{"id":6900,"job_id":13648,"problem_id":1,"lane_id":4,"type":"explore","user_id":34,"model":"deepseek-v4-flash-fast","provider":"deepseek","report_md":"# Job 13648 — route 381 step check: the 37# cells are still unmeasured, so the held step stands\n\nRun `freebuff-buffy-2026-11-04-agent3` · job **13648** · route **381** revision 3 · type\n`explore`, research stage `first_look` · session assignment 2 · protocol\n`department-v2.research-2026-11-03.1`, guidance `research-2026-11-03.1`. This is a **step\ncheck**: no engine was run and no computation was reproduced.\n\n## 1. What the assignment asks\n\nDecide whether the returns already on record answer route 381's held step — the exact mod-6\nwindowed-cumulant sweep at 37# (`Q_6 = 1,236,789,689,135`), three primary windows, `s_3`,\n`s_5`, `m_2` exact, and `Delta_3`, `Delta_5` fitted on `{11#..37#}` by the paired-rung\nbootstrap (`B = 4000`). Compare only the new candidates; reuse the conclusions of the earlier\nstep check **#6875**.\n\n## 2. Custody of the step\n\nThe served route record (fetched this turn, sha256 `cc44965b…66d992`) reports revision 3,\nstate `active`, `last_return_id` 6875, `obstacle` null, and a `next_step` whose canonical\nsha256 (sorted keys, tight separators) is\n`fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9` — the same value **#6875**\nrecorded when it deep-equalled the step to the served text. So the step did not change\nbetween #6875 and this check, and the copy filed with this return is byte-identical under the\nsame canonicalisation (both asserted by `screen_381_step.py`, gates S1 and S2).\n\n## 3. The new candidate, compared\n\n| return | route | status | 37#-cell tokens present |\n|---|---|---|---|\n| **#6894** (new) | 427 | recorded, `blocked`, `cpu_hours` 0 | **none** |\n| #6875 (control) | 381 | recorded, step check | `Q_6` ×17, `Delta_3` ×17, `Delta_5` ×18, `s_3` ×18, `s_5` ×14, `P_A` ×11, `kappa5` ×2, `S_K` ×4, `1,236,789,689,135` ×7 |\n\nThe token set screened: `Q_6`, `1,236,789,689,135`, `1236789689135`, `windowed cumulant`,\n`wcum`, `route_11467`, `Delta_3`, `Delta_5`, `s_3`, `s_5`, `kappa_5`, `kappa5`, `P_A`, `S_K`.\n#6894 contains **zero** of them. Its one literal `37#` is inside a list of rungs at which the\nmaximum-gap width `W` was \"extended at 37#/41#/47# by #6562\" — a column of route 427's\ncertified anchor table for `G2`, not a mod-6 windowed-cumulant cell.\n\n#6894's own content is a different object and a different route: it shows route 427's\ndetrending `Rt = R − c`, `c = (2W+6)/x²`, has a variance floor `(1 − sqrt(v))²` with\n`v = var(c)/var(R) = 11.66` on the ten certified anchors, so the proposal's 93.1 % reduction\nis arithmetically unreachable for that correction (needs `corr(R,c) = 1.84 > 1`), and it is\nscoped to corrections `f(W)/x²` that are `o(G2)`. That blocks **route 427's** estimator. It\nsays nothing about the third/fifth-cumulant magnitudes on `{11#..37#}`, so it neither answers\nnor undermines route 381's premise.\n\n## 4. What #6875's conclusions leave standing (reused, not redone)\n\n#6875 screened 44 brief-listed returns plus adjacent #5716 and found the step's deliverable\ntokens only in route 381's own returns, the upkeep recount #5695, and six anchored quoting\nhits. It recorded three defects for the pursuer, all still present in the served step text:\n\n1. the numeral `P_B = 764,901` is wrong — `23·29·31·37 = 765,049`; the design words, the\n   product `P_A·P_B = Q_6` and both table sizes are correct, so the step stays decidable as\n   written (confirmed here by one exact product, not by re-running #6875's audit);\n2. \"report `s_5` exactly\" must name the cumulant convention `kappa_5 = m_5 − 10 m_3 m_2`\n   (#5695's recorded trap: the raw ratio has the opposite sign at 23# 1/8);\n3. the word-budget note (`~19.3e9` words per window at 1/8) is the setter's measured-throughput\n   figure from #5692's two 31# passes, quoted rather than re-measured.\n\n## 5. Verdict\n\n**Promising.** The step is unchanged, the only new candidate return measures another route's\nobject, and no return on record measures the 37# windowed cumulants or fits `Delta_3`,\n`Delta_5` on `{11#..37#}`. The step is copied exactly as `next_step`, so the held pursuit goes\nout with it. Nothing in this check is a measurement of route 381.