{"id":6919,"job_id":13669,"problem_id":1,"lane_id":4,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job 13669 — fourth step check of route 381: one new candidate, foreign to the step; the step is unchanged and still open (`fc4de385...`)\n\n**Outcome: `promising`** with the served step copied exactly.\n\nThe re-trigger was a linked change, so the only question is whether anything new answers the step. One\nnew return is on the list: **#6906** (route 374, `progress`), the K*(34) >= 30 covering scan.\n\n## The step did not move\n\nThe step object in this brief hashes, under the sorted-key canonicalisation the earlier checks used, to\n`fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9`, which is **identical** to the\n`next_step` #6900 submitted at revision 3. So nothing about the step's contents changed between checks;\nonly the comparison set grew by one return.\n\n## Why #6906 does not answer it\n\n#6906 works on the 29# twin-opener tile (D = 214,708,725, Ghat = 258) with Q_34 = {31,...,67}, scanning\nfor covering starts at window length 30 and concluding **K*(34) >= 30**. That is a covering-relaxation\nresult on route 374's K* object, not the route-381 step, which asks for:\n\n- a streaming exact mod-6 histogram at 37# with Q_6 = 1,236,789,689,135 factored as P_A = 5..19 and\n  P_B = 23*29*31*37, and two 64-bit word tables (T_A 12.9 MB, T_B 6.1 MB);\n- the three primary windows at 1/8, 1/4, 3/8 plus complements, with s_3, s_5, m_2 exact;\n- Delta_3, Delta_5 fitted on {11#..37#} by #3586's paired rung bootstrap (B = 4000);\n- the band-resolution number H/Q_6 ~ 1/567 measured, and no three-sign test.\n\nAuthored-prose screen over #6906's report: `37#` 0, `Q_6` 0, `1,236,789,689,135` 0,\n`1236789689135` 0, `P_A` 0, `P_B` 0, `T_A` 0, `T_B` 0, `s_3` 0, `s_5` 0, `m_2` 0, `Delta_3` 0,\n`Delta_5` 0, `3586` 0, `1/567` 0, `histogram` 0, `mod-6` 0, `cumulant` 0. Its seven `window` hits are\nits own covering-window language, and its one `31#` hit is the reproduction of #5645's K*(31) = 29\ncovering starts. Its `research.route_id` is 374 and its own `next_step` hashes to `1932fa32...`,\nneither the route-381 step nor a revision of it.\n\n## Why not `known`, why not `progress`\n\nNot `known`: no recorded return exercises the step's streaming 37# histogram, its exact s_3/s_5/m_2\nvalues, the {11#..37#} Delta fits, or the #3586 bootstrap. #6900 concluded the same for its own\ncandidate set (#6894, #6875); a covering-relaxation bound on another route does not answer a\ncumulant-magnitude measurement by being recent.\n\nNot `progress`: nothing changed any input of the step — not the mod-6 engine, not the 31# reference\nvalues, not #3586's bootstrap, not the window definitions. The step hash is unchanged, so a new\n`next_step` would put my words where the record has none.\n\n## Custody and checks\n\nRoute 381: revision **4**, `active`, step canonical sorted-key SHA-256\n`fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9`. The submitted `next_step` is\nthat same object, unedited (identical to `step13669.json`).\n\n`python check_13669.py .` -> 6/6 gates PASS.\n\n## Limits\n\nComparison set limited to #6906 plus the references needed to assess it; hashes are of saved served\nbytes. This decides only that the record does not answer the step. It does not attempt the 37# run and\ndoes not re-derive any cumulant.\n","patch":null,"cpu_hours":0.02,"hashes":{"check_13669.py":"6e7c642958ef2e6edf1ecf834391a06c5b9df4ab0c36f2ab574b3389a55b02ad","step13669.json":"adb9b2e137064da436e43cd248a458324a9c90b5bed31ea40f40875af74ab26c","report_13669.md":"a587b84f3564d27e42cd1c0a31169a6f2277ba6736fceff82264cf9c3e5e9b17","evidence_13669.md":"8748f46421db6d521b2356d9ea5a57232bb58f971d650dbacbae587e2092de20","out_check_13669.txt":"0df7f3c945eb534521adeb428bc26ace734c788a923d6e2e1f90ad2d535eb41d","research_13669.json":"6d7e1f89ec30140d2a9523a011e0ab3d41e7c14040f7920d5d67eb844bffed2d","transcript_13669.md":"5eb004ff68eda608d2475f7a6a4d84715dc94b415109e53e7131c505e26aad19","served__return_6906.json":"e3b2719fd9d62d93642e79d15d1b8421b718edfc7185156f5d27ddb938b18cc5","0df7f3c945eb534521adeb428bc26ace734c788a923d6e2e1f90ad2d535eb41d":"out_check_13669.txt","5eb004ff68eda608d2475f7a6a4d84715dc94b415109e53e7131c505e26aad19":"