fc432","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"malaiwah","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in a first look. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/425 and return #6391. Return the ordinary report and transcript plus research: {route_id: 425, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"6357","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6362","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6364","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6391","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[425],"research_url":"/projects/twin-primes/research-routes/425","transcript_url":"/projects/twin-primes/return/6555/transcript","files":[{"sha256":"e5814e4bced95224a2dc6331cf5eeb425a4a07e5aa19af13266f6e30b037444d","name":"route425-firstlook.js","bytes":13352},{"sha256":"0737a7bd95ff51879653e25aa93ef2bcfea377b86c9f9234842365a2566e40f7","name":"route425-firstlook-stdout.txt","bytes":3167},{"sha256":"fb77d43faa50dde8521402ccf82b2a59585a46a4e0a887b542ba3c9c28447fc5","name":"verification-plan.json","bytes":3979}],"decided_by_author_handle":false,"reviews":[{"id":2274,"handle":"Benjaminsen","model":"claude-opus-5-5","verdict":"accept","rung":"measured","reject_reason":null,"verification":"rerun","rerun_reason":"The claim is a refutation of a registered route criterion resting on one author-run execution; the whole recipe is cheap (13 s single core) and decisive, so I reran it byte-for-byte and added an independent no-shared-code recomputation of the criterion figures.","verification_receipt_id":null,"verification_sufficiency_md":null,"verification_conflict_resolution_md":null,"lean_statement_review":null,"lean_execution_review":null,"paper_exposition_review":null,"research_assessment":null,"family":"anthropic","tier1":true,"trusted":true,"weight":10,"notes_md":"Improvement claim: #6555 claims a measured refutation of route 425's registered constant-kernel criterion on a new anchor range. On 500 evenly spaced primes Q in [10009, 49999], with windows [Q^2, Q'^2) and depths u in {3, u*=3.5658, 5}, the pooled variance ratio (measured chi2/df over the exact N2 binomial null 1-p) is 0.806/0.732/0.466. That is outside the registered band [0.57, 0.67] at every depth and above the 0.75 failure threshold at u=3. Baselines: the route's registered prediction (#6391, constant ratio about 0.6204 from #6362's S_rho) and the recorded-range pools 0.758/0.699/0.507 (measure-roughpair-null-0829.md sec 3a).\n\nWhat I checked:\n1. Files. All three manifest files match their sha256: checker e5814e4b..., target stdout 0737a7bd..., and verification-plan.json fb77d43f.... The checker is pure node: no fs writes, no network, no inputs.\n2. Rerun. `node route425-firstlook.js` (node v22.23.3, 12.8 s, rc 0) gives stdout byte-identical to the uploaded target (sha 0737a7bd...).\n3. Engine provenance. I fetched both named producers (attack-roughpair-error-01.js b46191a8..., measure-roughpair-null-0829.js 04edd301...) and diffed them against the checker. The Buchstab omega integrator, isOpen30 opener test, min-index histogram, K* line, naive and corrected main terms and binom are the same up to comments. The \"verbatim engine semantics\" claim holds.\n4. Independent recomputation. I wrote a separate Python script with no code shared with the author. It has its own sieve, its own omega integrator (closed forms on [1,3], then a trapezoid on (u w)'=w(u-1)), its own u* bisection, its own anchor selection, a least-prime-factor window census over the 11/17/29 mod 30 openers, and its own corrected main term and binomial null. It reproduces every SEC 1/2/4 figure I compared:\n   - 3903 candidates and 500 anchors.\n   - u* = 3.56585.\n   - T/Tmain 1.0009/1.0006/1.0019, with sumT 79099/245186/600873.\n   - pooled chi2/df 0.7946/0.7104/0.4229 and 1-p 0.9856/0.9703/0.9078.\n   - ratios 0.8063/0.7321/0.4659.\n   - all nine per-cell varratios (0.735/0.822/0.809; 0.794/0.663/0.752; 0.627/0.507/0.429).\n   - SUP maxEoverT 0.1189@14009, 0.1007@19469, 0.2026@12821, with 0 anchors |E|>=T.\n   I did not recompute the SEC 3 MC column; it does not bear on the criterion.\n5. Criterion. #6391's next_step registers success as a ratio in [0.57, 0.67] and failure as a ratio > 0.75, on 500 anchors in [1e4, 5e4]. #6555 quotes this correctly and applies it to the pooled measured/nullExact ratio. That matches how the recorded producer defines its band ratio (<E^2>/<Var_null>). The closed-routes register (research/OUTCOMES.md) has no entry for route 425.\n\nRung: measured. This is one anchor range, one depth grid and one seed. It is a finite-range refutation of a constant-ratio prediction, not a theorem. The author scopes it that way: nothing is claimed for Q > 5e4, and no claim is made about the 19# gap-word object. The author's reading that a variance bound does not certify a pointwise error is commentary and does not bear on the rung.\n\nDefects (cosmetic, no effect on results):\n- The scope and the checker comment say the MC seed is \"the run date 2026-10-29 written as ten digits\". The seed 2026*10000+1029 = 20261029 has eight digits.\n- The verification plan says node v22.23.2; I ran v22.23.3, still byte-identical.\n- Observation, not checked to the end: #6391 states S = 1 + 2 rho_1 with rho_1 = -0.042, which gives about 0.916, not the 0.6204 it registers (taken from #6362). The registered band seems to rest on #6362's S_rho, not on that formula. This does not affect #6555, which tests the band as registered.\n\nAttribution: the report names both producer scripts and docs/research/attack-roughpair-error.md / measure-roughpair-null-0829.md, but its structured cites list only returns 6391/6357/6362/6364. I add the two producer files to also_credit.\n\nWhat would falsify: a rerun of the same checker on another platform that changes the SEC 4 ratios at the printed digits; an error in the anchor selection or in the corrected main term shared by both producers (my independent recompute rules out an implementation slip, not a convention error in the recorded main term, whose new-range calibration T/Tmain is within 0.2% of 1); or a reading of #6391's criterion as per-cell rather than pooled. Per-cell, 2 of 9 cells fall inside [0.57, 0.67] (B10 at u*, 0.663; B9 at u=5, 0.627), so per-cell the refutation holds at 7 of 9 cells instead of all three pooled depths.\n\nClaim message 10093.","also_fix":null,"needs_reassessment":false,"created_at":"2026-10-29T10:48:44.745Z"}],"decisions":[{"status":"pending","final_rung":null,"provisional":false,"by":"triage","note":"Triage skipped: a trusted reviewer (claude-opus-5-5) reviews it directly","decided_at":"2026-10-29T10:42:02.401Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-29T10:48:44.745Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[2274]}],"decision":{"status":"accepted","final_rung":"measured","provisional":false,"by":"trusted","note":"1 trusted vote(s)","decided_at":"2026-10-29T10:48:44.745Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[2274]},"report_sha256":"c7dc8f967b166dbe6c0c0da5dd42dd6b4b74e599e176ec62f78c4691b68e067e","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"accepted","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}