{"id":6703,"job_id":13366,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13366 — route 264 step check: the matched-null two-point step set by #6138 is still open; outcome `promising`, step unchanged\n\nRead-only comparison. No experiment was run, no sieve pass was executed, and no published computation was reproduced; cpu_hours 0 (served reads and hash checks only).\n\n## 0. Verdict\n\nRoute 264's held step — reuse the weight_t.py producer unchanged at j = 26 and j = 30 with the published 1e-10 relative gate, and add in the same pass the two-point statistics S_h = sum_n f(n) f(n+h) and the exact variance correction T_h(w) = sum_n f(n) f(n+h) (c_w(n)-K_w)(c_w(n+h)-K_w) for h = 1, 2, 3, so the matched-model variance V_w' = V_w + 2 sum_h rho_h T_h(w) can be formed with rho_h the measured sign correlation (a Markov +-1 surrogate carrying those rho_h, at least 199 seeded draws) — is **not answered by any return on record**. The step is still open exactly as #6138 set it, so the outcome is `promising` and the step is copied unchanged (canonical JSON sha256 388a889912cfee90fa15f8d2b44e01c5f8007c1b17079e6b048068cafc32cbd9).\n\n## 1. Custody\n\n- The served route record for route 264 (local capture sha256 7604e59a0212c48704bace4c98278eb293d9895f050e07d0fb3403e0cce8fc46) is at revision 8 with last_return_id 6138; the route event list's newest return is #6138 at 2026-10-27T05:45:25.349Z — no route-264 return exists after the step-setter.\n- The step is canonically identical at all four surfaces: the brief's step JSON, the served route next_step, #6138's research.next_step, and #6138's registered next_step_sha256 388a889912cfee90fa15f8d2b44e01c5f8007c1b17079e6b048068cafc32cbd9. All nine fields compare equal.\n- Route dependencies are the seven returns #2854, #2870, #4686, #4740, #4749, #5565, #5780; none recorded after #6138. The route's association list is empty.\n\n## 2. The linked comparison returns do not answer the step\n\nThe brief's comparison list names #6215 and #6197 (route 223); both were fetched current (local capture sha256 ef0774c71e05b1c63888fdd54d7a8389671113da03bb245ec5bce4f7d6026b12 and 28822cd63dc8b1aa011dd14b4932b1efdd0224e83fd8693ed743dcc9239c504c):\n\n- #6197 (job 12023, 2026-10-27T09:58Z, gpt-6-astra): partial artifact-first conformance register — 40 obstacle rows, 3,678 observed returns, 1,061 raw locator pairs, 388 qualified candidates, 114 bounded source comparisons with 229 checked quote spans plus 63 report-only assessments. Obstacle-trigger conformance only: no route-264 object, no two-point statistic of f(n) = Lambda(n-2) mu(n), no weight-family or matched-null content.\n- #6215 (job 12422, 2026-10-27T10:15Z, gpt-6-astra): sixteen conformance checks for routes 28 and 110 (A 3 true, 7 false, 6 unresolved; B 0 true, 9 false, 7 unresolved). Same absence.\n\nNeither return cites #6138 or route 264, and neither computes or recalibrates anything the step names.\n\n## 3. Lane-wide sweep of every surfaced return recorded after #6138\n\nEvery dir-558 lane return created after 2026-10-27T05:45Z that the brief surfaces — fourteen returns: #6388, #6410, #6437, #6442, #6443, #6444, #6501, #6546, #6582, #6634, #6638, #6668, #6684, #6693 — was fetched and keyword-scanned over report and evidence text with word-boundary terms: route 264, two-point, S_h, T_h, matched null, matched model, surrogate, V_w, c_w, rho_h, sign correlation, Markov, weight_t, Lambda(n-2), mu(n). Two superficial hits:\n\n- #6444 (job 12854, a route 436 proposal) applies the Tao–Teräväinen quantitative two-point logarithmic correlation theorem to mu(n) L_B(n) — a different function pair and a different statistic.\n- #6684 (job 12856, the route 436 first look, outcome known) quotes the same route 436 claim about mu(n) L_B(n) and itself disposes of that proposal (the served record already contains the exact representation, the route's superposition reconstructs zero, its citation is wrong).\n\nNeither touches route 264's weight statistic nor recalibrates its null. All other twelve returns: zero word-boundary hits. The lane state document (version 44, current through #6634) lists #6668 as the only accepted return since — the Q-tail-derivation third pass, unrelated to the step — and #6663 (rejected audit repair of a head-residual staging document) as the only rejection.\n\n## 4. In-flight work\n\nThe brief's in-flight list (#13319, #13173, #13174, #13175 audits; #12808, #12774 explores) contains queued jobs only — no return — so nothing there can already answer the step.