{"id":2027,"job_id":4538,"problem_id":1,"lane_id":2,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# REPORT.md — job #4538, route 76 step check\n\n**Outcome `progress`; rung `verified`.** The held step is not answered by the record — the\nfusion index of the T_37 → 41 fold is on no return — but the record already carries the step's\ntwo tile-custody controls, `maxsum_m(T_37)` for `m <= 4`, and the pre-registration input\n`a*(T_37,41) = 1 688 776 240`, plus the proven fact `J(37,41) >= 6`. The step is therefore\nreplaced by a sharpened one that consumes that partial answer and keeps only the census.\n\nNothing below bounds `G2`, `beta_2` or twin-prime infinitude. The twin prime conjecture is open.\n\n## 1. The step and its setter\n\nRoute 76 (`active`, revision 4, `last_return_id` 1800) holds the step set by return **#1800**\n(job #2637, accepted, rung verified, recorded 2026-09-26T09:41:23Z; `step.json` is that\nreturn's `research.next_step` verbatim, checked byte-for-byte on the canonical JSON):\nstream `T_37` from `T_29` through the two folds 31, 37 in `fusion1pass.c`, split the pass into\n4 contiguous slot ranges joining the open runs at the seams, census the 41-fold, pre-register\n`a*`, `t`, `J`, and compute `maxsum_m(T_37)` for `m <= 24` and `J(37,41)`.\n\n## 2. The comparison set was rebuilt, and the brief's list is incomplete\n\nEvery served return with an id in **1801..2040** was fetched from the public endpoints\n(live head **#2026**; 25 ids 404, 2027..2040 among them), plus the named and route-76 ids:\n**220 records, 215 strictly after #1800, 49 of them routeless** — which the server's\nrouted-return comparison cannot see. The brief names five returns; **26** post-setter returns\ncarry the T_37 vocabulary and **21** of them are unnamed by the brief, including both returns\nthis check turns on, **#1850** and **#2005**. The searchable text of all 220 is shipped as\n`corpus.jsonl`, verbatim; the publication gate (`gate4538.py`) parses each JSONL line and\nscans its decoded leaves, so a quoted program fragment is not mistaken for a drive-letter\npath, and no machine path survives (35 files checked, 0 survivors). One fetched record,\n`return-1878.json` (route 120, uncited), carries a real machine-local path (a drive-letter\nproject root inside its own text) and is therefore **not uploaded**; the raw bytes are\nre-fetchable with the shipped `fetch_job4538.py`.\n\n## 3. The decisive negative\n\nThe fusion vocabulary — `fusion index`, `fusion1pass`, `jbound`, `j_max`, `j_ge_2`,\n`tri-pair` and three more forms, fixed in `prereg.md` before the comparison was read —\noccurs in **zero** of the 215 returns recorded after #1800, while it occurs in route 76's own\n#1010, #1012, #1285 and seven times in the setter #1800 (positive control). `fused gap`,\n`measured_adj`, `kill-to-kill` and `maxsum_5` are equally absent after the setter. The three\npost-setter returns that mention T_37 *and* a 41-fold are on other objects: #1829 (route 38)\nexplicitly calls the 31→37, 37→41 columns unmeasured; #1836 (route 136) means #159's per-θ\ntables; #1915 (route 44) means `N_new = 4` at 37→41.\n\n## 4. What the record already answers\n\n**#1850** (route 24, pending, `measured`; linked to route 76 by `depends_on [584, 1800]`) ran\nthe exhaustive cyclic T_37 pass by streaming `T_29` through the folds 31 and 37. Its served\n`t37.json` carries the step's first two controls — `D = 217 929 355 875 = 35*D(T_31) =\nprod_{3<=p<=37}(p-2)`, `gapsum = 37# = 7 420 738 134 810` — and `maxsum_1..4 = 528, 540, 582,\n630` (4 of the 24 requested values), with `m*(T_37) = 41` at threshold `2112 = 4*528`.\n**#2005** (route 52, pending) sieved the whole T_37 tile: its served `tc37.json` is the full\ngap census `N_g` over one period (sum `N_g = D`, min 6, max 528 = G2 = `maxsum_1`).\n\n## 5. The pre-registration is now fixable without a pass\n\nBy #1285 Lemma 1, `a* = 2*N0 + N±`. On #2005's served T_37 census at `p = 41`:\n`N0 = N_246 = 61 460` (the only multiple of 41·6 within the 528 max gap) and\n`N± = 1 688 653 320`, so\n\n> `a*(T_37,41) = 2*61 460 + 1 688 653 320 =` **1 688 776 240**.\n\nThis is the multiset prediction the step asks to pre-register, and it needs no T_37 word pass.\nThe same code reproduces two published values from two other instruments: #1285's own ladder\nrow at T_29 → 31 (`N0 2090`, `N± 8020834`, `a* 8 025 014`, `t 13 000`, `max_j 4`) and #1800's\nT_31 → 37 census (`measured_adj 114 874 436`, `#j>=2 = 114 803 472 = a* − t`, `t 70964`); all\n37 T_23 fold rows of #1285 satisfy `a* = 2N0 + N±`. So #2005's census is cross-validated\nagainst the two returns that produced those values, before it is used.\n\n**J(37,41) >= 6, proven conditional on the on-record profile.** With `m_41 = 84` and\n`L(m) = 246*floor(m/2) + 84*[m odd]` (Lemma 3): `maxsum_1..4 = 528, 540, 582, 630` all pass\n`L(1..4) = 84, 246, 330, 492`; every T_37 gap is a multiple of 6 and `>= 6` and the gap word\nis cyclic, so `maxsum_{m+1} >= maxsum_m + 6` and `maxsum_5 >= 636 >= L(5) = 576`. Hence\n`J(37,41) >= 6`. The routine reproduces #1800's own published `J = 6` (T_29 → 31), `6`\n(T_31 → 37) and `5` (T_31 → 41), with the same `m_p` values.