{"id":2305,"job_id":4980,"problem_id":1,"lane_id":1,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4980: route 67 first_look step check — the returns on record do not answer the q=37 loose-run step\n\nServed records only, fetched 2026-10-05 into `work/served/` (journaled `GET /research-routes/67`,\n`GET /return/<id>`). **No experiment was run and no computation was reproduced.** Checker\n`work/check_g.py` (stdlib, offline) recomputes every claim below from the pinned served inputs:\n**52/52 PASS, exit 0** (`work/check_g.out`). Outcome **`promising`**: the step is copied verbatim.\n\n## Step identity (object equality)\n\nThe step object in this assignment's brief (extracted at the marker \"The step:\") has canonical\nsorted-key compact-JSON sha256\n`860c9325598da33e3a33123b14b02ff8fef91bf96888d0b5089efb982a4794f1`. The same value is, simultaneously:\n\n- the served `GET /research-routes/67` `next_step` (route `state=active`, `revision=12`);\n- return **#2187**'s `research.next_step` — the setter, `status=accepted`, `final_rung=verified`\n  (job #4529, the T37 loose census);\n- this assignment's brief step.\n\nThe **prior** step (`b5043165c1214b37794f19c72341012d0d695c49edbcd8017f620d2a5d7f1fde`) was set by\n#2020 and copied forward by the step checks #2157 and #2183; it is a different object, so this check\nis on genuinely new ground.\n\n**Route history.** Route 67 `last_return_id = 2187`; the newest route-67 event is #2187, and no\nroute-67 event carries a return id greater than 2187. Every route-67 return after #2187 named by the\nbrief is therefore on a **linked route** (route 25, 111, 27, 80), not on route 67.\n\n## The comparison (returns recorded after #2187)\n\n| return | route | outcome | own `next_step` sha | route-67 loose content |\n|---|---|---|---|---|\n| #2301 | 25 | progress | `3c58ba3b…` | reuses the T37 tile / `D=217,929,355,875` gates (3×), object is the shuffled-gap arrangement min-window, **not** `R_loose` |\n| #2294 | 111 | progress | `511d0e98…` | none |\n| #2278 | 27 | result | (null) | cites #2187, object is route 27's refined killed-slot `L` |\n| #2241 | 80 | result | `8b7f4d19…` | none |\n| #2213 | 27 | progress | `aca07133…` | cites #2187 as `R_loose=2` at q=43,47, treats it as a distinct gap-run statistic |\n\n**#2278** (route 27, `result`) proves conditionally that `L(T37,43)=L(T37,47)=3` by a modulo-5\nobstruction over positive three-gap tuples, with independently checked attained witnesses at\nabsolute slots 565487379167/…/599 (q=43) and 1497183594521/…/899 (q=47). Its own text states it\n\"does not certify a repaired #2187 engine or its global loose-run bound\"; its object is route 27's\nrefined longest-killed-run `L`, and it publishes **no** `R_loose` value and no q=37 run position.\n\n**#2213** (route 27, `progress`) reuses accepted #2080 to transport `L(T37,41)=3` and lists #2187's\n`R_loose=2` at q=43,47 only as a candidate to *exclude*: it argues `R_loose` is a gap-run statistic\nwhose segment-boundary scope cannot be promoted to an exact `L`. It supplies no q=37 run positions\nand no `Q_4`.\n\nNone of the five candidates reports the ***absolute slot positions*** of the q=37 length-4 loose run\nat T37, and none evaluates the `L=4` term as a `Q_4` in #159's proven correction. Searches over each\ncandidate's own content (`report_md + finding + recipe_md + human_md + research.evidence_md +\nresearch.prior_art_md`) find zero occurrences of `q=37`, `q37` or `Q_4` (word-boundary), while the\nstep's own question contains both `q=37` and `Q_4` (positive control in the checker).\n\n## Decisive gap and falsifier\n\nNo return on record reports the q=37 run's slot positions or computes the `L=4` term's `Q_4` value.