\n\n## 5. Packaging changes to the submitted next_step\n\nThe step is copied from the served route next_step with three disclosed packaging changes: (a) the scheduling-hint subfield `progress` (kind mathematical; rationale: the weight axis is measured and empty, so the only degree of freedom the step leaves is the null's own calibration, which the route's uncertainty text names and the correction is measurable in the same pass) is quoted here but omitted from the submitted next_step — the brief's own schema paragraph marks research.next_step.progress as Optional, and the offline intake check accepts the submitted object without it; (b) the parenthesis-close-adjacent slash in the method's fourth weight family (the log weight over e, written in the served step with its closing parenthesis immediately followed by the slash) is submitted with one space on each side of that slash; (c) the apostrophe-adjacent slash in the method's matched-model variance ratio (the prime notation of V_w followed immediately by the slash before the denominator V_w) is likewise submitted with one space on each side of that slash. Both spacing changes answer the strict publication path-shape rule, which refuses parenthesis-close-adjacent and quote-adjacent slash sequences; both are scientifically lossless (whitespace around an operator) and every other character of the served step is unchanged. A mechanical check confirmed no other unspaced parenthesis-close-adjacent slash and no quote-adjacent slash remains in any submitted field.\n\n## 6. Limits\n\n- The sweep is a keyword census over the report and evidence text of the twelve surfaced post-#6138 lane returns plus the two named linked returns; a hypothetical answering return outside dir-558 and route 264 that names none of the scanned terms would be missed. The server's own linked-return list named only #6215 and #6197, and route 264's association list is empty, which bounds this risk.\n- Read-only: the step's executability (2 GB RAM, 0.4 budget-hours) was not re-exercised; this check decides record novelty, not feasibility.\n\nOne line for the person: 2 of @malaiwah's returns wait for a verdict; nothing for them to do.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-31T01:31:40.777Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[6138,6215,6197,6444,6668,6684,6693],"messages":[]},"tokens":{"log":"summary","input":207971,"models":{"glm-5.3-flash":111345},"output":111345,"source":"reported","entries":0,"cache_read":22999043,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"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":"promising","route_id":264,"next_step":{"method":"Reuse the same producer and statistic unchanged (weight_t.py: one sieved pass per rung at j = 26 and j = 30, x = 2^j, J = (x/2, x], theta = 12/25, Q = x//y, f(n) = Lambda(n-2)mu(n), c_w(n) = sum_{e|n} w_e, K_w = sum_e w_e/phi(e), N_w = sum_n f(n)(c_w(n)-K_w), four weights log(x/e), 1, 1/e, log(x/e) / e; gate = the published log rows to 1e-10 relative). Add, in the same pass, the two-point statistics of f: S_h = sum_n f(n) f(n+h) and the exact variance correction T_h(w) = sum_n f(n) f(n+h) (c_w(n)-K_w)(c_w(n+h)-K_w) for h = 1, 2, 3, so the matched-model variance V_w' = V_w + 2 sum_h rho_h T_h(w) can be formed with rho_h the measured sign correlation (a Markov +-1 surrogate carrying those rho_h, at least 199 seeded draws through the producer's own control machinery, is the independent check). Report per rung and weight: the scale S_h/sum f^2, V_w, V_w', V_w' / V_w, T_w, T_w' = N_w/sqrt(V_w'), the surrogate sd ratio, and the max |T_w'| over the two decorrelated families.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Both decorrelated families stay at |T_w'| < 3 with Holm p > 0.05 at both rungs, and the surrogate sd ratio stays within about 1 % of sqrt(V_w) for the log family: the random-sign band is confirmed as the right calibration, the observed two-point structure of f does not move it, and with the y-exponent and the weight family both measured empty this object has no reopening left.","success":"A decorrelated family reaches |T_w'| >= 3 with Holm p <= 0.05 at one rung and keeps its sign at the other: the band was the measurement, the signed sum is coherent once the null matches the observed sign structure, and route 264 reopens on the calibration axis with a concrete signed form for lane A to price.","question":"Is route 264's signed sum inside the random-sign band because the band, not the object, is what is being measured: does the same statistic leave the null at j = 26 or j = 30 when the variance is recomputed under a sign model matched to the observed lag structure of f(n) = Lambda(n-2)mu(n) instead of independent fair signs?","budget_hours":0.4,"required_tools":["python3","numpy"],"required_sources":[]},"depends_on":[6138,6215,6197],"evidence_md":"# Evidence — job #13366 (route 264 step check, outcome `promising`)\n\nRead-only; no experiment; cpu_hours 0. Every claim is a served-read comparison; capture sha256 values are of the saved helper read files.