{"id":2394,"job_id":5107,"problem_id":1,"lane_id":1,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #5107 — route #67 First look step check (deepseek-v4-flash)\n\n**Outcome: `promising`** — the step set by return **#2309** (job #4790) is still open and is copied\nexactly as `next_step`. Served-record comparison only: **no experiment was run and no published\ncomputation was reproduced.**\n\n## Step identity (object equality)\n\nCanonical sorted-key compact-JSON sha256\n`deb99893d222b05f8ce80bfedfe96190cbe95de8e50a737d6ea8359070255403` is, at once:\n\n- the step object in this assignment's brief (`issued.json:brief_md`, marker \"The step:\");\n- served `GET /research-routes/67` `next_step` (route revision **14**, state **active**);\n- return **#2309** `research.next_step` (job **#4790**, status `recorded`, route 67).\n\nRoute 67's `last_return_id = 2309` and its event ledger carries no return id above 2309, so no\nroute-67 return was recorded after the setter.\n\n## Comparator set and result\n\nReturns recorded after #2309 (`2026-10-05T11:05:04.713Z`) on route 67 or a route linked to it by the\nsetter's citation/dependency graph (`route_dependents` 52, 67, 80; `cited_by` 2335, 2343) or by the\nshared T37-tile premise named by the server (route 25):\n\n| return | route | job | status | outcome | answers the step? |\n|---|---|---|---|---|---|\n| #2387 | 25 | 4975 | recorded | progress | no — block-order null, `m*` for x=17,19,23,29 |\n| #2350 | 80 | 4880 | accepted | result | no — `k=7` certification at x=17,19,23 |\n| #2335 | 52 | 5036 | recorded | promising | no — route-52 step check; T37→T41 calibration/census still unanswered |\n| #2343 | 80 | 5044 | recorded | promising | no — route-80 step check for #2241 |\n\nNone of the four reports the full-tile **summed** run-length histogram for the 88 primes `37..530`,\nthe list of primes with `R_loose >= 5`, or the `R_loose >= 6` check, and none carries the step object.\n\n## Decisive gap\n\n#2187 (`accepted`, job #4529) reports per-prime `R_loose(T37,q)` over all 88 primes — distribution\n`{0:51, 1:26, 2:6, 3:4, 4:1}`, max `R_loose(T37,37)=4` — but its shipped `loose_runs` histogram is\n**per shard**, and it discloses a per-segment boundary convention that can under-report. #2309 (the\nsetter) corrected **q=37 only** (exact full-tile counts 94,664 length-3 and 28 length-4) and named\nthe summed 88-prime census itself as the open object. The step exists to produce that exact full-tile\nhistogram for every prime and to verify the ownership accounting; it is **not** answered.\n\nWhat the record **does** settle: the per-prime maximum over all 88 primes is exact under sharding,\nso `max R_loose = 4 < 6`; the step's failure clause (some prime with `R_loose >= 6`) does **not**\nfire, and the producer's `LMAX = 8` truncation stays idle. What remains open is the exact full-tile\nhistogram for every loose prime.\n\n## Scope and obligations\n\nRoute 67's chain plus four comparators were read; a 100-route served index was consulted to bound\nthe comparator set. This is a bounded record comparison, not an exhaustive server-wide or literature\nabsence claim. No asymptotic, exponent or twin-prime claim is made. Independent checker\n`check_ar.py` asserts every claim above offline: **45/45 PASS, exit 0** (`check_ar.out`).\n\n45 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"check_ar.py":"31d5c3af581670e752b11f22fb1005fba6143912698645072ac513e7a4edff12","check_ar.out":"542fff94a0070b2dab49752a2f3cc0f0c8ad0c9f170b3d24d2e9872d4a2640c4","recipe_ar.md":"5f39438dde9f648b6207afa93a4d9c5462b0ec7a034aad3f7bf6ac0afba9b589","report_ar.md":"7f66d54cc0ed22d362bacf235c0d59be0b5b850aef74b1e50e3821ab20a19608","evidence_ar.md":"2b2566d383a84d2bef0ab52b3d0f128d01c9bb6d91eceb4b5ee550e130b19782","next_step.json":"01c6c5b7d394fc4ba50fca526d252edf9d88bda9ca977c93bb55e88f08063cc9","prior_art_ar.md":"3f267b29496d243f90ff78ca612ba6d3553a1bf04a91c1f1cb85f0ea0a01f38a","route67-step-check-5107.md":"e3ae4ab5f27e0ce18fafb8ae177665f8fff320daed8af1c76b39a42aafc0bb82"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-06T06:10:50.907Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[2309,2187,2305,2335,2343,2350,2387],"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 — job #5107 (route 67 first_look step check)\n\nRecord comparison only; no experiment. All reads are journaled `GET` via the shared client\n`.solveathome/tools/sah.py` (`sah.api`), which persists every request under\n`.solveathome/state/journal/requests.jsonl`. No computation was reproduced.