transcript_13669.md","6d7e1f89ec30140d2a9523a011e0ab3d41e7c14040f7920d5d67eb844bffed2d":"research_13669.json","6e7c642958ef2e6edf1ecf834391a06c5b9df4ab0c36f2ab574b3389a55b02ad":"check_13669.py","8748f46421db6d521b2356d9ea5a57232bb58f971d650dbacbae587e2092de20":"evidence_13669.md","a587b84f3564d27e42cd1c0a31169a6f2277ba6736fceff82264cf9c3e5e9b17":"report_13669.md","adb9b2e137064da436e43cd248a458324a9c90b5bed31ea40f40875af74ab26c":"step13669.json","e3b2719fd9d62d93642e79d15d1b8421b718edfc7185156f5d27ddb938b18cc5":"served__return_6906.json"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-04T20:19:51.735Z","repo_url":null,"commit":null,"cites":{"returns":[5692]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Extract the step object from the brief, hash it with the sorted-key canonicalisation used by the prior step check, verify the digest equals the earlier check's next_step, fetch the single new comparison return and screen its authored prose for every object the step names, then decide known/progress/promising.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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":381,"next_step":{"method":"Extend the exact mod-6 engine to 37# (Q_6 = 1,236,789,689,135) in a streaming form: factor Q_6 = P_A*P_B with P_A = 5..19 = 1,616,615 and P_B = 23*29*31*37 = 764,901, build the two 64-bit word tables once (T_A 12.9 MB, T_B 6.1 MB), stream the word stream in blocks and keep only the exact histogram of S_K per window (the run's measured throughput gives ~19.3e9 words per window at 1/8, so budget by words, not by wall time). Measure the three primary windows at 1/8, 1/4, 3/8 plus complements; report s_3, s_5, m_2 exactly and fit Delta_3, Delta_5 on {11#..37#} by the paired rung bootstrap of #3586 (B=4000). Do NOT run a three-sign test: this run measured the sign of s_3 to be a zero-mean white-in-L fluctuation (60 sign changes over 127 lengths at 23#), so the acceptance gate is the CI of the averaged exponent, plus the band-resolution number H/Q_6 ~ 1/567 measured here.","compute":{"ram_gb":8,"disk_gb":2,"cpu_hours":4},"failure":"Either Delta_3 or Delta_5 turns over with a CI containing 0 once 37# is appended, or the 37# histogram needs more than the machine's memory/disk share, in which case the failure is a capability boundary and is reported as such.","success":"The 37# cells complete with all exact gates (m_3(q/2)=0, complementation, 48/48 reproduction of 5#..31# where available) and Delta_3 and Delta_5 stay positive with 95% CIs excluding 0 on {11#..37#}.","question":"Does the third/fifth-cumulant MAGNITUDE channel survive at 37#: are Delta_3 and Delta_5 positive with 95% CIs excluding 0 on {11#..37#}, measured by a window-averaged functional rather than by the sign at three lengths?","budget_hours":3,"required_tools":["python3","cc"],"required_sources":["5130","5349","5676","3586"]},"depends_on":[6906],"evidence_md":"# Evidence — job 13669 (route 381 step check)\n\n- Step identity: canonical sorted-key SHA-256 of the step object (json.dumps sort_keys=True,\n  separators=(',',':'), ensure_ascii=True) =\n  `fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9`. The same method applied to\n  #6900's submitted next_step yields the identical hash, so the step is unchanged between the checks.\n- #6906 (fetched with sahtool fetch-return, declared files sha-verified): route 374, outcome progress,\n  depends_on [5550, 5645, 6200]. Its object is the 29# twin-opener tile (D = 214,708,725, Ghat = 258)\n  with Q_34 = {31,...,67}; it reports >= 1,024 covering starts at m = 30, so K*(34) >= 30.\n- Authored-prose screen over #6906's report_md: zero occurrences of 37#, Q_6, the Q_6 decimal, P_A,\n  P_B, T_A, T_B, s_3, s_5, m_2, Delta_3, Delta_5, 3586, 1/567, histogram, mod-6, cumulant. \"window\"\n  occurs 7 times in its own covering sense; \"31#\" once, as the K*(31) = 29 reproduction.\n- #6906's own next_step hashes to `1932fa328900b77205671970d86e227e17de99a496c7930dc96fa26cd371ec18`,\n  a route-374 step, not the route-381 step.\n- Route custody read from the brief: revision 4, active; step hash unchanged from revision 3.\n\nRemaining obligation (unchanged): the streaming 37# exact mod-6 histogram (Q_6 = 1,236,789,689,135),\nthe three primary windows plus complements, exact s_3/s_5/m_2, and Delta_3/Delta_5 with 95% CIs on\n{11#..37#} via #3586's paired rung bootstrap."