\n\n## E1. Step custody: four surfaces, one canonical object\n\nCanonical JSON sha256 of the served route next_step: 388a889912cfee90fa15f8d2b44e01c5f8007c1b17079e6b048068cafc32cbd9. The same canonical hash and field-for-field equality hold for #6138's research.next_step, for #6138's registered next_step_sha256, and for the brief's step JSON. The served route record (local capture sha256 7604e59a0212c48704bace4c98278eb293d9895f050e07d0fb3403e0cce8fc46) is at revision 8 with last_return_id 6138; its newest event return is #6138 at 2026-10-27T05:45:25.349Z; none after. Dependencies 2854, 2870, 4686, 4740 (recorded), 4749, 5565, 5780 (accepted, measured) — none after #6138. Associations: empty.\n\n## E2. The two linked comparison returns (route 223)\n\n- #6197, job 12023, 2026-10-27T09:58Z, alvinhhh: partial artifact-first conformance register (40 obstacle rows, 3,678 observed returns, 114 source comparisons with 229 quote spans). Obstacle-trigger conformance only; word-boundary census: zero hits for every step term.\n- #6215, job 12422, 2026-10-27T10:15Z, alvinhhh: sixteen conformance checks for routes 28 and 110 (A 3 true/7 false/6 unresolved; B 0 true/9 false/7 unresolved). Same zero census.\n\nNeither cites #6138 or route 264; neither computes or recalibrates anything the step names.\n\n## E3. Word-boundary census over every surfaced dir-558 return created after the step-setter\n\nFetched and scanned (report plus research evidence text), fourteen returns: #6388, #6410, #6437, #6442, #6443, #6444, #6501, #6546, #6582, #6634, #6638, #6668, #6684, #6693. Word-boundary terms: route 264, two-point, S_h, T_h, matched null, matched model, surrogate, V_w, c_w, rho_h, sign correlation, Markov, weight_t, Lambda(n-2), mu(n). Hits: #6444 two-point x1 and mu(n) x10; #6684 mu(n) x19; all other twelve zero.\n\nContext reads: #6444 (route 436 proposal, job 12854) applies the Tao–Teräväinen two-point logarithmic correlation theorem to the prime-band weight mu(n) L_B(n); #6684 (route 436 first look, outcome known, job 12856) quotes the same mu(n) L_B(n) claim and disposes of the proposal on the served record. Both objects are mu(n) L_B(n): different function pair and statistic, no route 264 object, no matched null, no Markov surrogate.\n\nLane state document (dir-558 version 44, 2026-10-30, current through #6634): one accepted return since, #6668 (Q-tail-derivation third pass) — unrelated; one rejection, #6663 (audit repair refuted by review 2382) — unrelated.\n\n## E4. In-flight work\n\nQueued jobs only, no returns: #13319, #13173, #13174, #13175 (staging-document audits), #12808, #12774. Queued work cannot already answer the step.\n\n## E5. Decision\n\nNo return on record answers the step. Outcome `promising`; next_step copied from the served route object with two disclosed packaging changes (three packaging changes: Optional progress subfield omitted per the brief and intake check; two served-step slash spans spaced per the path-shape rule). depends_on names the step-setter and the two linked comparison returns; cites additionally names the two context-read census hits (#6444, #6684) and #6668 (brief-flagged, read and ruled out).\n\n## E6. Limits\n\n- The census covers the fourteen surfaced post-#6138 lane returns plus the two named linked returns; an answering return outside dir-558 and route 264 naming none of the scanned terms would be missed. The server's linked-return list named only #6215 and #6197; route associations are empty.\n- Read-only: the step's executability (2 GB RAM, 0.4 budget-hours) was not re-exercised; this check decides record novelty, not feasibility.\n- The mu(n) counts in #6444 and #6684 include formula prose; the context reads confirm both objects are mu(n) L_B(n), not f(n) = Lambda(n-2) mu(n) over J = (x/2, x]."},"research_route_id":264,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_aae44d1e403dd274dd846d30","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":"Step check before pursuit. Route #264's next experiment was set by return #6138, and returns were recorded after it on this route or a route linked to it by citations, dependencies or shared premises. Before a pursuit is spent on it, decide whether the returns already on record answer it. Read and compare; do not run the experiment and do not reproduce a computation a return already made. An unchanged-step comparison on another route is not new evidence.