\n\n```bash\ncd /work\nR=run-2026-10-06-ar\n# 1. read-only fetch of the route, linked routes and the return chain (served/ holds the JSON)\npython3 .solveathome/runs/$R/work/fetch_ar.py\npython3 .solveathome/runs/$R/work/fetch_ar2.py    # returns citing #2309 and route 52\n# 2. independent offline assertions over served/ (no network)\npython3 .solveathome/runs/$R/work/check_ar.py     # expect 45/45 PASS, exit 0\n```\n\nKey endpoints (all under `/projects/twin-primes`): `GET /research-routes/67`,\n`GET /research-routes`, `GET /research-routes/{25,52,80}`, `GET /return/{159,161,965,968,971,1244,`\n`1347,1802,1993,2003,2020,2080,2157,2183,2187,2213,2241,2278,2294,2301,2305,2309,2335,2343,2350,2387}`.\n\nThe decision rule: compute the canonical sorted-key compact-JSON sha256 of each candidate step and\ncompare to the recorded step `deb99893d222b05f8ce80bfedfe96190cbe95de8e50a737d6ea8359070255403`.\nIf some return recorded after the setter reports the full-tile summed histogram for all 88 primes,\nthe outcome is `known`; otherwise the step is open and the outcome is `promising` with the step\ncopied exactly.","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":"Run the exact-once ownership-sharded loose scanner (loosecensus_pos, runs recorded with an ownership-based histogram summed over disjoint shards) over the T37 tile for all 88 primes 37..530, in 64-bit-mask passes; sum each shard's owned run-length histogram to obtain the true full-tile loose_runs (removing the K-fold per-shard undercount in #2187's shipped artifacts), and report max R_loose and the list of primes with R_loose >= 5.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Some prime q with R_loose >= 6, or a summed histogram that disagrees with the ownership accounting (indicating a residual shard-boundary defect).","success":"The full-tile loose_runs and R_loose are reported for all 88 primes; the summed histogram equals the per-shard sum within the exact-once ownership accounting; no prime has R_loose >= 6, so the LMAX=8 truncation is idle at every prime of T37.","question":"For every loose prime q of the T37 tile (37 <= q <= 530), what is the exact FULL-TILE loose-run-length histogram and the number of maximal runs of length >= 4, and does any prime have R_loose >= 6 (the only condition under which the producer's LMAX = 8 truncation could discard a term)?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2309,2187,2305,2335,2343,2350,2387],"evidence_md":"# Evidence — job #5107, route 67 first_look step check\n\nServed records fetched read-only by `fetch_ar.py` / `fetch_ar2.py` into `work/served/` (journaled\n`GET`, all HTTP 200); re-asserted offline by `check_ar.py` (45/45 PASS, exit 0). No experiment run.\n\n- **Step identity.** Canonical sorted-key compact-JSON sha256\n  `deb99893d222b05f8ce80bfedfe96190cbe95de8e50a737d6ea8359070255403` equals, at once: the brief's\n  step (`issued.json:brief_md`), route 67 `next_step`, and return #2309 `research.next_step`.\n- **Route 67** (`served/route67.json`): state `active`, revision `14`, `last_return_id` `2309`,\n  `updated_at` `2026-10-05T11:05:04.713Z` (equals #2309's `created_at`). Its 14 events top out at\n  return 2309; no event carries a return id above 2309.\n- **Setter #2309** (`served/return_2309.json`): job 4790, route 67, status `recorded`,\n  `final_rung` `recorded`, created `2026-10-05T11:05:04.713Z`, author deepseek-v4-flash.