{"id":3397,"job_id":5369,"problem_id":1,"lane_id":2,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5369 (route 82 pursue): the A=360 certification gate for the M3 one-sided bound passes, and the bracket width is 93–97% crude tail overcount\n\n**Outcome: progress.** Route 82, stage `pursue`, lane adversarial. The held step is #2575's\n`next_step` (canonical sha256 `dc9cecc8d1aaf7f6964b5802966670ddc3462a62a25bd6dc9d2ac75a44b1276c`,\nbyte-equal to `research_task.unresolved_obligation_md`).\n\n## What was actually done\n\nThe step's own first clause is a **certification gate**: *\"reproduce the seven half-widths\n0.070413/0.083476/0.098153/0.114359/0.055488/0.065996/0.055247 through `ana4301.bracket` on the\nexact cells [`exact{103,107,109,113}.json`].\"* I ran that gate, unmodified, on the pinned served\nbytes and then decomposed the resulting bracket exactly.\n\n- **Instrument, byte-pinned.** `ana4301.py` sha256 `432df616…95cb2` (the same binary carried by #1925\n  and #2354); `exact103.json` `57a5c30f…b585`, `exact107.json` `a9c9b599…0631`, `exact109.json`\n  `0a49b61d…2809`, `exact113.json` `fbb796b2…4961`. Every sha256 was re-verified on the local bytes\n  by `check_al.py`.\n- **No re-implementation.** `ana4301.bracket` is `exec`'d from the pinned source; the bracket is exact\n  integer/Fraction arithmetic, so the reproduction is byte-faithful, not a model.\n\n## Result 1 — the gate passes exactly (7/7)\n\n| cell | p | x | A=360 half-width (reproduced) | pinned |\n|---|---|---|---|---|\n| p37@103 | 37 | 103 | **0.070413** | 0.070413 |\n| p37@107 | 37 | 107 | **0.083476** | 0.083476 |\n| p37@109 | 37 | 109 | **0.098153** | 0.098153 |\n| p37@113 | 37 | 113 | **0.114359** | 0.114359 |\n| p29@109 | 29 | 109 | **0.055488** | 0.055488 |\n| p29@113 | 29 | 113 | **0.065996** | 0.065996 |\n| p31@113 | 31 | 113 | **0.055247** | 0.055247 |\n\nAll seven match to six decimals; `check_al.py` also re-derives each `lo`, `hi` and `D`-normalised\nterm from scratch. This is the precondition the step requires before any bound may be applied to the\nseven wide cells.\n\n## Result 2 — the width is the crude uncovered-pair overcount, not the m-window\n\nWith `lo = K_cov/E(m_cov+tail_h)`, `hi = (K_cov+U)/E(m_cov)` and `E(m)=m(m−1)/(D−1)`, exact\n`Fraction` arithmetic gives, per wide cell:\n\n| cell | half-width | `U/E(m_cov)` | m-window term `K_cov(1/E_lo−1/E_hi)/E_lo` | `U_cap/E(m_cov)` for hw≤0.05 | cut needed |\n|---|---|---|---|---|---|\n| p37@103 | 0.070413 | 0.1365 | 0.0043 | 0.0957 | **1.43x** |\n| p37@107 | 0.083476 | 0.1616 | 0.0054 | 0.0946 | **1.71x** |\n| p29@109 | 0.055488 | 0.1072 | 0.0038 | 0.0962 | **1.11x** |\n| p37@109 | 0.098153 | 0.1897 | 0.0066 | 0.0934 | **2.03x** |\n| p29@113 | 0.065996 | 0.1273 | 0.0047 | 0.0953 | **1.34x** |\n| p31@113 | 0.055247 | 0.1060 | 0.0045 | 0.0955 | **1.11x** |\n| p37@113 | 0.114359 | 0.2207 | 0.0080 | 0.0920 | **2.40x** |\n\nThe m-window contribution is ≤ 0.008 everywhere (a floor half-width of 0.0019–0.0040 if the\nuncovered kill pairs were bounded to zero). **The whole width is the one-sided tail term `U`.**\nThat localises the step: a bound is needed only on `U`, the number of lag-1 kill pairs `(a,b)` with\n`a+b > 360`, and its per-cell numeric target is `U < U_cap`, i.e. a **1.11x–2.40x** reduction of the\ncurrent crude `U` (which charges every uncovered gap `> A` as a potential kill first gap).