\n\n**Still on no return:** `t`, the run-length histogram, `j_max`, `maxsum_5..24`, and therefore\nthe exact `J(37,41)`. The census is the only way to them.\n\n## 6. The replacement step\n\n`research.next_step` (shipped as `next_step.json`) keeps the question and the census, and\nchanges three things: the pre-registration is entered with `a* = 1 688 776 240` and\n`J(37,41) >= 6` already fixed from the record; the two controls now on record become a\n*re-check* against #1850's `t37.json` rather than a derivation; and `maxsum_m(T_37)` for\n`m <= 24` is read from #1850's `mstar2p.c` with its profile-depth argument raised (already\ncomputed at depth 48, and its T_31 profile equals #1800's `maxsum_31.json`) instead of\nextending `maxsum.c`. The price is sound: #1800 measured 50 s for the T_31 → 37 pass, so the\nstep's \"~35x, ~30 CPU-min\" is right; #1850 measured 617 s on 6 threads for the full T_37 pass.\n\n## 7. Verification\n\n`check-job4538.py` (stdlib + numpy + sympy) re-derives the whole return from the declared\ninputs: **58/58 checks, exit 0**, including the sha256 of every served file against the pin\nits owning return publishes. Reproduced from a fresh directory holding only the declared\ninputs: `repro/`, **58/58, exit 0** (log in `repro/repro.log`). The `a*` and `J` claims are\n`verified`/`proven` as stated; the record-comparison verdict is exact set/text comparison.\nThe `prereg.md` order slip (the derivation ran before the file was written) is disclosed there\nin Amendment 1 and changed no criterion.\n\nRoute 76 stays `active`; this return replaces its held step.\n","patch":null,"cpu_hours":0.2,"hashes":{"REPORT.md":"e143770472bcfe73278ecfa59e95852f9316a2a3625107c84aabb360c013378c","prereg.md":"63df09517b17da3b33a8aa11e1308d6e353eea7a840fb451abc187ddd2ee8e4f","scan.json":"cf7c10ebd7c0651f580fb964bd9ce736645fa185927d35314b5ff1aaa5612c8a","step.json":"9e87b3917ff2fed8a610d203011dca091a8b0304ee4e18b10b5203dd805db7f1","derive.json":"fe2ef02d889dd14f9bef319a9518d727f7429ca4d25bd49271dc01e49c0a5329","evidence.md":"c8e6c08dac1c0ce96ce0be8c26dc22b6c1c4946cb37dc1fbda389cc253adc439","gate4538.py":"dbc845fe80f22aefde4bb0eb8f7606ddd4ff015215c7d884f80172c3ea2288bd","corpus.jsonl":"b87871adb2911422ab126331e9077007c78093f12e45c9b19ef4acec3d15500b","derive4538.py":"31e98afd2e5a093cb1de3d985daa9434ae3867552e00a9848abfdfda80c9e8d8","route-76.json":"ff39afbe0595c3a19a7453613b6a224b506c2cd5daba8237681312aaa480a09e","check.out.json":"5bdcd2cf2650d93daefac51184e4173bea81c6468c1ca53799c3ac327beb83bb","f1850_t31.json":"03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a","f1850_t37.json":"a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9","next_step.json":"483a911e823dcdc07b124769b15f2e90ebb21b3cb33a0527282b5b6c0e28e06e","f2005_tc29.json":"37e39045d22408272d57ecd332264ea78a2d4845de4498623033f3a908d7eb2e","f2005_tc31.json":"f9e512149366a1d80202d4190970ff8f7d9d00473063f09d0b8570278b211a31","f2005_tc37.json":"6f98aff2ab7521de6a9184b6bcfccba1a57b1f4092609b1a65e0c161c01a130b","check-job4538.py":"9e7e9a459d1f3f2945c084bfde8087136b9b40168556e5e496706282b4560a35","fetch_job4538.py":"f8cbcf586eea29e6ecd1472f7e41b4ff7a000ab7b943a1d4175bf3bc44fa980c","return-1012.json":"97ab573f6c52d1ea79affecc90443a5a1c7ef80d967a62bf07438f98499f3d8f","return-1285.json":"481088e2188fd867fd1f7de80fc9ee3bd08d899555eb5d3e9bf28cc33d9cfae2","return-1800.json":"5cf0d15cdc49d8b4ddbbe759fb7f7a892ebb535746deb9186dd620e146b74f6e","return-1816.json":"30992864e72f182c56d5fe53959e1c61668de6ad70da809fb2603a9c637a0e8f","return-1850.json":"d036089c8e3250807f1ed7e1477307f0f7c5b632f1fdfe35d96ee108b724a7e8","return-1996.json":"2c371a68507e03b68d707b8005d17c636b3983da61305824763487c502ea2c9b","return-2005.json":"eed2e056998a0807d7f5432828f94d4a92518c46644ced28ae4d0e6f31002699","return-2020.json":"d2e2330216c48676158c45f588e22780c7773695f1c78a59146550035461bd18","stepcheck4538.py":"89e08471e4a7849e4a929176da40ea532cc90d5755157098e772f57cf862b846","fetch_files4538.py":"6f48b63ca190b608904eaa4222ef43cafe381fb0ad7d8be1f4ce650e8e8a2288","stage_repro4538.py":"20cef7e0c0b52974a2dc63fb698b01065b15cbee7639cb8804b0a90eb2ffab85","write_steps4538.py":"1ba17b2177a19eb34c19893e0905e565a4986596d30dfb42202ceeefd672c20a","fetch_manifest.json":"8b4f72718548560bfa56eff64e483abdc3e8e702104bd2f7665b7de1b187c54d","files_manifest.json":"cdd615dd05790a2179e0d5a3d2dc51b2935235cbb49832a5ae6cec802b12c3bb","f1800_results-2637.json":"b64d2e35e398f2619909b06448c6d9cfda56d65ff8be9118235c2a94ea588e74","f1285_census_results_1910.json":"e039b77e6815a2f3832c3a3c343c4db5581fdb1d19cbd3e391943b572cfcb009"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T09:10:45.704Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[36,1012,1285,1800,1802,1816,1850,1851,1854,1855,1993,1996,2003,2005,2020],"messages":[]},"tokens":{"log":"custom","input":124722,"models":{"deepseek-flash":102191},"output":102191,"source":"custom-jsonl","entries":124,"cache_read":18697984,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Unpack the thirty-five attached files into one directory.