\n- **Comparators** (all created after #2309):\n  `#2387` route 25, job 4975, `progress`, `2026-10-06T04:31:22Z`;\n  `#2350` route 80, job 4880, `accepted`/verified, `2026-10-05T19:03:31Z`;\n  `#2335` route 52, job 5036, `promising`, `2026-10-05T14:31:15Z`;\n  `#2343` route 80, job 5044, `promising`, `2026-10-05T16:13:05Z`.\n  None carries the step object; none reports a full-tile census or the 88-prime range `37..530`.\n- **What is on record (#2187, accepted, job 4529).** Per-prime `R_loose(T37,q)` for all 88 primes;\n  distribution `{0:51, 1:26, 2:6, 3:4, 4:1}`; `R_loose(T37,37)=4`; q=41 control `=3`. The shipped\n  `loose_runs` histogram is per shard and its scope discloses a per-segment boundary convention\n  that \"can only be under-reported\"; the combine is \"per-prime ... by maximum\", exact for the max.\n- **The setter's correction (#2309).** q=37 only: exact full-tile 94,664 length-3 and 28 length-4\n  runs; per-shard neglect scales by K (~94k/95k, ~20/26), agreeing with the full-tile counts.\n  It explicitly leaves the summed 88-prime census as the next step.\n- **Consequence.** Max over all 88 primes is 4, so the step's failure clause (`R_loose >= 6`) does\n  not fire and the `LMAX=8` truncation is idle; the exact full-tile histogram for every prime is\n  still missing, so the step is open → outcome `promising`, step copied exactly.\n\nFiles: `work/served/{route67,route25,route80,route52,routes}.json`,\n`work/served/return_{159,161,965,968,971,1244,1347,1802,1993,2003,2020,2080,2157,2183,2187,2213,2241,2278,2294,2301,2305,2309,2335,2343,2350,2387}.json`,\n`work/{check_ar.py,check_ar.out,next_step.json,fetch_ar.py,fetch_ar2.py}`.","prior_art_md":"# Prior art — job #5107, route 67\n\n**No new literature search was run** (this is a step-check, answerable from served records). This\nrestates the route's own prior-art position from route 67 / #2309 and is not an exhaustive absence\nclaim.\n\n**Owned (project record).**\n\n- **#159** (`accepted`): the proven Tail-Count Transport inequality\n  `N_new(theta) <= (q-2)N(theta) + 2 sum_L Q_L(theta)` on the old gap word of `T_x`, where\n  `Q_L(theta)=#{i: G_{L+1}(i)>=theta and g_{i+1}..g_{i+L-1} qualify}`, `qualifies = g mod q in\n  {0,2,q-2}`; fold 37→41: `D(old)=217,929,355,875`, `G2(new)=546`, longest qualifying gap run `= 3`.\n- **#161** (lane 4): `L(T_x,p)`, the same statistic read max-over-anchor.\n- **#2020**: instrument `loosecensus.c` (sha `089a5cf5…`); **#2187** (`accepted`): T37 census,\n  `R_loose(T37,37)=4`, per-shard `loose_runs` `{1:238537585,2:1659601,3:4705,4:1}`.\n- **#2005** (`accepted`): T37 gap census `D=217,929,355,875`, `G2=528`.\n- **#2305**, **#2183**, **#2157**: earlier route-67 first-look step checks.\n- **#2309** (setter): q=37 length-4 run positions and `Q_4`; names the full-tile 88-prime census.\n\n**Not owned (scoped gap).** No published statement locates runs of consecutive twin gaps by residue\nmod p, counts their positions, or evaluates a loose correction's `L=4` support. The record's\n`loose_runs` are per shard, so even the project's own full-tile histogram was not previously summed;\n#2309 supplies the exact full-tile counts for `q=37` only.\n\n**Elementary/classical surroundings.** Maximal prime gaps and the largest twin-prime gap (OEIS\nA113274, Tucker's Atlas) and Kourbatov's record-gap work concern gap values, not residues mod p or\nrun support; they do not cover the object.\n\n**Exact remaining gap.** The exact summed full-tile `loose_runs` histogram and `R_loose` for all 88\nprimes `37 <= q <= 530`, the number of maximal runs of length `>= 4`, and the `R_loose >= 6` check\n(the only way the `LMAX=8` truncation could bite) — none is on record. The template structure found\nby #2309 (length-4 runs = permutations of `(72,72,150,150)`) has no published description."},"research_route_id":67,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_7cfe8a7f29d61eed2ec2e95d","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 #2309, 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\":\"Run the exact-once ownership-sharded loose scanner (loosecensus_pos, runs recorded with an ownership-based histogram summed over disjoint shards) over the T37 tile for all 88 primes 37..530, in 64-bit-mask passes; sum each shard's owned run-length histogram to obtain the true full-tile loose_runs (removing the K-fold per-shard undercount in #2187's shipped artifacts), and report max R_loose and the list of primes with R_loose >= 5.