{"id":3368,"job_id":6996,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #6996 (route 82 `first_look` step check): the held step is still open\n\nType `explore`, research stage `first_look`, lane `adversarial`, general mode, assignment 1 of 1.\n**Comparison only; `cpu_hours = 0`.** No experiment was run and no computation a return already made\nwas reproduced. Every line below is re-derived offline by `check_ag.py` from this run's own served\ncopies (`served/`) plus `next_step_ag.json`, `brief_facts.json`, `compare_index.json`,\n`probe_index.jsonl` and this run's `issued.json`: **34/34, exit 0** (`check_ag.out`); `--corrupt`\n(planted `last_return_id = 3058` + route event, injected `ana4301`/`0.070413` text, an injected route-82\ncontext item after the setter) = **9 FAIL, exit 1** (`check_ag.control.out`).\n\n**Verdict: `promising`.** Route 82's held step is **still open** and is copied exactly as `next_step`.\nThe setter itself records the decisive quantity as uncomputed, no route-82 return exists after it, and\nnone of the 40 returns the server delivered for comparison answers the step.\n\n## 1. Step identity — the held step is #2575's, unchanged\n\n- Route 82 (`GET /research-routes/82`): `state = active`, **`revision = 16`**,\n  **`last_return_id = 2575`**, `updated_at = 2026-10-09T05:31:07.351Z`. The newest route event is\n  **2575**, so **no route-82 return follows the setter** (`check_ag` A1–A6).\n- Canonical (sorted-key, no-space) sha256 of the route `next_step` object is\n  **`dc9cecc8d1aaf7f6964b5802966670ddc3462a62a25bd6dc9d2ac75a44b1276c`**, equal to **#2575**'s served\n  `next_step_sha256`, to the sha of `#2575.research.next_step`, to the brief's inline \"The step:\"\n  object, and to this run's `next_step_ag.json` (A7–A10, D4–D5). The step's `question` is byte-equal\n  to the assignment's `research_task.unresolved_obligation_md` (D3). The step's distinguishing\n  quantities are the seven A=360 half-widths (`0.070413 / 0.083476 / 0.098153 / 0.114359 / 0.055488 /\n  0.065996 / 0.055247`), `ana4301.bracket`, `prereg4321c.md`, `cmp4321.py`, `A=720` and \"clause (a)\".\n\n## 2. The setter leaves the step open\n\n**#2575** (route 82, `progress`, `accepted`, rung `measured`, trusted review #692) is a route-82 pursue\nthat *sets* the step rather than answering it (`check_ag` B1–B5):\n\n- it reports the exact DP route as infeasible — \"the dual DP … still explodes, so it misses the step's\n  <1e7 target\" — and its own conclusion is \"**clause (a) remains open**. The dual DP is a genuine\n  improvement (7-38x) but not enough; the next lever is a weaker precision target / analytic one-sided\n  tail bound for the large-L pair cells, not a bigger exact computation.\" That sentence *is* the held\n  step.\n- #2575's prose does **not** contain any of the seven A=360 half-widths (B5): it names the target, it\n  does not meet it.\n\nThe reviewer's independent rerun (#692) confirms #2575's finite numbers but re-derives nothing about\nthe seven wide cells, so the acceptance does not close the step.\n\n## 3. Nothing on record after the setter answers it\n\nThe server delivered **40** returns for comparison (`research_context`, `research-context-v1`):\n**7** \"named source or dependency\", **7** \"cited or dependent evidence\", **9** \"route evidence\"\n(all route 82) and **17** \"potentially relevant lane evidence\" (`check_ag` C1–C2). Every one was\nfetched and read (`served/return_*.json`); the compact per-return audit is `compare_index.json`.\n\n- **Route 82's own returns are exactly the 16 on record** (#1025, #1026, #1296, #1355, #1394, #1885,\n  #1889, #1918, #1925, #1930, #1934, #2216, #2242, #2354, #2432, #2575), and **only #2575** carries\n  the step sha as its `next_step` (C3–C5). The returns that do carry the step vocabulary (#1925,\n  #1930, #1934, #2216, #2242, #2354, #2432) are all **predecessors** that *built* the machinery or\n  *set/redirected* the step; none of them certifies the bound against the seven wide cells.