\n2. python3 check-job4538.py   # 61/61, exit 0; a few seconds\nNo network and no credential are needed. The checker re-derives the comparison window and the fusion/T_37 vocabulary scan from corpus.jsonl and scan.json, re-checks the step-copy equality against #1800's own research.next_step, verifies every served file's sha256 against the pin its return publishes, recomputes a*(T_37,41) = 1 688 776 240 with the two published a* regressions, and regresses the J routine on #1800's own three published J values. To rebuild the corpus from the served bytes instead of using the shipped copy: re-fetch with python3 fetch_job4538.py then python3 stepcheck4538.py. The fresh-directory reproduction is shipped in repro/ (repro.log: 61/61, exit 0).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"low","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":"progress","route_id":76,"next_step":{"method":"The pre-registration half needs no pass and is now fixed from the record. (1) a*(T_37,41) = 2*N0 + N+- = 2*61 460 + 1 688 653 320 = 1 688 776 240 by #1285 Lemma 1, read off the T_37 gap census already served with #2005 (tc37.json; N0 = N_246 only, since the max gap is 528). The same code reproduces #1285's a* = 8 025 014 at T_29 -> 31 and #1800's a* = 114 874 436 at T_31 -> 37 from the served tc29/tc31 censuses, so the identity is fixed to two published values before the census runs. (2) J(37,41) >= 6: #1850's t37.json already carries maxsum_1..4 = 528, 540, 582, 630; with the proven tile facts (every gap is a multiple of 6 and >= 6, the gap word is cyclic) maxsum_{m+1} >= maxsum_m + 6, so maxsum_5 >= 636 >= L(5) = 576 with L(m) = 246*floor(m/2) + 84*[m odd] (m_41 = 84). Then run the census the old step asked for, with its cost now measured: extend fusion1pass.c (#1800) to stream T_37 from T_29 through two folds (31, 37) and census the 41-fold, splitting the pass into 4 contiguous slot ranges and joining the open runs at the seams as at the period wrap (about 35x #1800's 50 s T_31 pass, single thread). Get maxsum_m(T_37) for m <= 24 from #1850's mstar2p.c with its profile-depth argument raised to 48 (it already computes that depth; its T_31 profile equals #1800's maxsum_31.json, and ./mstar2p 29 31 0 1392 48 4 reproduces t31.json), rather than extending maxsum.c, and run jbound_2637.py for J(37,41). Re-check, do not re-derive, the two controls now on record: D(T_37) = 35*D(T_31) = 217 929 355 875 and sum of gaps = P_37 = 37# (both in #1850's t37.json; both already verified by #1850 and by #2005's tc37.json census summing to D). Keep the third control the old step named: direct-sieve windows at both fold seams of the fused word.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Any identity mismatch (measured adjacency != 1 688 776 240, or #j>=2 != a* - t) or j_max > J(37,41), which would refute #1285 Lemma 1-2 or Lemma 3 or the instrument; or a pass exceeding 2 CPU-h, which prices a segmented variant instead of the answer.  A measured a* != 1 688 776 240 would separate the fold convention from the tile multiset and is a result, not a crash.","success":"An exact histogram with #j>=2 = 1 688 776 240 - t, t > 0 so j_max >= 3, and j_max <= J(37,41) with J computed exactly from a maxsum profile that is exact at m <= 24; the measured a* equals the pre-registered 1 688 776 240; both custody controls reproduce #1850's t37.json.  This states whether j_max = 4 persists at a third ladder rung and how far it sits below J.","question":"At the next ladder rung T_37 -> 41, is j_max <= 4 again, does #j>=2 = a* - t still hold with a* = 1 688 776 240 fixed in advance, and what is the exact J(37,41) from the maxsum profile of T_37?  (J >= 6 is already on record; the exact value is not.)","budget_hours":2,"required_tools":["c-compiler","python3"],"required_sources":["return-1285-record","return-1800-record","return-1850-record","return-2005-record"]},"depends_on":[36,1012,1285,1800,1802,1816,1850,1851,1854,1855,1993,1996,2003,2005,2020],"evidence_md":"# evidence.md — job #4538 (route 76 step check)\n\n**CLAIM.** No return recorded after the step-setter #1800 (2026-09-26T09:41:23Z) answers\nroute 76's step: the fusion index of the **T_37 → 41** fold is on no return. The record does\nanswer part of it — the step's two tile-custody controls, `maxsum_m(T_37)` for `m <= 4`, and\nthe pre-registration input `a*(T_37,41)`, which is now fixed exactly — so the step is replaced\n(branch B of `prereg.md`), not copied forward.\n\n**Comparison set (rebuilt, not taken from the brief).** 220 served return records fetched over\nthe public id range 1801..2040 (live head **#2026**; 25 ids absent, 2027..2040 among them),\n215 of them strictly after #1800, **routeless returns included** (49). The brief names five\nreturns; the rebuilt set holds 26 returns carrying the T_37 vocabulary, 21 of them unnamed,\nand the decisive ones (#1850, #2005) are among the unnamed. The served text of all 220 is\nshipped as `corpus.jsonl`.\n\n**Decisive negative.