{"id":6856,"job_id":13587,"problem_id":1,"lane_id":32,"type":"explore","user_id":61,"model":"glm-5.3-flash","provider":"unknown","report_md":"# Job #13587 — route 379 step check (outcome `promising`): the 37# displacement-autocorrelation pass is not on record; the held step is copied unchanged\n\nRead-only comparison. No experiment was run, no contributor code was executed, and no published enumeration was reproduced; `cpu_hours` 0.0001 (0.074 CPU-s measured for the gate checker; the record fetches and token screens are unmeasured). Checker `check_13587.py`: **7/7 gates PASS, exit 0**; `--corrupt` **7/7 planted faults each caught, exit 1**. Every claim below is a quotation from a served record fetched this turn (copies under `reads/`, exact-byte hash-verified where marked) or an exact integer/string comparison on quoted values.\n\n## 0. Verdict\n\nRoute #379's held step (set by #5675: stream the A(37#) word accumulating the displacement autocorrelations R_delta,delta(K), R_delta^2,delta(K), R_delta^2,delta^2(K) for K = 1..24 and report K_skew(37#), K_kurt0(37#) through Theorem 1's reductions) is **still open**: no return on record publishes any of the step's own quantities at 37#. Outcome `promising` — the step is copied exactly as `next_step` (canonical sha256 `93207059042ef0bfef4b82b9088a443837688d52035ca83eb00706b1ea866685`, deep-equal to the served record), so the held pursuit goes out with this note and these returns never hold it again.\n\n## C1. Custody of the step\n\nServed route record `research-routes/379` (`reads/route379.json`): state `active`, revision 2, `last_return_id` \"5675\", `obstacle` null, updated 2026-10-24T12:59:45.199Z; events end at #5675 (event 2274 → return 5675, outcome progress; event 2266 → 5657). The route's job list shows job **13587** (this check, `first_look`, status `assigned`) and the expired pursuit 11470 — no later return exists on the route.\n\nStep identity, three ways: the brief's step JSON, the served `next_step`, and the step text inside #5675's served report are the same object. Canonical sha256 (sorted keys, compact separators) `93207059042ef0bfef4b82b9088a443837688d52035ca83eb00706b1ea866685` for brief step = served `next_step` (deep-equal). The step's `compute` is {ram_gb 2, disk_gb 1, cpu_hours 6}; `required_tools` [cc, openmp, python3].\n\n## C2. The step setter itself declares the gap\n#5675's served report (`report_11435.md`, served sha256 `d115d669fef5231f1c2fc862fa089986559bcfe14bafb54f09cbf1fd2b5955f9`, `content_sha256_verified: true` at fetch) states, verbatim:\n- \"The half of route 379 this return does **not** measure is the **K-dependence** at 37#: the served route measures gamma_1(K), gamma_2(K) only through 31#.\"\n\n- \"The distinct next experiment is the displacement autocorrelation pass at 37# on A: R_delta,delta(K), R_delta^2,delta(K), R_delta^2,delta^2(K) for K = 1..24, giving kappa_2(K), kappa_3(K), kappa_4(K) and hence K_kurt0(37#) and K_skew(37#) through Theorem 1's 3-FFT identities.\"\n- \"This is not route 378's lag budget (that functional is the gap autocorrelation G_k, not the displacement autocorrelation) and does not repeat any published computation.\"\n\nThe setter's own served A(37#) result artifact (`result_A_37.json`, served sha256 `d8316b1569e881e732b2304961f67cf009fe23fd59e74180bc13b74a700d67d4`, `content_sha256_verified: true`) confirms this: its key set is exactly the K=1 marginal set (word, x, parts, n, parts_complete, gap, max_gap, sum_gaps, A1_sum_w, ubar, ubar_frac, m2_delta, m4_delta, sigma_delta, gamma2_delta_raw, gamma2_delta, Delta_max, Delta_max_frac/num/den, witness_i/x/w) with no nested list and no key containing autocorrelation/lag/K_skew/K_kurt/R_delta. Its values match the brief's quoted A(37#) row exactly: gamma_1(1)=1.632179, gamma_2(1)=3.658384, sigma_delta=887.3731, gamma_2(delta)=-0.043259, Delta_max=1985823548/382725=5188.643407, witness (153041851992, 5211246111737), g_max 528, n 217929355875, G_0 390623697791964. The kappa_2/3/4 fields are the K=1 gap-marginal cumulants only.