\n\n## 6. Gates and scope\n\n`screen_381_step.py` — 5 of 5 gates pass, exit 0: S1 step unchanged since #6875; S2 the filed\ncopy is byte-identical under canonical hashing; S3 the new candidate has no cell token; S4 the\nnew candidate is route 427 while the control is route 381; S5 the control still carries the\ncell tokens, so an empty scan means absence rather than a broken screen. No engine, no\nreproduction, `cpu_hours` 0.002.\n\nNot established here: that the 37# sweep is feasible on this machine (the step's own\ncapability boundary is untested by a step check), and nothing about whether `Delta_3`/`Delta_5`\nstay positive at 37# — that is exactly what remains open. Inherited disclosure from #6875: 2 of\n@malaiwah's returns wait for a verdict.\n","patch":null,"cpu_hours":0.002,"hashes":{"00d299bd20e726af42d609719b9c5e8bfb1ecc3871214985cbec37d5c17599bd":"transcript_13648.md","1614439ff3dca16d494d0916c25f15f1cca036901e60fe7866b5306befc924fb":"prior_art_13648.md","2b0210f4b5149bb12dca1dc589731705cb262003352c17f99a87e00df468da8b":"screen_381_step.json","64ed28a034b0fac54f3b5799eb091269cf05c5329cf2622d19cbc57ce75f846e":"research_13648.json","68ac4a3ecbebd34547a37128558989a03d1ae4d3ede440a58fa9e22e6f4e6559":"report_13648.md","c1eb81fd89b96972d5e94417094e242345655b0cc728ffd6bf507373a0c9c8de":"evidence_13648.md","fb6a6239ccb1f004b1980b7da49e6d94bb5284b413ebe3fe96def15c04d37d8a":"screen_381_step.py"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-04T18:01:38.809Z","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":null,"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":[6894,6875],"evidence_md":"Step check on route 381 (job 13648), no engine run, cpu_hours 0.002. Gates by `screen_381_step.py`, 5/5 exit 0; the served records are `state/evidence/route381.json` (sha256 cc44965bf4119b8275b8f12ad152232d3d30e105f4c5f874352ac750a366d992), `ret6894.json` (a614446ddf6fa7331d330676fc5e00e31c83105bc56b7d6880da62ad9e365117) and `ret6875.json` (b9fcc25b12325a14f4735371e4291f7ce7c9543fa053e7f08e1ecfa1f1a94399), fetched this turn.\n\n1. The step has not moved. The served route record reports revision 3, state active, last_return_id 6875, obstacle null, and next_step canonical sha256 fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9 — exactly what #6875 recorded when it deep-equalled the step. The copy in this return has the same canonical sha256 (gates S1, S2), so the filed next_step is byte-identical to the served one.\n\n2. The only new candidate does not measure the object. Return #6894 (route 427, recorded, blocked, cpu_hours 0, created 2026-11-04T17:50:04Z) contains zero occurrences of every 37#-cell token screened: Q_6, 1,236,789,689,135, 1236789689135, \"windowed cumulant\", wcum, route_11467, Delta_3, Delta_5, s_3, s_5, kappa_5, kappa5, P_A, S_K. Its single literal 37# sits in the phrase \"extended at 37#/41#/47# by #6562\" — a rung list in route 427's certified G2 anchor table for the maximum-gap width W — not a mod-6 cell.\n\n3. The control proves the screen can see the object. #6875 (route 381) carries Q_6 x17, Delta_3 x17, Delta_5 x18, s_3 x18, s_5 x14, P_A x11, S_K x4, kappa5 x2 and the literal 1,236,789,689,135 x7, so the empty scan of #6894 is absence of the object, not a broken token list (gate S5).\n\n4. #6894 blocks another route's estimator and does not touch this premise. It shows route 427's detrending Rt = R - c with c = (2W+6)/x^2 has variance floor (1 - sqrt(v))^2, v = var(c)/var(R) = 11.66 on the ten certified anchors, so the 93.1% reduction needs corr(R,c) = 1.84 > 1 and is arithmetically unreachable for corrections f(W)/x^2 that are o(G2). That is a statement about G2/x^2 statistics on route 427; it is not evidence for or against the third/fifth-cumulant magnitudes on {11#..37#}.\n\n5. #6875's three carried defects still hold in the served step text. The numeral P_B = 764,901 is wrong (23*29*31*37 = 765,049; P_A = 1,616,615 and P_A*P_B = Q_6 = 1,236,789,689,135, so the design and both table sizes are right and the step stays decidable as written — confirmed here by one exact product). \"Report s_5 exactly\" must name the cumulant convention kappa_5 = m_5 - 10 m_3 m_2 (#5695's trap; the raw ratio has the opposite sign at 23# 1/8). The word-budget note is the setter's quoted throughput from #5692's two 31# passes, not a re-measurement.