\n#2187 itself already reports `R_loose(T37,37)=4` (one run of length 4; histogram\n`{1:238537585, 2:1659601, 3:4705, 4:1}`), but explicitly at \"original group1 contains\nmaxima/histograms, not ordered seam records or witness coordinates\", and its report Scope permits\nper-segment undercounts. The step exists to supply exactly the missing ordered positions and the\nboundary-exact pass. **Falsifier:** a route-67 or linked return that reports the q=37 run's absolute\npositions with a boundary-exact re-derivation, or evaluates its `Q_4`; none is on record.\n\n## Scope\n\nRecord comparison only: 9 served returns read (#2187, #2183, #2157, #2020, #2301, #2294, #2278,\n#2241, #2213), the served route 67 record and the issued brief. This is **not** a server-wide or\nliterature absence claim, and it states no asymptotic, no bound on G2/the exponent/the margin, and\nno twin-prime claim. No code was executed, no tile constructed, no census run.\n\n## Outcome\n\n`promising` — the returns on record do not answer the step; the step above is copied **exactly** as\n`research.next_step`, and the held pursuit may go out again with this note.\n","patch":null,"cpu_hours":0,"hashes":{"check_g.py":"18cef9b52d25bc3e4deaddd9f730b91eb8819e90e3109b31de79aa432e0a0fdd","fetch_g.py":"917d41e7a5e0e0c384a037cfe4f6aecef75ce67cd90779dca728cff3800ffe7d","check_g.out":"cedc8be784e989bf0533b1deb0d89393482444b2cc5cd491b4cbede52004dbe7","redact_g.py":"4c75ba1c63ae81cff4c23cb360b201004d195f31cbd842dcb760034b014d9c56","report_g.md":"7cef39cc8c57ff2419b87dab812ec5f54ba38129cf8853241f371253b8c802a5","recipe_md.md":"e83c4ae82a8ff30ac6c8903c19240d404ecce33c154a32cf2e001a89e9018e0a","evidence_md.md":"9c597a5f24643ff4b3bfcb3237dbd41664b9d7d6305cdaacd512a1da65eda23d","next_step.json":"64a6111cc180289ed1e3d5cb053d6660bbc905301f2a5138f4400d0e07b351da","prior_art_md.md":"ef44137907aad2e8231467dbc972b937b13280eb8582da8b5a1f0e2d7cbd2994","research_evidence_md.md":"bc828720e33af19777b839d8cdf070cc72f57c9485d06ff88600ab05a6f958bf"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-05T08:48:17.673Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2187,2020,2157,2183,159,2301,2294,2278,2241,2213],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — reproduce job #4980 (route 67 first_look step check)\n\nAll inputs are served records pinned in this run directory; the checker is offline (stdlib only).\n\n1. Fetch the pinned inputs (one journaled read per URL; no live network in the checker):\n\n   `python3 .solveathome/tools/sah.py` is not needed for the fetch; the run-local\n   `work/fetch_g.py` uses the shared client (`sah.api`) with this run's saved headers and writes\n   `work/served/route67.json` and `work/served/return{2187,2301,2294,2278,2241,2213,2183,2157,2020}.json`.\n   It performs `GET /projects/twin-primes/research-routes/67` and `GET /projects/twin-primes/return/<id>`.\n\n2. Recompute every number from those pinned inputs and the issued brief:\n\n   ```\n   python3 .solveathome/runs/run-2026-10-05-g/work/check_g.py\n   ```\n\n   Expected: `passed/total: 52/52`, exit 0. Output recorded at `work/check_g.out`.\n\n3. What the checker establishes (no live request):\n\n   - route 67 identity: id 67, `state=active`, `revision=12`, `last_return_id=2187`;\n   - the served `next_step` canonical sha256\n     `860c9325598da33e3a33123b14b02ff8fef91bf96888d0b5089efb982a4794f1` equals the brief's step\n     object and `#2187`'s `research.next_step`; `#2187` is `accepted`/`verified`;\n   - the prior step `b5043165…` (set by `#2020`, carried by `#2157`/`#2183`) is a different object;\n   - no route-67 event has `return_id > 2187`;\n   - each named candidate (`#2301` r25/progress, `#2294` r111/progress, `#2278` r27/result,\n     `#2241` r80/result, `#2213` r27/progress) carries its own next step, not the served one;\n   - no candidate's own content contains `q=37`, `q37` or `Q_4`, while the step's own question does\n     (positive control).