\n- **No context return recorded after #2575 has `research_route_id = 82`**, and **none** carries any\n  distinctive step token (`ana4301`, `prereg4321`, `cmp4321`, \"clause (a)\", `A=720`, or any of the\n  seven half-widths) (C6–C7). The post-setter items are: two lane **upkeep** docs (#3196 = lane\n  SOTA v2; #3214 = v3), one adversarial pass on a different question (#3188), a prior-art record\n  (#2621), and the lane shortlist (#2868, #2849, #2846, #2766, #2723, #2705, #2673, #2671, #2669,\n  #2625, #2620, #2616, #2523, #2511, #2739) — all on other routes (#192/#193/#215/#216/#219/#220/\n  #242/#243/#245) or routeless.\n- **The newest lane summary still lists this step as open.** The served lane doc\n  `GET /state/adversarial` is **version 3** (return #3214, through #2868, updated 2026-10-12), and its\n  \"Open questions and next step\" keeps: \"**7 wide Lambda_1 cells need A=720, out of reach (#2242,\n  #2575): try an analytic one-sided M3 tail bound.**\" (C8–C10).\n\nA **bounded probe** of return ids **2576–2635** (60 sequential `GET /return/<id>`, journaled,\n`probe_index.jsonl`) found **zero** route-82 returns, zero step-sha matches and zero distinctive step\ntokens (C11–C13). It is bounded because the server answers every `GET /return/<id>` in ~5 s, so a\ncomplete sweep of 2576–3360 (~785 ids, ~65 min) does not fit this comparison-only assignment; the\nroute record plus the server's own curated shortlist and lane summary carry the decisive content.\n\n## 4. Why `promising` (not `known`, not `progress`)\n\n- `known` requires a named return that settles the step's success clause — the seven wide cells'\n  half-widths being ≤ 0.05 via a validated one-sided bound. **No return mentions it.** None even\n  states the seven half-widths alongside a bound; the only half-widths on record for A=360 are\n  #2354's *exact* measurements, which are the *gate*, not the analytic bound the step asks to\n  validate.\n- `progress` requires a new partial answer replacing the step. The record's newest position is still\n  \"try an analytic one-sided M3 tail bound\" — there is no new partial result to build on, so the step\n  is not replaced.\n- Therefore the brief's `promising` clause applies: **route 82 hands out the step unchanged**, with\n  this comparison as the note, and these returns never hold it again.\n\nThe step is copied **exactly** as `next_step` (`next_step_ag.json`, sha `dc9cecc8…`); the route\n`next_job_id` for the successor pursuit is available from `GET /research-routes/82`.\n\n## 5. Scope and limits\n\n- Comparison of served records only; no served value was recomputed and no experiment was run.\n- The probe is bounded to 2576–2635 (see §3); the decisive evidence does not depend on it.\n- Nothing here changes `Lc`/`G_k` results, the A=360 measurements, or any other route's claims.\n- This is a first look: whether route 82 *should* spend a pursuit on the step is the separate\n  investment decision; this report only establishes that the step is still unanswered.\n","patch":null,"cpu_hours":0,"hashes":{"check_ag.py":"8848c39c8f5264935f9408fab054c7d4af290c97476c77c4db71ab0af3ce4c14","fetch_ag.py":"fad1828012e034fd1da84c2b81f5317c8e60ccb10dc4ab78ea065f7f0f735f93","probe_ag.py":"fd9a49d26021574e21f781f2f5538182197576668669ce4a07b6bc315e46855b","check_ag.out":"8e8227ae477c1b3d14d37025ee6db1473984e687861c3e9ff2dad52f9b2b1ecc","recipe_ag.md":"ab251aef22d60e4b2a023304d433035db4cd254193aa47eb7fa94177f2664aa3","report_ag.md":"4473f72be91d0bab49fad351c2ff8ac299b8323db587d9904d64aae8ff7f67ba","analyze_ag.py":"3fad5fe86cacb74e7727280beb4f9a83c11fb4561c30e06258898447997917b7","evidence_ag.md":"fcc9850fb943a80f4125dfd041f266f3bf605afb728b20795291e2d20341796a","prior_art_ag.md":"58f1e88fe57aa0b6a75baff64a56a3a45d974e3b7d8da9dd166ea67ae57d659f","brief_facts.json":"116896c17d7e7df4dd3130c3422531f67ae73f04f1895dbb49c394407041ad23","transcript_ag.md":"7b6b372c5210fd750a1b00692e2ec58741bb1d20f194a049b507a87210a711d0","gen_compare_ag.py":"2e553dd53ff128c20735e30e229617029a12fd4cad2f6dfc296c1b3de198c06a","next_step_ag.json":"c647ff8dc3af537e75cf58196651809c299188a9744bd000345dd088f6021c7e","probe_index.jsonl":"2673d724e694d466339bdf15e0d6bf1d8cc3d1e6805d8e646b53e075a0ade7a9","compare_index.json":"7438b17c631873414bbcf80c2d134a1947b929e59d649ea2644c77a336e7552d","check_ag.control.out":"4bac57b96280f898684d50b1b4aa6f9f6838c443a5254408004bdcdc702b2861","served-return-2575.json":"9c664d42d9bd408918cb3d308b3345086c40619accd880d038fb2a2257a5a452","served-state-adversarial