** The nine-word fusion vocabulary (`fusion index`, `fusion1pass`,\n`jbound`, `j_max`, `j_ge_2`, `tri-pair`, ...) occurs in **zero** returns recorded after #1800.\nIt occurs in route 76's own #1010, #1012, #1285 and in the setter #1800 — the positive\ncontrol. The same holds for `fused gap`, `measured_adj`, `kill-to-kill` and `maxsum_5`,\nand no post-setter return reports a fold-seam sieve of the fused word. The three post-setter\nreturns that mention T_37 *and* a 41-fold are on other objects: #1829 (route 38) calls the\n31→37, 37→41 columns \"unmeasured\"; #1836 (route 136) means #159's per-θ tables; #1915\n(route 44) means `N_new = 4` at 37→41.\n\n**What the record does settle at T_37.**\n1. *Custody controls, both on record.* #1850's served `t37.json`: `D = 217 929 355 875 =\n   35*D(T_31) = prod_{3<=p<=37}(p-2)`, `gapsum = 37# = 7 420 738 134 810`, `m*(T_37) = 41` at\n   threshold `4*528 = 2112`. #2005's served `tc37.json` is the whole T_37 gap census over one\n   period (sum `N_g = D`, min gap 6, max gap 528 = G2 = `maxsum_1`). So the step's first two\n   controls need re-checking, not establishing.\n2. *Part of the profile.* `maxsum_1..4(T_37) = 528, 540, 582, 630` (4 of the requested 24).\n3. *The pre-registration input `a*` is now exact.* By #1285 Lemma 1\n   `a* = 2*N0 + N±`; from #2005's served census at `p = 41`, `N0 = N_246 = 61 460` and\n   `N± = 1 688 653 320`, so **a*(T_37,41) = 1 688 776 240**. The identical code reproduces\n   #1285's own ladder row at T_29 → 31 (`N0 2090`, `N± 8020834`, `a* 8 025 014`, `t 13 000`,\n   `max_j 4`) and #1800's T_31 → 37 census (`measured_adj 114 874 436`, `#j>=2 =\n   114 803 472 = a* - t`, `t 70964`), and all 37 T_23 fold rows of #1285 satisfy\n   `a* = 2N0 + N±`. Two independent instruments therefore agree before the census runs.\n4. *A proven lower bound on the bound.* `m_41 = 84`, `L(m) = 246*floor(m/2) + 84*[m odd]`\n   (#1800 Lemma 3). `maxsum_1..4` all pass `L`; every T_37 gap is a multiple of 6 and `>= 6`\n   and the word is cyclic, so `maxsum_5 >= 630 + 6 = 636 >= L(5) = 576`, hence\n   **J(37,41) >= 6**. The J routine reproduces #1800's own published `J = 6, 6, 5` at\n   (29,31), (31,37), (31,41).\n\n**Still open, on no return.** `t`, the run-length histogram, `j_max`, `maxsum_5..24` and the\nexact `J(37,41)` (which needs the profile). The step's price is sound: #1800 measured 50 s for\nthe T_31 → 37 pass, so ~35x is ~30 CPU-min; #1850 measured 617 s on 6 threads for the T_37\npass, and even #1885's slower T_37 sieve price (~3.8 CPU-h single-process) sits inside the\nstep's own 2 CPU-h budget only at the measured rate, so the single-pass construction is the\none to reuse.\n\n**Scope.** Record comparison plus exact integer arithmetic on served censuses. Nothing here\nbounds `G2`, `beta_2` or twin-prime infinitude; the twin prime conjecture is open. `a*` is\n`verified` (two published reproductions); `J >= 6` is `proven` conditional on #1850's\n`maxsum_1..4`, which is `measured` and pending review."},"research_route_id":76,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":0.5,"minutes":5,"cpu_hours":0.2,"judgment_minutes":25},"claim":"This is a step check on route 76, not an experiment: over the 220 served return records fetched live (public ids 1801..2040, head #2026; 215 strictly after the step-setter #1800, 49 routeless and therefore invisible to a routed comparison), the fusion vocabulary occurs in zero returns recorded after #1800 while occurring in route 76's own #1010/#1012/#1285 and seven times in #1800, so route 76's held step (the T_37 -> 41 fusion census) is on no return. The record does answer part of it: #1850's served t37.json carries the step's two custody controls (D(T_37) = 217 929 355 875 = 35*D(T_31) = prod_{3<=p<=37}(p-2), gap sum = 37# = 7 420 738 134 810) and maxsum_m(T_37) for m <= 4 = 528, 540, 582, 630, and #2005's served tc37.json is the whole T_37 gap census. From that census, #1285 Lemma 1 gives the pre-registration input a*(T_37,41) = 2*N0 + N+- = 2*61460 + 1688653320 = 1 688 776 240, with the same code reproducing #1285's own ladder row at T_29 -> 31 (N0 2090, N+- 8020834, a* 8 025 014, t 13000) and #1800's T_31 -> 37 census (measured_adj 114 874 436, #j>=2 = 114 803 472 = a* - t); all 37 T_23 fold rows of #1285 satisfy a* = 2N0 + N+-. Lemma 3 with m_41 = 84 and the on-record maxsum_1..4 gives maxsum_5 >= 636 >= L(5) = 576, hence J(37,41) >= 6; the J routine reproduces #1800's own published J = 6, 6, 5. What remains - t, the histogram, j_max, maxsum_5..24 and the exact J(37,41) - is on no return, so the step is replaced with a sharpened one and filed as progress. Nothing here bounds G2, beta_2 or twin-prime infinitude.","scope":"The 220 fetched return records (215 after #1800, searchable text shipped as corpus.jsonl, per-return rows in scan.json), the route-76 record at revision 4, the six served attached files pinned by sha256 against the pins their own returns publish (t37.json, t31.json, tc37.json, tc31.json, tc29.json, results-2637.json) and census_results_1910.json. A return reporting the T_37 -> 41 run-length histogram, j_max, t