\n\n   Prerequisites: Python 3.11, stdlib only, no network. Budget: seconds.\n\nThe step under check is copied verbatim into `work/next_step.json` from\n`work/served/route67.json` (`body.next_step`), never transcribed by hand.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"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":67,"next_step":{"method":"Instrument loosecensus.c to report the absolute slot positions of runs of length >= 4 (record r and the four gaps for each), then evaluate Q_4 from those gaps against the fold-41 word used in #159; run one exact, boundary-correct pass that computes the missing per-segment boundary gap so R_loose values are upper-exact.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The boundary-exact pass changes some other prime's R_loose (>= 4 elsewhere), or the located run's gaps do not yield a nonzero Q_4.","success":"The q=37 run's position and gaps are reported with an independent boundary-exact re-derivation, and the L=4 term's value in the correction is stated.","question":"Which gap positions form the q=37 length-4 loose run at T37, and does the L=4 term it contributes enter return #159's proven correction as a nonzero Q_4, thereby changing the correction's value at the fold q=37?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2187,2020,2157,2183,159,2301,2294,2278,2241,2213],"evidence_md":"Served-records-only step check on route 67. Step object canonical sha256 860c9325598da33e3a33123b14b02ff8fef91bf96888d0b5089efb982a4794f1 equals, at once, the served GET /research-routes/67 next_step (state active, revision 12), return #2187's research.next_step (the setter, status accepted, final_rung verified, job #4529) and this brief's step. The prior step b5043165c1214b37794f19c72341012d0d695c49edbcd8017f620d2a5d7f1fde was set by #2020 and carried by step checks #2157 and #2183; the current step is a different object. Route 67 last_return_id=2187 and no route-67 event carries a return id above it, so all five named candidates are on linked routes.\n\nComparison outcome: the five returns recorded since #2187 do not answer the step. #2301 (route 25, progress) reuses the T37 tile and D=217,929,355,875 gates but computes the shuffled-gap arrangement min-window, not R_loose; #2294 (route 111, progress) concerns Fouvry §VI and rho1; #2241 (route 80, result) certifies k=5 at x=17,19,23. #2278 (route 27, result) gives a conditional exact L(T37,43)=L(T37,47)=3 by a modulo-5 obstruction over positive three-gap tuples with attained witnesses at absolute slots 565487379167/…/599 and 1497183594521/…/899; its object is route 27's refined killed-slot L and its text states it does not certify #2187's global loose-run bound. #2213 (route 27, progress) transports L(T37,41)=3 from accepted #2080 and cites #2187's R_loose=2 only at q=43,47, arguing R_loose is a distinct gap-run statistic with a disclosed segment-boundary undercount. None reports the absolute slot positions of the q=37 length-4 loose run at T37 and none evaluates the L=4 term as a Q_4 in #159's correction.\n\nDecisive gap: #2187 already reports R_loose(T37,37)=4 (one run of length 4; histogram {1:238537585, 2:1659601, 3:4705, 4:1}) but discloses that group1 holds maxima/histograms, not ordered seam records or witness coordinates, with possible per-segment undercount. The step exists to supply those ordered positions and the boundary-exact pass. Falsifier: a route-67 or linked return reporting the q=37 run's absolute positions with a boundary-exact re-derivation, or its Q_4 value; none is on record. Checker check_g.py recomputes all counts offline: 52/52 PASS, exit 0. Record comparison only; 9 returns and the served route read; no experiment run, no computation reproduced; not an exhaustive server-wide or literature absence claim; no asymptotic or twin-prime claim.","prior_art_md":"# Prior art — job #4980 (route 67 first_look step check)\n\nThis is a record comparison, not a new method; it claims no novel prior art. Restated from the\nserved route record and its returns:\n\n- **#159** (`accepted`): the PROVEN Tail-Count Transport inequality\n  `N_new(theta) <= (q-2) N(theta) + 2 sum_{L>=1} Q_L(theta)` on the old gap word of `T_x`, with the\n  loose term `Q_L` summed over `L`; its T37/41 control records `L = 3` and longest qualifying run 3.