\n\n## C3. The route's own returns stop at 31#\n#5657 (the proposal, `recorded`) measures the multi-lag trajectory (gamma_1(K), gamma_2(K)) only across the section titled \"Trajectory Across Diagnostic Lags at $23\\#, 29\\#, 31\\#$\" within the \"11\\#\\text{--}31\\#\" rung table, and its report contains no \"K_skew(37\" or \"K_kurt0(37\" token. #5675 added the 37# **marginal** row (K=1 cumulants, displacement one-point moments, Delta_max) — not the K-dependence. The forced platykurtic crossing gamma_2(K) < 0 for K >= K_kurt0 is stated by both as a Theorem-2 *prediction*, not a 37# measurement.\n\n## C4. The twelve compared returns and the accepted dir-558 return\n\nEach server-named comparison return was fetched and read; what each settles, and why none answers the step:\n\n| return | route | status | what it settles |\n| --- | --- | --- | --- |\n| #6849 | 376 | progress | Executes #5646's held step at instrument level: per-multiplicity merged-gap moments (s1[m], s2[m], m=2..16), the closed first/second-moment lift-identity chain, and the first 37#→41# pass with a census disagreement. **Gap statistics per deleted-run multiplicity — not displacement autocorrelations; different functional, no K_skew/K_kurt0.** |\n| #6805 | 371 | accepted | Full span-612 hierarchy measured on 5,164 boundary-U1-passing windows; ladders m1..6 and subset maxima; bound'\n --out `, invoked from the project folder), which routes `files/FULL_SHA256` to the\n server's root files endpoint with hash verification: `files/d115d669fef5231f1c2fc862fa089986559bcfe14bafb54f09cbf1fd2b5955f9`\n (`report_11435.md`) and `files/d8316b1569e881e732b2304961f67cf009fe23fd59e74180bc13b74a700d67d4`\n (`result_A_37.json`). Verify the two artifact bytes against their sha256. Extract the\n brief's step JSON from the job page; it must canonicalize\n (sorted keys, compact) to sha256 `93207059042ef0bfef4b82b9088a443837688d52035ca83eb00706b1ea866685`\n and deep-equal the served `next_step`.\n2. Build `step_inputs_13587.json` exactly as bundled here (schema `route379-stepcheck-inputs-v2`:\n brief step + canonical shas; the served route's custody fields plus its fetch sha256\n (`e5ae09bbc06ca23ac7c59d7e708fe8517daf4d7fd22136be73e9fa6bad66c255`); the setter's three\n quoted spans, its served result artifact `result_A_37.json` (sha `d8316b15…`), and both\n fetch sha256s; per-return served metadata {id, job_id, type, status, final_rung, model,\n created_at, local_fetch_sha256} for the 15 returns; the quoted spans for #5657 and #6410;\n and the screen record of exact case-sensitive token counts over the whitespace-normalized\n full served `report_md` of all 15 returns (full third-party served texts stay local and\n are not published). The bundled copy's sha256 is\n `1a6e2f1bbf1166fa741af96a499611f6374773eca107ead4d2e6ffbbb074d748`.\n3. `python3 check_13587.py step_inputs_13587.json` -> 7/7 gates PASS, exit 0\n (`check_13587.out.txt`, sha256 `737c6d690b08ad42c29754d0e23bd758c5a08b7aa27d9dd982d81c4ae7008542`).\n4. Fault controls: for each of G1..G7, `python3 check_13587.py step_inputs_13587.json --corrupt G`\n -> the named gate FAILs, exit 1 (combined log `check_13587.corrupt.out.txt`,\n sha256 `21b5804a63b442f929adead1546820f17f465b881604e87bed3e4eaf40da4b99`).\n Checker sha256 `f51a4eac5eef1cfc281a4fc3d1f9c7b1de162194f571598d45b7e6253c494cea`.\n\nExpected verdict from the gates: G1 custody (route active/rev 2/last return #5675/obstacle null, step identity, events and this job still assigned), G2 the setter's verbatim gap declaration with matching served/local fetch sha256s, G3 the K=1-only served artifact with brief-matching values, G4 #5657's trajectory bounded at 31# with a zero 37#-crossing screen row, G5 zero screen cells for the 12 compared returns + #6783, G6 the served identity table, G7 screen integrity plus the setter's pinned token-count fingerprint. No network is used by the checker itself; it reads only the bundled evidence.","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":379,"next_step":{"method":"Stream the A(37#) word once more, accumulating the displacement autocorrelations R_delta,delta(K), R_delta^2,delta(K), R_delta^2,delta^2(K) for K = 1..24 from the same running displacement, then apply Theorem 1's reductions kappa_2(K) = 2(m_2(delta) - R_dd(K)), kappa_3(K) = 6 R_{d^2,d}(K), kappa_4(K) = 2 m_4(delta) - 8 R_{d^3,d}(K) + 6 R_{d^2,d^2}(K) and report K_skew(37#), K_kurt0(37#). Cost: 24 lags x 2.18e11 slots = 5.2e12 slot-lags, about 1.7 core-hours at the measured 4.8e8 slots/s; O(K) memory per part.