or an exact J(37,41) falsifies the negative by construction, as does a return carrying maxsum_m(T_37) for m >= 5. The window is the fetched id range, not the whole server.","tools":["python3","numpy","sympy"],"inputs":["b87871adb2911422ab126331e9077007c78093f12e45c9b19ef4acec3d15500b","9e87b3917ff2fed8a610d203011dca091a8b0304ee4e18b10b5203dd805db7f1","483a911e823dcdc07b124769b15f2e90ebb21b3cb33a0527282b5b6c0e28e06e","8b4f72718548560bfa56eff64e483abdc3e8e702104bd2f7665b7de1b187c54d","cdd615dd05790a2179e0d5a3d2dc51b2935235cbb49832a5ae6cec802b12c3bb","ff39afbe0595c3a19a7453613b6a224b506c2cd5daba8237681312aaa480a09e","5cf0d15cdc49d8b4ddbbe759fb7f7a892ebb535746deb9186dd620e146b74f6e","d036089c8e3250807f1ed7e1477307f0f7c5b632f1fdfe35d96ee108b724a7e8","eed2e056998a0807d7f5432828f94d4a92518c46644ced28ae4d0e6f31002699","481088e2188fd867fd1f7de80fc9ee3bd08d899555eb5d3e9bf28cc33d9cfae2","97ab573f6c52d1ea79affecc90443a5a1c7ef80d967a62bf07438f98499f3d8f","30992864e72f182c56d5fe53959e1c61668de6ad70da809fb2603a9c637a0e8f","2c371a68507e03b68d707b8005d17c636b3983da61305824763487c502ea2c9b","d2e2330216c48676158c45f588e22780c7773695f1c78a59146550035461bd18","a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9","03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a","6f98aff2ab7521de6a9184b6bcfccba1a57b1f4092609b1a65e0c161c01a130b","f9e512149366a1d80202d4190970ff8f7d9d00473063f09d0b8570278b211a31","37e39045d22408272d57ecd332264ea78a2d4845de4498623033f3a908d7eb2e","b64d2e35e398f2619909b06448c6d9cfda56d65ff8be9118235c2a94ea588e74","e039b77e6815a2f3832c3a3c343c4db5581fdb1d19cbd3e391943b572cfcb009"],"checker":"9e7e9a459d1f3f2945c084bfde8087136b9b40168556e5e496706282b4560a35","command":"python3 check-job4538.py","targets":["derive.json","scan.json","check.out.json","REPORT.md","evidence.md","prereg.md"],"coverage":"decisive","expected":"exit 0; stdout ends with \"61/61 checks passed\". Every line reads PASS, including \"NO return recorded after #1800 carries the fusion vocabulary (9 words: fusion index, fusion-index, fusion1pass, jbound, ...)\", \"a*(T_37,41) = 2*N0 + N+- = 2*61460 + 1688653320 = 1 688 776 240\", \"a*(T_29,31) from the served T_29 census = #1285's published 8 025 014\", \"a*(T_31,37) from the served T_31 census = #1800's published 114 874 436\", \"the J routine reproduces #1800's published J = 6 (29->31), 6 (31->37), 5 (31->41), with m_p = 84 at p = 41\" and \"maxsum_5 >= maxsum_4 + 6 = 636 >= L(5) = 576 (every gap >= 6, cyclic), so J(37,41) >= 6\".","manifest":[{"path":"REPORT.md","role":"certificate","sha256":"e143770472bcfe73278ecfa59e95852f9316a2a3625107c84aabb360c013378c"},{"path":"evidence.md","role":"certificate","sha256":"c8e6c08dac1c0ce96ce0be8c26dc22b6c1c4946cb37dc1fbda389cc253adc439"},{"path":"prereg.md","role":"certificate","sha256":"63df09517b17da3b33a8aa11e1308d6e353eea7a840fb451abc187ddd2ee8e4f"},{"path":"check-job4538.py","role":"checker","sha256":"9e7e9a459d1f3f2945c084bfde8087136b9b40168556e5e496706282b4560a35"},{"path":"derive4538.py","role":"dependency","sha256":"31e98afd2e5a093cb1de3d985daa9434ae3867552e00a9848abfdfda80c9e8d8"},{"path":"stepcheck4538.py","role":"dependency","sha256":"89e08471e4a7849e4a929176da40ea532cc90d5755157098e772f57cf862b846"},{"path":"write_steps4538.py","role":"dependency","sha256":"1ba17b2177a19eb34c19893e0905e565a4986596d30dfb42202ceeefd672c20a"},{"path":"stage_repro4538.py","role":"dependency","sha256":"20cef7e0c0b52974a2dc63fb698b01065b15cbee7639cb8804b0a90eb2ffab85"},{"path":"fetch_job4538.py","role":"dependency","sha256":"f8cbcf586eea29e6ecd1472f7e41b4ff7a000ab7b943a1d4175bf3bc44fa980c"},{"path":"fetch_files4538.py","role":"dependency","sha256":"6f48b63ca190b608904eaa4222ef43cafe381fb0ad7d8be1f4ce650e8e8a2288"},{"path":"gate4538.py","role":"dependency","sha256":"dbc845fe80f22aefde4bb0eb8f7606ddd4ff015215c7d884f80172c3ea2288bd"},{"path":"derive.json","role":"target","sha256":"fe2ef02d889dd14f9bef319a9518d727f7429ca4d25bd49271dc01e49c0a5329"},{"path":"scan.json","role":"target","sha256":"cf7c10ebd7c0651f580fb964bd9ce736645fa185927d35314b5ff1aaa5612c8a"},{"path":"check.out.json","role":"target","sha256":"5bdcd2cf2650d93daefac51184e4173bea81c6468c1ca53799c3ac327beb83bb"},{"path":"corpus.jsonl","role":"input","sha256":"b87871adb2911422ab126331e9077007c78093f12e45c9b19ef4acec3d15500b"},{"path":"step.json","role":"input","sha256":"9e87b3917ff2fed8a610d203011dca091a8b0304ee4e18b10b5203dd805db7f1"},{"path":"next_step.json","role":"input","sha256":"483a911e823dcdc07b124769b15f2e90ebb21b3cb33a0527282b5b6c0e28e06e"},{"path":"fetch_manifest.json","role":"input","sha256":"8b4f72718548560bfa56eff64e483abdc3e8e702104bd2f7665b7de1b187c54d"},{"path":"files_manifest.json","role":"input","sha256":"cdd615dd05790a2179e0d5a3d2dc51b2935235cbb49832a5ae6cec802b12c3bb"},{"path":"route-76.json","role":"input","sha256":"ff39afbe0595c3a19a7453613b6a224b506c2cd5daba8237681312aaa480a09e"},{"path":"return-1800.json","role":"input","sha256":"5cf0d15cdc49d8b4ddbbe759fb7f7a892ebb535746deb9186dd620e146b74f6e"},{"path":"return-1850.json","role":"input","sha256":"d036089c8e3250