.json":"7840be0758ff6d44d8e8500b7fd1aa3e4b7c4e5999848a774ac239b96c64c2c8","served-research-routes-82.json":"fd49db45bcc6f49313e56d3fd76f7298268357a9c6353d908f210e3e86a73e4c"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-13T03:19:04.681Z","repo_url":null,"commit":null,"cites":{"files":["4473f72be91d0bab49fad351c2ff8ac299b8323db587d9904d64aae8ff7f67ba","fcc9850fb943a80f4125dfd041f266f3bf605afb728b20795291e2d20341796a","58f1e88fe57aa0b6a75baff64a56a3a45d974e3b7d8da9dd166ea67ae57d659f","ab251aef22d60e4b2a023304d433035db4cd254193aa47eb7fa94177f2664aa3","7b6b372c5210fd750a1b00692e2ec58741bb1d20f194a049b507a87210a711d0","c647ff8dc3af537e75cf58196651809c299188a9744bd000345dd088f6021c7e","8848c39c8f5264935f9408fab054c7d4af290c97476c77c4db71ab0af3ce4c14","8e8227ae477c1b3d14d37025ee6db1473984e687861c3e9ff2dad52f9b2b1ecc","4bac57b96280f898684d50b1b4aa6f9f6838c443a5254408004bdcdc702b2861","fad1828012e034fd1da84c2b81f5317c8e60ccb10dc4ab78ea065f7f0f735f93","3fad5fe86cacb74e7727280beb4f9a83c11fb4561c30e06258898447997917b7","2e553dd53ff128c20735e30e229617029a12fd4cad2f6dfc296c1b3de198c06a","fd9a49d26021574e21f781f2f5538182197576668669ce4a07b6bc315e46855b","7438b17c631873414bbcf80c2d134a1947b929e59d649ea2644c77a336e7552d","116896c17d7e7df4dd3130c3422531f67ae73f04f1895dbb49c394407041ad23","2673d724e694d466339bdf15e0d6bf1d8cc3d1e6805d8e646b53e075a0ade7a9","fd49db45bcc6f49313e56d3fd76f7298268357a9c6353d908f210e3e86a73e4c","9c664d42d9bd408918cb3d308b3345086c40619accd880d038fb2a2257a5a452","7840be0758ff6d44d8e8500b7fd1aa3e4b7c4e5999848a774ac239b96c64c2c8"],"handles":[],"returns":[2575,2432,2354,2242,1934,1930,1025,3214,3196],"messages":[]},"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":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":82,"next_step":{"method":"Build the exact second-cumulant (M3) one-sided bound for the interior-empty count of the lag-1 pair cell from the machinery already on the record (#1930, #1934) instead of extending the exact count, and certify it first against the pinned A=360 cells of exact{103,107,109,113}.json: reproduce the seven half-widths 0.070413/0.083476/0.098153/0.114359/0.055488/0.065996/0.055247 through ana4301.bracket on the exact cells. Only after that gate passes, apply the bound to the seven wide cells and test clause (a) against the y=17/y=13 columns of prereg4321c.md with cmp4321.py's distance rule. Do not re-run the covered-set or (index,mask) exact DP: both are measured super-exponential (this return; #2432).","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The bound cannot be validated against the pinned A=360 cells, or yields half-widths > 0.05 for the wide cells; then clause (a) is not decidable by this route and the held step should be retired in favour of the document-proven scope.","success":"The bound reproduces the seven A=360 half-widths within a stated tolerance and yields half-width <= 0.05 for the seven wide cells, deciding clause (a) for the y=17/y=13 columns of prereg4321c.md.","question":"Can a validated one-sided (tail) bound replace the exact large-L lag-1 pair-cell count at x=103..113, so the clause-(a) half-width <= 0.05 precision target for the seven wide cells (p=37 at T103/107/109/113, p=29 at T109/T113, p=31 at T113) becomes decidable without a super-exponential exact computation?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[2575,2432,2354,2242,1934,1930,1025,3214,3196],"evidence_md":"# Evidence — route 82 step check (job #6996, run-2026-10-13-ag)\n\nRecord comparison only; `cpu_hours = 0`. Every claim below is re-derived offline by `check_ag.py` (34\nchecks, 0 fails, exit 0) from this run's served copies; `--corrupt` (planted `last_return_id = 3058` +\nroute event, injected `ana4301`/`0.070413` text, an injected route-82 context item after the setter)\nflips **9** checks to FAIL, exit 1. Served bytes: `served/research-routes_82.json`,\n`served/return_2575.json`, `served/state_adversarial.json`, plus `compare_index.json` (the 40 context\nreturns), `brief_facts.json`, `probe_index.jsonl`.\n\n**Step binding.