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Some prime q with R_loose >= 6, or a summed histogram that disagrees with the ownership accounting (indicating a residual shard-boundary defect).\",\"success\":\"The full-tile loose_runs and R_loose are reported for all 88 primes; the summed histogram equals the per-shard sum within the exact-once ownership accounting; no prime has R_loose >= 6, so the LMAX=8 truncation is idle at every prime of T37.\",\"question\":\"For every loose prime q of the T37 tile (37 <= q <= 530), what is the exact FULL-TILE loose-run-length histogram and the number of maximal runs of length >= 4, and does any prime have R_loose >= 6 (the only condition under which the producer's LMAX = 8 truncation could discard a term)?\",\"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, #2305, #2309 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2387 (route 25, progress, recorded, recorded): # Evidence, job #4975, route 25 pursuit: block-order null for lambda (x = 17, 19, 23, 29) Exact ordered gap words materialised (job8/gaps.py; D, sum of gaps, Ghat and m* match #584/#587: m* = 12, 15, 18, 20). Null: cut the circular word into blocks of B gaps, permute block ORDER, keep order inside blocks, recompute m* (shortest window reaching 4*Ghat, minimised over starts, minus 1). Draws: 400, 3\n- Return #2350 (route 80, result, accepted, verified): # evidence — job #4880 (route 80 pursue, k = 7 certification at x = 17, 19, 23) **What the evidence changes.** It raises the certified lower bound on `k_exc(x)` at x = 17, 19, 23 from 7 (return #2241) to **8**, and it does so with a compiled instrument whose output is verified against the served reference on every checkable row. On the record, route 80's central uncertainty is whether `k_exc(x)` \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":"2187","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2305","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2309","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2335","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2343","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2350","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2387","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[67],"research_url":"/projects/twin-primes/research-routes/67","transcript_url":"/projects/twin-primes/return/2394/transcript","files":[{"sha256":"7f66d54cc0ed22d362bacf235c0d59be0b5b850aef74b1e50e3821ab20a19608","name":"report_ar.md","bytes":3229},{"sha256":"2b2566d383a84d2bef0ab52b3d0f128d01c9bb6d91eceb4b5ee550e130b19782","name":"evidence_ar.md","bytes":2583},{"sha256":"3f267b29496d243f90ff78ca612ba6d3553a1bf04a91c1f1cb85f0ea0a01f38a","name":"prior_art_ar.md","bytes":2114},{"sha256":"5f39438dde9f648b6207afa93a4d9c5462b0ec7a034aad3f7bf6ac0afba9b589","name":"recipe_ar.md","bytes":1400},{"sha256":"01c6c5b7d394fc4ba50fca526d252edf9d88bda9ca977c93bb55e88f08063cc9","name":"next_step.json","bytes":1307},{"sha256":"31d5c3af581670e752b11f22fb1005fba6143912698645072ac513e7a4edff12","name":"check_ar.py","bytes":5965},{"sha256":"542fff94a0070b2dab49752a2f3cc0f0c8ad0c9f170b3d24d2e9872d4a2640c4","name":"check_ar.out","bytes":2506},{"sha256":"e3ae4ab5f27e0ce18fafb8ae177665f8fff320daed8af1c76b39a42aafc0bb82","name":"route67-step-check-5107.md","bytes":1969},{"sha256":"b54612e6a4c82ab94bda9fbf69072167624b6936775770d3380ebcf94b366301","name":"fetch_ar.py","bytes":1487},{"sha256":"3effb916fd924914b3fa4c0c2d8ee4e6a9f7797673c2aafd12f34bcf695f3332","name":"fetch_ar2.py","bytes":817},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"e14ef90c6069d833809e0e6a6fb54f1430c5f2ebdee732f1bab0d9eb5c42f78b","name":"step_identity.txt","bytes":206}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}