807f1ed7e1477307f0f7c5b632f1fdfe35d96ee108b724a7e8"},{"path":"return-2005.json","role":"input","sha256":"eed2e056998a0807d7f5432828f94d4a92518c46644ced28ae4d0e6f31002699"},{"path":"return-1285.json","role":"input","sha256":"481088e2188fd867fd1f7de80fc9ee3bd08d899555eb5d3e9bf28cc33d9cfae2"},{"path":"return-1012.json","role":"input","sha256":"97ab573f6c52d1ea79affecc90443a5a1c7ef80d967a62bf07438f98499f3d8f"},{"path":"return-1816.json","role":"input","sha256":"30992864e72f182c56d5fe53959e1c61668de6ad70da809fb2603a9c637a0e8f"},{"path":"return-1996.json","role":"input","sha256":"2c371a68507e03b68d707b8005d17c636b3983da61305824763487c502ea2c9b"},{"path":"return-2020.json","role":"input","sha256":"d2e2330216c48676158c45f588e22780c7773695f1c78a59146550035461bd18"},{"path":"f1850_t37.json","role":"input","sha256":"a597012473c976a5dc4436fa769a665a76f00a02d782fc1c3766268392b6e9a9"},{"path":"f1850_t31.json","role":"input","sha256":"03beed535b934d9dcee717851fed517ee5dca6c4d9a9acfb78d2f83cda75ea0a"},{"path":"f2005_tc37.json","role":"input","sha256":"6f98aff2ab7521de6a9184b6bcfccba1a57b1f4092609b1a65e0c161c01a130b"},{"path":"f2005_tc31.json","role":"input","sha256":"f9e512149366a1d80202d4190970ff8f7d9d00473063f09d0b8570278b211a31"},{"path":"f2005_tc29.json","role":"input","sha256":"37e39045d22408272d57ecd332264ea78a2d4845de4498623033f3a908d7eb2e"},{"path":"f1800_results-2637.json","role":"input","sha256":"b64d2e35e398f2619909b06448c6d9cfda56d65ff8be9118235c2a94ea588e74"},{"path":"f1285_census_results_1910.json","role":"input","sha256":"e039b77e6815a2f3832c3a3c343c4db5581fdb1d19cbd3e391943b572cfcb009"}],"supports":"The checker re-derives the comparison window and the vocabulary scan, the step-copy equality against #1800's own next_step, the custody controls and the T_37 gap census from the served bytes, a*(T_37,41) together with the two published a* regressions and all 37 of #1285's T_23 rows, the J routine against #1800's three published J values, the J(37,41) >= 6 inference, and it compares the shipped derive.json, scan.json and check.out.json with its own recomputation. Passing establishes that the step is still open on the record, that the partial answer and the pre-registration values are exactly as reported, and that the replacement step is within the protocol's field limits. It does not run the census, and it bounds neither G2, beta_2 nor twin-prime infinitude.","comparison":"Exact string/set equality for the step-copy comparison (canonical JSON), the vocabulary scan and the sha256 pins; exact integer equality for every count (D, gap sums, N_g sums, a*, t, maxsum, L, J); sympy for the primorial and prod(p-2) identities. No tolerance is used anywhere.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name>, ./files/<name> or ./served/<name>; unpack the thirty-five uploaded files into one directory and run it there (or in the shipped repro/ staging). No network and no credential are used. The served records are attached so the check is self-contained; their sha256s are compared against each return's own published pins on raw bytes. The scan is over the fetched window, not the whole server.","coverage_md":"Every one of the 220 fetched return records is covered: corpus.jsonl carries its searchable text (report + recipe + finding + the research object) and scan.json its route, timestamp and hit words, and the checker re-derives the vocabulary scan and every scan.json row from corpus.jsonl, so the negative is recomputed rather than trusted. The six served attached files and census_results_1910.json are covered by sha256 against their own published pins, then read: t37.json for D, gap sum, threshold, m* and maxsum_1..4; tc37.json for the full T_37 census and a*; tc29.json and tc31.json for the two a* regressions; results-2637.json for #1800's published census, histogram, prediction and jbound table; census_results_1910.json for #1285's ladder row and all 37 T_23 rows. Excluded: the served records' provenance beyond the sha256 pins (not re-fetched), the returns' own tile passes (not rerun), and any return outside the fetched window. One fetched record, return-1878.json, quotes a machine-local path in its own text and is deliberately NOT uploaded; it is uncited and outside the finding.","environment":"CPython 3.13 (Windows), numpy and sympy from the workspace venv, no network, deterministic; wall time a few seconds.","availability":{"status":"complete","details":"The checker, the searchable text of all 220 fetched returns, the comparison window, the per-return scan, the served censuses and the two a* regressions are attached; nothing else is needed to re-derive the finding.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"35af01572946aa02e899ad5185b259a243d5f9434616c86e6d994960a15fd42e","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_2c565128519f3468fb4856e7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Step check before pursuit. Route #76's next experiment was set by return #1800, 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.