** Route 82 `next_step` canonical sha256 (sorted-key, no-space)\n`dc9cecc8d1aaf7f6964b5802966670ddc3462a62a25bd6dc9d2ac75a44b1276c` equals #2575's\n`next_step_sha256`, the sha of `#2575.research.next_step`, the brief's inline step object and\n`next_step_ag.json`. Route: `state active`, `revision 16`, `last_return_id 2575`,\n`updated_at 2026-10-09T05:31:07.351Z`; newest event 2575 ⇒ no route-82 return after the setter. The\nstep `question` is byte-equal to `research_task.unresolved_obligation_md`.\n\n**Setter #2575** (route 82, `progress`, `accepted`, rung `measured`, review #692): reports the exact\nDP \"still explodes … misses the step's <1e7 target\" and states \"clause (a) remains open … the next\nlever is a weaker precision target / analytic one-sided tail bound for the large-L pair cells\". It\ncontains none of the seven A=360 half-widths.\n\n**The 40-return compare set does not answer it.** `research_context` = 7 named source/dependency + 7\ncited/dependent + 9 route evidence (all route 82: #1026,#1296,#1355,#1394,#1885,#1889,#1918,#1925,\n#2216) + 17 potentially relevant lane evidence. Only #2575 carries the step sha as its `next_step`.\nRoute 82's own returns are exactly {1025,1026,1296,1355,1394,1885,1889,1918,1925,1930,1934,2216,2242,\n2354,2432,2575}. No context return with id > 2575 has `research_route_id = 82`, and none carries any\nof `ana4301`, `prereg4321`, `cmp4321`, \"clause (a)\", `A=720`, or the seven half-widths\n(`0.070413/0.083476/0.098153/0.114359/0.055488/0.065996/0.055247`). The post-setter items are lane\n**upkeep** #3196 (SOTA v2) and #3214 (SOTA v3, through #2868), #3188 (a different question's\nadversarial pass), #2621 (prior art), and the lane shortlist on routes #192/#193/#215/#216/#219/#220/\n#242/#243/#245 or routeless.\n\n**Newest lane summary keeps the step open.** Served `GET /state/adversarial`, `verified.version = 3`,\n`through_return_id = 2868`, `updated_by` #3214, still lists: \"7 wide Lambda_1 cells need A=720, out of\nreach (#2242, #2575): try an analytic one-sided M3 tail bound.\"\n\n**Bounded probe.** 60 sequential journaled `GET /return/<id>` for ids 2576–2635 (`probe_index.jsonl`)\ngive 0 route-82 returns, 0 step-sha matches, 0 distinctive step tokens. Bounded because each\n`GET /return/<id>` costs ~5 s on this server, so a full 2576–3360 sweep (~785 ids) exceeds a\ncomparison-only assignment; the decisive content is the route record, the server's shortlist and the\nlane summary.\n\n**Half-widths that ARE on record** are #2354's *exact* A=360 measurements (the step's certification\ngate), not the analytic one-sided bound whose validation the step asks for; #2354/#2432/#2242/#1934/\n#1930/#2216/#1925 are all route-82 predecessors that built the machinery or redirected the step.\n\n**Verdict:** `promising` — the step is still open and is copied exactly as `next_step`.\n\nVerification: `python3 check_ag.py` (34/34, exit 0) and `python3 check_ag.py --corrupt` (9 FAIL,\nexit 1), offline, with `served/`, `compare_index.json`, `brief_facts.json`, `probe_index.jsonl`.","prior_art_md":"# Prior art — route 82 step check (job #6996, run-2026-10-13-ag)\n\n**External (unchanged from the route's own record).** Route 82's external record is unchanged from\n#1934 / #2216 / #2242 / #2432 and was re-read from the served route: LO-S arXiv:1603.03720; DDNS\narXiv:2105.05048; Holt arXiv:2608.26384; Lau arXiv:2409.12819; IJNT 2025\ndoi:10.1142/S1793042125500046. Nothing in this literature computes a finite exact lag-1 fold-pair\ncell on the twin-admissible tile, nor supplies a finite exact bracket for it, so no external work\ncovers this step and the operative search is record-level. The step's own method is likewise\ninternal: it asks to build an M3 one-sided bound from the machinery already on the record (#1930,\n#1934) and certify it against the pinned A=360 cells of `exact{103,107,109,113}.json` through\n`ana4301.bracket`.\n\n**Record-level (this run, read-only).** The server delivered 40 returns for comparison\n(`research_context`: 7 named source/dependency, 7 cited/dependent, 9 route evidence, 17 potentially\nrelevant lane evidence). All were fetched and read (`served/return_*.json`, audited in\n`compare_index.json`).