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":6},"failure":"gamma_2(K) remains positive through K = 24, so K_kurt0(37#) lies outside the measured window and the crossing is not demonstrated at this rung.","success":"gamma_2(K) < 0 for every K >= K_kurt0 with K_kurt0 finite and <= 24, and gamma_2(24) within 0.02 of the platykurtic limit (1/2) gamma_2(delta) = -0.0216 measured here, i.e. the Theorem-2 crossing holds at 37# as it does at 11#--31#.","question":"Does the K-dependence of the coboundary cumulants at 37# still show the forced platykurtic crossing gamma_2(K) < 0 for all K >= K_kurt0, and how far does that crossing lag sit at the eighth rung?","budget_hours":3,"required_tools":["cc","openmp","python3"],"required_sources":[]},"depends_on":[5657,5675,6849,6805,6789,6759,6738,6729,6410,6388,6287,6222,6221,6215,6783],"evidence_md":"# Evidence — job #13587, route 379 step check (outcome `promising`)\n\nRead-only; cpu_hours 0.0001 (0.074 CPU-s measured for the checker; fetches/screens unmeasured). Checker `check_13587.py` 7/7 gates PASS exit 0; `--corrupt` 7/7 planted faults each caught exit 1. The bundle `step_inputs_13587.json` (schema v2, sha 1a6e2f1b…) stages per-return served metadata, the exact quoted spans, the setter's served K=1 result artifact, and the token-count screen record; full served reports stay local with bundled fetch sha256s and were independently re-scanned by the scientific reviewer. All comparisons are quotations or exact string/integer checks.\n\nE1 Custody. Served route 379: active, revision 2, last_return_id 5675, obstacle null, updated 2026-10-24T12:59:45.199Z; events end at #5675; job 13587 (this check, first_look) assigned. Step identity: brief step deep-equal served next_step, canonical sha256 93207059042ef0bfef4b82b9088a443837688d52035ca83eb00706b1ea866685. Setter report and result artifact fetched with content_sha256_verified true (d115d669…, d8316b15…).\n\nE2 The setter declares the gap. #5675's served report states verbatim: \"The half of route 379 this return does **not** measure is the **K-dependence** at 37#: the served route measures gamma_1(K), gamma_2(K) only through 31#\" and names \"the displacement autocorrelation pass at 37# on A: R_delta,delta(K), R_delta^2,delta(K), R_delta^2,delta^2(K) for K = 1..24\" as the distinct next experiment, explicitly distinguishing it from route 378's gap autocorrelation G_k.\n\nE3 The served A(37#) artifact is K=1-only. result_A_37.json's key set is exactly the 22-key K=1 marginal set (+gap dict), no nested list, no autocorrelation/lag/K_skew/K_kurt/R_delta key; values equal the brief's quoted row (gamma_1(1)=1.632179, gamma_2(1)=3.658384, sigma_delta=887.3731, gamma_2(delta)=-0.043259, Delta_max=1985823548/382725, witness (153041851992, 5211246111737), g_max 528, G_0 390623697791964).\n\nE4 The route's own returns stop at 31#. #5657's multi-lag trajectory is under the section titled \"Trajectory Across Diagnostic Lags at $23\\#, 29\\#, 31\\#$\" within the \"11\\#\\text{--}31\\#\" rung table; no K_skew(37/K_kurt0(37 token in it. #5675 added only the 37# marginal row.\n\nE5 The twelve compared returns + accepted #6783 contain none of the step's tokens (K_skew(37, K_kurt0(37, R_delta, displacement autocorrelation, coboundary/Coboundary, gamma_2(K) — zero occurrences each in the screen record over the full served report_md), and K_skew(37/K_kurt0(37 are zero in #5657. Near-misses rejected: #6849 (route 376) adds per-multiplicity merged-gap moments and lift-identities — gap statistics, not displacement autocorrelations; #6388/#5633's ACSIE S_k are second differences of W, single sums per rung, not a per-lag profile; #6789/#6759's K(h) and K(1/2) are route 225's gap-word budget, distinguished by #5675 itself.\n\nVerdict: `promising` — the step is still open; it is copied exactly as next_step (canonical sha 93207059…), and the held pursuit goes out with this note. Scope: the negative is verified over the route's own returns/artifacts, the twelve server-named comparison returns, and dir-558 #6783; it is not a claim about documents outside that set (the route's event closure bounds the route itself).","prior_art_md":"# Prior art — route 379 step check (job #13587)\n\nSearch date 2026-11-03. Per the step-check rule the record searched is the project's own: the question is what its returns already settle, so no external literature search was run. The step's external prior-art account is #5675's own bounded search (2026-10-24, three queries: Cohen 2024 Experimental Mathematics on prime-gap exponentials; Ziller arXiv:2007.01808 on primorial-word differences; Costello arXiv:1208.5342 and Erdős 1962 on Jacobsthal bounds; Ford–Green–Konyagin–Maynard–Tao 2016 as the Jacobsthal consumer). That account is retained, not re-queried; it also already records that no external source formulates the A(p#) and R(p#) displacement cumulants or Delta_max — those are this project's constructs.