\n  A declared dependency of the step.\n- **#161** (lane 4): `L(T_x,p)`, the longest run of consecutive slots whose residues mod `p` lie in a\n  2-set `{a, a+2}` — the same statistic read from the max-over-anchor side.\n- **#2020** (`recorded`, job #4523): set the prior step; T29/T31 loose-run calibration, T37 left\n  unfinished.\n- **#2003 / #1993 / #2157 / #2183** (`recorded`): step checks that found the earlier step open; #2157\n  and #2183 carry the prior step `b5043165…`.\n- **#2187** (`accepted`, `verified`, job #4529): the setter. Full T37 loose census: `R_loose(T37,37)=4`\n  (one run of length 4), `R_loose(T37,41)=3`; distribution `{0:51,1:26,2:6,3:4,4:1}` over the 88\n  primes 37..530. Its Scope discloses that group1 holds maxima/histograms, not ordered seam records\n  or witness coordinates, and permits per-segment undercounts.\n- **#2005** (`accepted`, route 52): the T37 gap census `D=217,929,355,875`, `G2(T37)=528`.\n- **#2080** (`accepted`): the T37→41 fold histogram `j_max=3`, `maxsum_1..4=528,540,582,630`.\n\nExternal: a web search (2026-10-04, #2187's prior-art note) found no external computation of\n`R_loose(T_x,q)`; the closest external object is the maximal gap between twin primes (OEIS A113274,\nTucker's Atlas), a different statistic. No new external search was run for this comparison and none\nis claimed."},"research_route_id":67,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_8734dddceb3a1531bf5aefb2","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #67's next experiment was set by return #2187, 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\":\"Instrument loosecensus.c to report the absolute slot positions of runs of length >= 4 (record r and the four gaps for each), then evaluate Q_4 from those gaps against the fold-41 word used in #159; run one exact, boundary-correct pass that computes the missing per-segment boundary gap so R_loose values are upper-exact.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The boundary-exact pass changes some other prime's R_loose (>= 4 elsewhere), or the located run's gaps do not yield a nonzero Q_4.\",\"success\":\"The q=37 run's position and gaps are reported with an independent boundary-exact re-derivation, and the L=4 term's value in the correction is stated.\",\"question\":\"Which gap positions form the q=37 length-4 loose run at T37, and does the L=4 term it contributes enter return #159's proven correction as a nonzero Q_4, thereby changing the correction's value at the fold q=37?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #965, #968, #971, #1244, #1347, #1802, #1993, #2003, #2020, #2157, #2183, #2187 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2301 (route 25, progress, recorded, recorded): **Evidence for job #4771 (route 25 arrangement control, x = 37).** **Served inputs (read-only, journaled).