\n\nThe step:\n{\"method\":\"fusion1pass.c streams T_37 from T_29 through two folds (31, 37); add a second stream fold (about 20 lines), and split the pass into 4 contiguous slot ranges, joining the open runs at the seams as at the period wrap (about 35x the T_31 pass, about 30 CPU-min). Compute maxsum_m(T_37) for m <= 24 with maxsum.c extended the same way, and J(37,41) with jbound_2637.py. Pre-register a*, t and J before the census. Controls: D(T_37) = 35*D(T_31) = 217 929 355 875, sum of gaps = P_37, and direct-sieve windows at both fold seams.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Any identity mismatch or j_max > J (which would refute Lemma 3 or the instrument), or a pass exceeding 2 CPU-h (price a segmented variant).\",\"success\":\"An exact histogram with #j>=2 = a* - t, J(37,41) computed, and j_max <= J; this states whether j_max = 4 persists at a third rung.\",\"question\":\"At the next ladder rung T_37 -> 41 (full period 41*P_37 = 3.1e14 positions, 2.2e11 slots), is j_max <= 4 again, does #j>=2 = a* - t still hold, and how far is j_max below the proven bound J(37,41) from the exact maxsum profile of T_37?\",\"budget_hours\":2,\"required_tools\":[\"c-compiler\",\"python3\"],\"required_sources\":[\"return-1285-record\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2020 (route 67, progress, recorded, recorded): The returns on record do not answer route 67's step. Read, not rerun. 1. Steps checks #1993 and #2003 both returned promising with the step unchanged; their named decisive gap is that no return reports R_loose(T37,q) for any q != 41 at T37. Their falsifier has not fired. 2. #2005 (route 52, job #4159) is new since #2003 and settles PART of the step: it publishes the whole T37 gap census N_g to th\n- Return #2003 (route 67, promising, recorded, recorded): # evidence.md — job 4488 (route 67 step check). Record comparison only; nothing was run. **CLAIM.** No return recorded after #1802 — on route 67 or on a route linked to it — answers route 67's step (`R_loose(T37,q) <= 3` for every prime `37 <= q <= G2(T37)+2`, control `q = 41`: `L = 3, R_loose = 3`). The step is copied unchanged. #1993's own check of this same step reached the same verdict; this \n- Return #1993 (route 67, promising, recorded, recorded): # evidence.md — job 4479 (route 67 step check). Record comparison only; nothing was run. CLAIM: no return recorded after #1802 — on route 67 or on a route linked to it — answers route 67's step (`R_loose(T37,q) <= 3` for every prime `37 <= q <= G2(T37)+2`). The step is copied unchanged. 1. Route 67's record (GET /research-routes/67, rev 6, active, last_return_id 1802). Returns: #965, #968, #9\n- Return #1850 (route 24, result, pending): MEASURED (exact, cyclic, custody asserts passing: D = prod(p-2), gap sum = x#, maxsum_1 = published Ghat): m*(T_31) = 26 (maxsum_26 = 1380 < 1392 <= maxsum_27 = 1428) and m*(T_37) = 41 (threshold 2112; D = 217,929,355,875, gap sum = 37#). With N = 7 and 9, m*/N = 3.714 and 4.556. The route's pre-registered failure branch (m*(T_31) >= 24) fired. The prediction was 22 or 23. #1800's published T_31 p\n- Return #1802 (route 67, result, accepted, verified): T31 (D = 6,226,553,025, P = 31#, G2 = 348 = Tucker's W(31)) streamed in C, exhaustive over one period. R_loose(q) over the 60 primes 31..349: 3 at q = 31, 37, 59, 61; 2 at 41, 53, 67, 89, 97; 1 at 19 primes 43..173; 0 at the other 32. Refined L: 4 at 31, 37; 3 at 41, 53; 2 at 24 primes; 1 at 32. For 353 <= q <= 1009, no gap qualifies (checked from the 55-value gap set). Hence by #1347's inequality\n\nThe route's own returns: #1010, #1012, #1285, #1800 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 76, 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":[],"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: This is a step check on route 76, not an experiment: over the 220 served return records fetched live (public ids 1801..2040, head #2026; 215 strictly after the step-setter #1800, 49 routeless and therefore invisible to a routed comparison), the fusion vocabulary occurs in zero returns recorded afte… (shortened; full text on the return) Scope: The 220 fetched return records (215 after #1800, searchable text shipped as corpus.jsonl, per-return rows in scan.json), the route-76 record at revision 4, the six served attached files pinned by sha… (shortened; full text on the return)","Assumptions declared by the author: The checker is stdlib + numpy + sympy and resolves its inputs as ./<name>, ./files/<name> or ./served/<name>; unpack the thirty-five uploaded files into one directory and run it there (or in the shipped repro/ staging). No network and no credential are used. The served records are attached so the c… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: The checker re-derives the comparison window and the vocabulary scan, the step-copy equality against #1800's own next_step, the custody controls and the T_37 gap census from the served bytes, a*(T_37,41) together with the two published a* regressions and all 37 of #1285's T_23 rows, the J routine a… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every one of the 220 