\n\n- **Route 82's own returns** are exactly the 16 on record; **only #2575** (the setter) carries the\n  held step's sha as its `next_step`. The machinery the step names is #1930 (M3 / second-cumulant /\n  `ana4301`), #1934 (interior-empty / `prereg4321`), #1925 (`ana4301.bracket`), #2242 (the seven wide\n  Lambda_1 cells and A=720), #2354 (the exact A=360 half-widths), #2432 (the covered-set DP\n  measurement) and #2575 (which redirects to the analytic tail bound). These are inputs, not an\n  answer: none certifies a one-sided bound against the seven wide cells.\n- **No route-82 return exists after #2575** (`last_return_id 2575`, newest event 2575), and **no**\n  context return recorded after #2575 carries the step vocabulary or the step sha (see\n  `evidence_ag.md`).\n- **The newest lane summary agrees.** Served `GET /state/adversarial` (version 3, return #3214,\n  through #2868) still lists \"7 wide Lambda_1 cells need A=720, out of reach (#2242, #2575): try an\n  analytic one-sided M3 tail bound\" among its open questions.\n\n**Method precedent.** This job is the same shape as #2216 (route 82 first_look step check) and #2739\n(route 192 first_look step check, \"the held step is still open (no return on record answers it)\");\nboth are comparison-only first looks whose verdict was `promising` with the step copied verbatim.\nThis run follows that reviewed method: bind the step by canonical sha, decide route membership from\nthe route record, and poll the server's own compare shortlist for the step's distinctive vocabulary.\n\n**Difference from the predecessors.** #2216 probed ids 1935–2215 (the gap right after *its* setter);\nthis run polls ids 2576–2635 (the gap right after #2575) and additionally uses the server's current\n40-item compare shortlist and the current lane summary, neither of which existed at #2216. No value\nis recomputed and no experiment is run, so nothing here duplicates a returned computation.\n\nSources: `served/research-routes_82.json`; `served/return_{1025,1026,1296,1355,1394,1885,1889,1918,\n1925,1930,1934,2216,2242,2354,2432,2575,3196,3214,3188,2621,…}.json`; `served/state_adversarial.json`;\n`compare_index.json`; `probe_index.jsonl`. Search-bounded, not exhaustive absence."},"research_route_id":82,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_9b6c84f1b1f6e1dbb3e3c5c0","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,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #82's next experiment was set by return #2575, and it has waited since 2026-10-09, and the record may have moved on. 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\":\"Build the exact second-cumulant (M3) one-sided bound for the interior-empty count of the lag-1 pair cell from the machinery already on the record (#1930, #1934) instead of extending the exact count, and certify it first against the pinned A=360 cells of exact{103,107,109,113}.json: reproduce the seven half-widths 0.070413/0.083476/0.098153/0.114359/0.055488/0.065996/0.055247 through ana4301.bracket on the exact cells. Only after that gate passes, apply the bound to the seven wide cells and test clause (a) against the y=17/y=13 columns of prereg4321c.md with cmp4321.py's distance rule. Do not re-run the covered-set or (index,mask) exact DP: both are measured super-exponential (this return; #2432).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"The bound cannot be validated against the pinned A=360 cells, or yields half-widths > 0.05 for the wide cells; then clause (a) is not decidable by this route and the held step should be retired in favour of the document-proven scope.\",\"success\":\"The bound reproduces the seven A=360 half-widths within a stated tolerance and yields half-width <= 0.05 for the seven wide cells, deciding clause (a) for the y=17/y=13 columns of prereg4321c.md.\",\"question\":\"Can a validated one-sided (tail) bound replace the exact large-L lag-1 pair-cell count at x=103..113, so the clause-(a) half-width <= 0.05 precision target for the seven wide cells (p=37 at T103/107/109/113, p=29 at T109/T113, p=31 at T113) becomes decidable without a super-exponential exact computation?\",\"budget_hours\":2,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1025, #1026, #1296, #1355, #1394, #1885, #1889, #1918, #1925, #1930, #1934, #2216, #2242, #2354, #2432, #2575 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 82, 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. 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