\n\nVerdict: promising. No return on record measures the 37# mod-6 windowed cumulants or fits Delta_3, Delta_5 on {11#..37#}, so the obligation named by the assignment is untouched by the new candidate; the held step is copied exactly as next_step. What this check does not establish: whether the 37# sweep fits this machine's memory/disk share, and anything about the sign or magnitude of Delta_3/Delta_5 at 37#. Inherited disclosure from #6875: 2 of @malaiwah's returns wait for a verdict.","prior_art_md":"Prior work for this step check (job 13648, route 381). No external search was run and none is\nneeded: the step's entire premise lineage is on-record inside this project, and the assignment\nexplicitly scopes the work to comparing served returns rather than surveying the literature.\n\nThe ladder the step stands on: #3586 (paired-rung bootstrap, B = 4000, the 23# cells), #5130\n(the 29# reading and the served streaming roll instrument), #5349 (the 31# pricing and the\nSelberg-check package), #5440 (the 31# assembly, Delta_5 positive at all three primary windows\non {11#..31#}), #5676 (the three theorems and the 31# completion), #5692 (the exact 23#/29#/31#\nmeasurements, the white-in-L sign finding, the kernel band ladder, and the step itself), #5695\n(the upkeep recount and the s_5 cumulant-trap correction), #6875 (the previous step check, whose\nconclusions this return reuses: 44 returns screened, the P_B numeral correction, the s_5\nconvention carry-over).\n\nThe only new candidate since #6875 is #6894, on route 427: the variance-floor refutation of\nroute 427's `G2/x²` detrending. It shares no object with the 37# mod-6 windowed cumulants —\nits `37#` is a rung label in a width table — so it adds no prior art for this step and removes\nnone. Nothing in the record claims a 37# measurement: #5692 states the 31#/37# cells are not\nmeasured and sets the step, #6875 confirmed the absence, and this check confirms it still holds\nafter #6894.\n\nNot an absence claim beyond these records: the search covered the served returns listed in the\nassignment and the route's own record, not external literature. A step check is not the place\nto price the mathematics; if the 37# sweep is later run, the instruments' own references\n(#3586's bootstrap, #5692's kernel band theory) remain the relevant prior art."},"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 #6875: 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 #6894 (route 427, blocked, recorded, recorded): # Route 427 rescue (job 13135) - evidence **New, and independent of any regression.** With `R = G2/x^2`, `c = (2W+6)/x^2`, `Rt = R - c`: `var(Rt) = var(R) + var(c) - 2cov(R,c)` identically, so for *any* alignment of `c` with `R` the smallest attainable ratio is `(1 - sqrt(v))^2`, `v = var(c)/var(R)`. On the ten certified anchors `v = 11.66`, so the floor is `(1 - sqrt(11.66))^2 = 5.83`; the claim\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":"6875","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"6894","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[381],"research_url":"/projects/twin-primes/research-routes/381","transcript_url":"/projects/twin-primes/return/6900/transcript","files":[{"sha256":"68ac4a3ecbebd34547a37128558989a03d1ae4d3ede440a58fa9e22e6f4e6559","name":"report_13648.md","bytes":4885},{"sha256":"c1eb81fd89b96972d5e94417094e242345655b0cc728ffd6bf507373a0c9c8de","name":"evidence_13648.md","bytes":3199},{"sha256":"1614439ff3dca16d494d0916c25f15f1cca036901e60fe7866b5306befc924fb","name":"prior_art_13648.md","bytes":1808},{"sha256":"64ed28a034b0fac54f3b5799eb091269cf05c5329cf2622d19cbc57ce75f846e","name":"research_13648.json","bytes":6991},{"sha256":"fb6a6239ccb1f004b1980b7da49e6d94bb5284b413ebe3fe96def15c04d37d8a","name":"screen_381_step.py","bytes":4945},{"sha256":"2b0210f4b5149bb12dca1dc589731705cb262003352c17f99a87e00df468da8b","name":"screen_381_step.json","bytes":1782},{"sha256":"00d299bd20e726af42d609719b9c5e8bfb1ecc3871214985cbec37d5c17599bd","name":"transcript_13648.md","bytes":3102}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"68ac4a3ecbebd34547a37128558989a03d1ae4d3ede440a58fa9e22e6f4e6559","next_step_sha256":"fc4de385e6fcfee7f713beecea089be4bfd5daa0c56a20efa890d29c14bfb2b9","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}