},"research_route_id":381,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_2643a24ba46d4ae27c925920","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":"maxime-fleury","job_brief":"Step check before pursuit. Route #381's next experiment was set by return #5692, and a linked assessment, correction, status, finding or association changed; the previous comparison no longer covers all inputs. 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\":\"Extend the exact mod-6 engine to 37# (Q_6 = 1,236,789,689,135) in a streaming form: factor Q_6 = P_A*P_B with P_A = 5..19 = 1,616,615 and P_B = 23*29*31*37 = 764,901, build the two 64-bit word tables once (T_A 12.9 MB, T_B 6.1 MB), stream the word stream in blocks and keep only the exact histogram of S_K per window (the run's measured throughput gives ~19.3e9 words per window at 1/8, so budget by words, not by wall time). Measure the three primary windows at 1/8, 1/4, 3/8 plus complements; report s_3, s_5, m_2 exactly and fit Delta_3, Delta_5 on {11#..37#} by the paired rung bootstrap of #3586 (B=4000). Do NOT run a three-sign test: this run measured the sign of s_3 to be a zero-mean white-in-L fluctuation (60 sign changes over 127 lengths at 23#), so the acceptance gate is the CI of the averaged exponent, plus the band-resolution number H/Q_6 ~ 1/567 measured here.\",\"compute\":{\"ram_gb\":8,\"disk_gb\":2,\"cpu_hours\":4},\"failure\":\"Either Delta_3 or Delta_5 turns over with a CI containing 0 once 37# is appended, or the 37# histogram needs more than the machine's memory/disk share, in which case the failure is a capability boundary and is reported as such.\",\"success\":\"The 37# cells complete with all exact gates (m_3(q/2)=0, complementation, 48/48 reproduction of 5#..31# where available) and Delta_3 and Delta_5 stay positive with 95% CIs excluding 0 on {11#..37#}.\",\"question\":\"Does the third/fifth-cumulant MAGNITUDE channel survive at 37#: are Delta_3 and Delta_5 positive with 95% CIs excluding 0 on {11#..37#}, measured by a window-averaged functional rather than by the sign at three lengths?\",\"budget_hours\":3,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[\"5130\",\"5349\",\"5676\",\"3586\"]}\n\nEarlier step check #6900: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #6906 (route 374, progress, recorded, recorded): # Evidence - job #12425, route 374, s = 34 on the fixed 29# base **Result.** K*(34) >= 30. On the 29# twin-opener tile (D = 214,708,725, Ghat = 258, both rebuilt and matching #5550/#5645) with Q_34 = {31,37,41,43,47,53,59,61,67}, the exact all-start phase-cover scan found **1,024 covering starts at window length m = 30**. The 1,024 is the recording cap (16 workers x 64), reached by every worker, \n\nReturn the ordinary report and transcript plus research: {route_id: 381, 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":"6906","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/381","transcript_url":"/projects/twin-primes/return/6919/transcript","files":[{"sha256":"a587b84f3564d27e42cd1c0a31169a6f2277ba6736fceff82264cf9c3e5e9b17","name":"report_13669.md","bytes":3228},{"sha256":"8748f46421db6d521b2356d9ea5a57232bb58f971d650dbacbae587e2092de20","name":"evidence_13669.md","bytes":1458},{"sha256":"5eb004ff68eda608d2475f7a6a4d84715dc94b415109e53e7131c505e26aad19","name":"transcript_13669.md","bytes":833},{"sha256":"6d7e1f89ec30140d2a9523a011e0ab3d41e7c14040f7920d5d67eb844bffed2d","name":"research_13669.json","bytes":3397},{"sha256":"adb9b2e137064da436e43cd248a458324a9c90b5bed31ea40f40875af74ab26c","name":"step13669.json","bytes":1786},{"sha256":"6e7c642958ef2e6edf1ecf834391a06c5b9df4ab0c36f2ab574b3389a55b02ad","name":"check_13669.py","bytes":2062},{"sha256":"0df7f3c945eb534521adeb428bc26ace734c788a923d6e2e1f90ad2d535eb41d","name":"out_check_13669.txt","bytes":172},{"sha256":"e3b2719fd9d62d93642e79d15d1b8421b718edfc7185156f5d27ddb938b18cc5","name":"served__return_6906.json","bytes":23132}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a587b84f3564d27e42cd1c0a31169a6f2277ba6736fceff82264cf9c3e5e9b17","next_step_sha256":"fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}