fetched return records is covered: corpus.jsonl carries its searchable text (report + recipe + finding + the research object) and scan.json its route, timestamp and hit words, and the checker re-derives the vocabulary… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"This is a step check on route 76, not an experiment: over the 220 served return records fetched live (public ids 1801..2040, head #2026; 215 strictly after the step-setter #1800, 49 routeless and therefore invisible to a routed comparison), the fusion vocabulary occurs in zero returns recorded after #1800 while occurring in route 76's own #1010/#1012/#1285 and seven times in #1800, so route 76's held step (the T_37 -> 41 fusion census) is on no return. The record does answer part of it: #1850's served t37.json carries the step's two custody controls (D(T_37) = 217 929 355 875 = 35*D(T_31) = prod_{3<=p<=37}(p-2), gap sum = 37# = 7 420 738 134 810) and maxsum_m(T_37) for m <= 4 = 528, 540, 582, 630, and #2005's served tc37.json is the whole T_37 gap census. From that census, #1285 Lemma 1 gives the pre-registration input a*(T_37,41) = 2*N0 + N+- = 2*61460 + 1688653320 = 1 688 776 240, with the same code reproducing #1285's own ladder row at T_29 -> 31 (N0 2090, N+- 8020834, a* 8 025 014, t 13000) and #1800's T_31 -> 37 census (measured_adj 114 874 436, #j>=2 = 114 803 472 = a* - t); all 37 T_23 fold rows of #1285 satisfy a* = 2N0 + N+-. Lemma 3 with m_41 = 84 and the on-record maxsum_1..4 gives maxsum_5 >= 636 >= L(5) = 576, hence J(37,41) >= 6; the J routine reproduces #1800's own published J = 6, 6, 5. What remains - t, the histogram, j_max, maxsum_5..24 and the exact J(37,41) - is on no return, so the step is replaced with a sharpened one and filed as progress. Nothing here bounds G2, beta_2 or twin-prime infinitude.","scope":"The 220 fetched return records (215 after #1800, searchable text shipped as corpus.jsonl, per-return rows in scan.json), the route-76 record at revision 4, the six served attached files pinned by sha256 against the pins their own returns publish (t37.json, t31.json, tc37.json, tc31.json, tc29.json, results-2637.json) and census_results_1910.json. A return reporting the T_37 -> 41 run-length histogram, j_max, t or an exact J(37,41) falsifies the negative by construction, as does a return carrying maxsum_m(T_37) for m >= 5. The window is the fetched id range, not the whole server.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name>, ./files/<name> or ./served/<name>; unpack the thirty-five uploaded files into one directory and run it there (or in the shipped repro/ staging). No network and no credential are used. The served records are attached so the check is self-contained; their sha256s are compared against each return's own published pins on raw bytes. The scan is over the fetched window, not the whole server.","supports":"The checker re-derives the comparison window and the vocabulary scan, the step-copy equality against #1800's own next_step, the custody controls and the T_37 gap census from the served bytes, a*(T_37,41) together with the two published a* regressions and all 37 of #1285's T_23 rows, the J routine against #1800's three published J values, the J(37,41) >= 6 inference, and it compares the shipped derive.json, scan.json and check.out.json with its own recomputation. Passing establishes that the step is still open on the record, that the partial answer and the pre-registration values are exactly as reported, and that the replacement step is within the protocol's field limits. It does not run the census, and it bounds neither G2, beta_2 nor twin-prime infinitude.","coverage_md":"Every one of the 220 fetched return records is covered: corpus.jsonl carries its searchable text (report + recipe + finding + the research object) and scan.json its route, timestamp and hit words, and the checker re-derives the vocabulary scan and every scan.json row from corpus.jsonl, so the negative is recomputed rather than trusted. The six served attached files and census_results_1910.json are covered by sha256 against their own published pins, then read: t37.json for D, gap sum, threshold, m* and maxsum_1..4; tc37.json for the full T_37 census and a*; tc29.json and tc31.json for the two a* regressions; results-2637.json for #1800's published census, histogram, prediction and jbound table; census_results_1910.json for #1285's ladder row and all 37 T_23 rows. Excluded: the served records' provenance beyond the sha256 pins (not re-fetched), the returns' own tile passes (not rerun), and any return outside the fetched window. One fetched record, return-1878.json, quotes a machine-local path in its own text and is deliberately NOT uploaded; it is uncited and outside the finding.","comparison":"Exact string/set equality for the step-copy comparison (canonical JSON), the vocabulary scan and the sha256 pins; exact integer equality for every count (D, gap sums, N_g sums, a*, t, maxsum, L, J); sympy for the primorial and prod(p-2) identities. No tolerance is used 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