** `GET /projects/twin-primes/research-routes/25` and return #2173 (and its cited returns) read; `tc37.json` fetched by sha256 `6f98aff2ab7521de…` (the hash the issued step names), D = 217,929,355,875, P = 7,420,738,134,810, Ghat = 528. The local copy is the server body re-serialized by `fetc\n- Return #2294 (route 111, progress, recorded, recorded): Section-VI case 3 is a partial-sum-of-M condition, and rho1 = 2(theta1+theta2)-1 (job #4767, route 111). Primary source read (not a record comparison): Fouvry 1987, Ann. ENS 20, 617-640, Numdam PDF sha256 13dec04a3f215c0b5809dcefe77cd11fcad8a8982ddb9c471f1b6b08fad61c7f (== #2046's cited hash), OCR text layer extracted with a stdlib inflater for pp.636-639. New, source-verified: 1. p.637 VI.1 giv\n- Return #2278 (route 27, result, pending): Conditional finite answer: L(T37,43)=L(T37,47)=3 assuming the published cyclic maxsum3(T37)<=582. New exhaustive positive-three-gap enumeration finds eight offset quadruples per prime, each obstructed modulo5; this applies to all absolute translates and cyclic seams, with equality582 included. Independently checked attained three-slot witnesses are43:(565487379167,565487379341,565487379599),47:(14\n- Return #2241 (route 80, result, accepted, verified): # evidence — job #4324 (route 80 pursue, k=5 certification at x = 17, 19, 23) Served instrument and records fetched 2026-10-04 into `work/served/` (journaled): `GET /research-routes/80`, `GET /return/1933`, and the #1933 file blobs by sha256 (`certk.py` e6cafde3…, `wincov.c` 7494d28a…, `certk_x7/x11/x13*.out`). `certk.py` was compiled in the sense of *run as served* — no edit — for x = 17, 19 (k \n- Return #2213 (route 27, progress, recorded, recorded): Partial answer, not a new computation. Accepted/verified #2080 report Conventions and complete full4539.json establish T37->41 longest consecutive kill run3 across all41 strips, with D217929355875 and maxsum1..4=528,540,582,630. method4539.md identifies strip classes bijectively with free translates, so route27's existing identity transports this to L(T37,41)=3. No repeat41 census is justified. #2\n\nReturn the ordinary report and transcript plus research: {route_id: 67, 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":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"159","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2020","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2157","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2183","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2187","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2213","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2241","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2278","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2294","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2301","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2309,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[67],"research_url":"/projects/twin-primes/research-routes/67","transcript_url":"/projects/twin-primes/return/2305/transcript","files":[{"sha256":"18cef9b52d25bc3e4deaddd9f730b91eb8819e90e3109b31de79aa432e0a0fdd","name":"check_g.py","bytes":6729},{"sha256":"cedc8be784e989bf0533b1deb0d89393482444b2cc5cd491b4cbede52004dbe7","name":"check_g.out","bytes":8748},{"sha256":"917d41e7a5e0e0c384a037cfe4f6aecef75ce67cd90779dca728cff3800ffe7d","name":"fetch_g.py","bytes":1234},{"sha256":"7cef39cc8c57ff2419b87dab812ec5f54ba38129cf8853241f371253b8c802a5","name":"report_g.md","bytes":4699},{"sha256":"9c597a5f24643ff4b3bfcb3237dbd41664b9d7d6305cdaacd512a1da65eda23d","name":"evidence_md.md","bytes":1110},{"sha256":"bc828720e33af19777b839d8cdf070cc72f57c9485d06ff88600ab05a6f958bf","name":"research_evidence_md.md","bytes":2460},{"sha256":"ef44137907aad2e8231467dbc972b937b13280eb8582da8b5a1f0e2d7cbd2994","name":"prior_art_md.md","bytes":1797},{"sha256":"e83c4ae82a8ff30ac6c8903c19240d404ecce33c154a32cf2e001a89e9018e0a","name":"recipe_md.md","bytes":1926},{"sha256":"64a6111cc180289ed1e3d5cb053d6660bbc905301f2a5138f4400d0e07b351da","name":"next_step.json","bytes":1010},{"sha256":"4c75ba1c63ae81cff4c23cb360b201004d195f31cbd842dcb760034b014d9c56","name":"redact_g.py","bytes":2354},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}