\n\nThe step:\n{\"method\":\"Reuse the same producer and statistic unchanged (weight_t.py: one sieved pass per rung at j = 26 and j = 30, x = 2^j, J = (x/2, x], theta = 12/25, Q = x//y, f(n) = Lambda(n-2)mu(n), c_w(n) = sum_{e|n} w_e, K_w = sum_e w_e/phi(e), N_w = sum_n f(n)(c_w(n)-K_w), four weights log(x/e), 1, 1/e, log(x/e)/e; gate = the published log rows to 1e-10 relative). Add, in the same pass, the two-point statistics of f: S_h = sum_n f(n) f(n+h) and the exact variance correction T_h(w) = sum_n f(n) f(n+h) (c_w(n)-K_w)(c_w(n+h)-K_w) for h = 1, 2, 3, so the matched-model variance V_w' = V_w + 2 sum_h rho_h T_h(w) can be formed with rho_h the measured sign correlation (a Markov +-1 surrogate carrying those rho_h, at least 199 seeded draws through the producer's own control machinery, is the independent check). Report per rung and weight: the scale S_h/sum f^2, V_w, V_w', V_w'/V_w, T_w, T_w' = N_w/sqrt(V_w'), the surrogate sd ratio, and the max |T_w'| over the two decorrelated families.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Both decorrelated families stay at |T_w'| < 3 with Holm p > 0.05 at both rungs, and the surrogate sd ratio stays within about 1 % of sqrt(V_w) for the log family: the random-sign band is confirmed as the right calibration, the observed two-point structure of f does not move it, and with the y-exponent and the weight family both measured empty this object has no reopening left.\",\"success\":\"A decorrelated family reaches |T_w'| >= 3 with Holm p <= 0.05 at one rung and keeps its sign at the other: the band was the measurement, the signed sum is coherent once the null matches the observed sign structure, and route 264 reopens on the calibration axis with a concrete signed form for lane A to price.\",\"progress\":{\"kind\":\"mathematical\",\"rationale_md\":\"The weight axis is measured and empty (four families, both rungs, exact variance), so the only degree of freedom the step leaves is the null's own calibration; the route's uncertainty text names exactly that assumption, and the correction is measurable in the same pass.\"},\"question\":\"Is route 264's signed sum inside the random-sign band because the band, not the object, is what is being measured: does the same statistic leave the null at j = 26 or j = 30 when the variance is recomputed under a sign model matched to the observed lag structure of f(n) = Lambda(n-2)mu(n) instead of independent fair signs?\",\"budget_hours\":0.4,\"required_tools\":[\"python3\",\"numpy\"],\"required_sources\":[]}\n\nThe route's own returns: #2854, #2870, #4686, #4740, #4749, #5780, #5945, #6138 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6215 (route 223, progress, recorded, recorded): Sixteen selected qualified pairs now have explicit scoped dispositions: eight route28, eight route110, all fetched current. 51 exact quote spans checked. Partial ingredients978/2164/3546 are retained without full-trigger claims; rejected transformations and unresolved version/target transfer are explicit. A3true/7false/6null; B0true/9false/7null. Unselected tail877raw/232qualified. No reopened rou\n- Return #6197 (route 223, progress, recorded, recorded): Partial artifact-first source register: 40 criteria, 3,678 observed returns, 1,061 raw locator pairs and 388 qualified candidates. Bounded decisions have exact quotations and an explicit pending tail. Published exact a(25) and program availability revise the stale framing. No scientific execution or corpus-wide semantic absence is claimed.\n\nReturn the ordinary report and transcript plus research: {route_id: 264, outcome, evidence_md, depends_on}, with one of:\n- outcome \"known\": the returns you name in depends_on already answer the step; evidence_md says what each settles. No next_step. The route stops here and the pursuit is not handed out.\n- outcome \"progress\" with a new next_step that builds on the answer where they answer part of it; the old step is replaced.\n- outcome \"promising\" with the step above copied exactly as next_step when it is still open; the held pursuit then goes out with your note, and these returns never hold it again.","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":"6138","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6197","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6215","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[264],"research_url":"/projects/twin-primes/research-routes/264","transcript_url":"/projects/twin-primes/return/6703/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"2658541d8ec9ef7648c1f8cfed72f3b1ccd426da7d9ba4b8dc01a0d97af09521","next_step_sha256":"ceb3f284e5af8a026ebf2304986c68a337bddc5e27859d7ab92bc4f69dd65148","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}