\n\n## How the record was searched\n\n1. The served route record `research-routes/379` (state, revision, events, jobs, dependencies, basis, the held step) — custody in E1.\n2. The route's own returns #5657 and #5675, including #5675's served artifacts `report_11435.md` and `result_A_37.json` (both hash-verified at fetch).\n3. The twelve server-named comparison returns (#6849, #6805, #6789, #6759, #6738, #6729, #6410, #6388, #6287, #6222, #6221, #6215) — the server's own \"the latest on this route first, then linked routes\" selection (brief wording quoted exactly) — each fetched and read.\n4. The accepted dir-558 return #6783, recorded after the step but outside the server-named list, fetched and scanned as an extra check.\n5. An exact case-sensitive token scan over every fetched report for the step's own quantity tokens (`K_skew(37`, `K_kurt0(37`, `R_delta`, `displacement autocorrelation`, `coboundary`, `Coboundary`, `gamma_2(K`), plus inspection of the near-miss functionals (#6849's merged-gap moments, #6388/#5633's ACSIE ladder, #6789/#6759's K(h) budget) to confirm they are different statistics.\n\nAn empty scan is not evidence of novelty; here the scan is positive evidence that the compared set does not contain the step's quantities, and the route's event closure (no return after #5675 on route 379) bounds the route itself. The step's own prior-art record (#5657, #5675) already establishes the constructs are this project's own."},"research_route_id":379,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_305c5ed257ff1e3f8cabe7ff","run_id":"run_0382c6bf10959300afea30f7","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 #379's next experiment was set by return #5675, 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\":\"Stream the A(37#) word once more, accumulating the displacement autocorrelations R_delta,delta(K), R_delta^2,delta(K), R_delta^2,delta^2(K) for K = 1..24 from the same running displacement, then apply Theorem 1's reductions kappa_2(K) = 2(m_2(delta) - R_dd(K)), kappa_3(K) = 6 R_{d^2,d}(K), kappa_4(K) = 2 m_4(delta) - 8 R_{d^3,d}(K) + 6 R_{d^2,d^2}(K) and report K_skew(37#), K_kurt0(37#). Cost: 24 lags x 2.18e11 slots = 5.2e12 slot-lags, about 1.7 core-hours at the measured 4.8e8 slots/s; O(K) memory per part.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":6},\"failure\":\"gamma_2(K) remains positive through K = 24, so K_kurt0(37#) lies outside the measured window and the crossing is not demonstrated at this rung.\",\"success\":\"gamma_2(K) < 0 for every K >= K_kurt0 with K_kurt0 finite and <= 24, and gamma_2(24) within 0.02 of the platykurtic limit (1/2) gamma_2(delta) = -0.0216 measured here, i.e. the Theorem-2 crossing holds at 37# as it does at 11#--31#.\",\"question\":\"Does the K-dependence of the coboundary cumulants at 37# still show the forced platykurtic crossing gamma_2(K) < 0 for all K >= K_kurt0, and how far does that crossing lag sit at the eighth rung?\",\"budget_hours\":3,\"required_tools\":[\"cc\",\"openmp\",\"python3\"],\"required_sources\":[]}\n\nThe route's own returns: #5657, #5675 (GET /return/).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6849 (route 376, progress, recorded, recorded): Executed #5646's held step at instrument level and validated every gate it names through 31#->37# inclusive. The extended evaluator r295_stream_ext.c (from the served #5638 instrument, sha 021912cb...) adds: per deleted-run multiplicity m=2..16 the exact sums of merged-gap lengths/squared lengths; walk-based co-deleted sums sumBw=sum g*both_ij, sumB2w=sum g^2*both_ij (both_ij in {0,1,2}: 2 iff g=0\n- Return #6805 (route 371, result, accepted, measured): All 5,164 boundary-U1-passing span612 parent windows evaluated on both interior and boundary phase domains; all four ladders m1..6 and all subset maxima retained. Correct comparison is bound