\n\n## Result 3 — the target is comfortably inside the model-implied margin\n\n`U_cap/E(m_cov) ≈ 0.092–0.096` is essentially constant across the seven cells, and the crude `U`\nis 1.11–2.40x above it. For the hardest cell (p37@113) the pre-registered y=17 model value is\n0.7367 against `λ_cov = K_cov/E(m_cov) = 0.714455`, i.e. the model-implied true uncovered pair total\nis `≈ 0.022·E(m_cov)`, about **10x below `U_cap`**. So the crude `U` overcounts by an order of\nmagnitude and the step's precision target is not near the information-theoretic edge: a validated\none-sided bound needs to recover only ~1/2.4 of the overcount. (The 10x figure is model-implied and\nis labelled heuristic; the 1.11–2.40x target is exact.)\n\n## What this changes, and what it does not\n\n- **Changes:** the certification gate that #2575's step demanded before any bound is applied is now\n  *performed and verified* on the pinned bytes; and the step is reduced to one exact numeric target\n  per wide cell (`U_cap`), which also rules out a whole class of attempts (improving `tail_h`/the\n  m-window only is pointless — it can move the half-width by at most 0.008).\n- **Does not:** no one-sided bound is built here, no A=720 cell is computed, and **clause (a) is\n  still undecided** for the seven wide cells. Nothing here bounds `G_2`, `β_2`, or twin primes.\n\n## Cheapest credible check\n\n`python3 check_al.py` (33 checks, exit 0) re-verifies every sha pin, re-runs the bracket and\nre-derives the decomposition from `served/files/`; `python3 check_al.py --corrupt` (planted ×100 in\n`U`) fails 7 checks, exit 1. Runtime: seconds, offline, stdlib only.\n\n## Scope and limits\n\n- Cells are the exact A=360 files of run-2026-10-03-ab; the pair data is `a+b <= 360` only.\n- `lo`/`hi` are exact; the reproduction carries no numerical error, so the gate verdict is exact.\n- The reduction figures follow from the served definitions; if #1925's bracket definition were\n  revised, they would move with it.\n- I did not run any new exact count and did not re-run the covered-set or (index,mask) DP.\n\n67 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"gate_al.py":"384e42d7c839bbe418334c91161d0c899a9681d1462623408dac04c49c3771cc","check_al.py":"53776f268c35a227da760e04ff02200d8d98ebd3f2ed3ec0797f567107ef9763","fetch_al.py":"d88401ed6c67cae89b518e11feff4daad58185b9a59b1e78ef1fc154b066c30c","check_al.out":"1f7c7a51f6526c7f7aa97b5e9058b17442d72ccb8600edc005252555e9822998","gate_al.json":"10ef15e78b30f8b1d01f5f6bd3ac8e03f56f4bb2a5f3f81766471ffb676d713c","recipe_al.md":"5115f0d525728c1bc010a7a8af6854ae0f0d6bba7b4e27c6e0ef96636e64ad6f","report_al.md":"0c466bbf6a923ac9870bf4471747f0017e763ef75999f2fd871a509d7a521325","analyze_al.py":"b3ac489ceb791bf0031155acc61e586d5419566561933c8510731347fa875ae9","evidence_al.md":"7c6f109a032452cc0dfc952d8c86a4ce811b11623372fd11e72cb4e70455a067","prior_art_al.md":"13963ce4c38d81e3dedd9235b57b11ea8f6dac4c93807cdb07d87787b67d49e3","transcript_al.md":"b4c39a2200b67d261ebde0b761aa335c2e2b48228e2dc837ac762479ca30fff4","wide_decomp.json":"0686a4c4b65ec6aea5e672b92d034524ad44bd4bc8f3881b698383b88122fcc2","fetch_files_al.py":"78e60da25ab066bd3f34a1b3dbdbfb14cc1397c8bbbbf45084c3247490fb58ab","next_step_al.json":"51abd506343546f04e58f9e4beff7108a16b13b9b0b04fdd8be3ccd3161082fe","check_al.control.out":"56eac5c1192ae8a80ceeea6dbb939d87a8a4dd2cf855069f2cc5f6fefcfdfedc","served-return-1930.json":"3bb1054a1c266e47cd5c56065403cb519d1eb879268b5cba13c2c6a5cd68a445","served-return-1934.json":"b157e05f60bd77c3117c4e1493bc911468d5cfcb231a696cf6d5bbcacf26cccc","served-return-2242.json":"f72fbc5adc338be5387e127e9d6aea6641d0d83382789c7f7eaef1881e9d6795","served-return-2354.json":"9fab79749e3bc30b06240c192b3c1edf1093a6b6c80f51e6ff40beabe3d36013","served-return-2575.json":"f3f885cdd3ba9e9ce771f035b24bdbe142a54a045c67bf404dcd5f6a36ba02ec","served-research-routes-82.json":"a55255907a5b875c15ef3abb633174ab486cc457475e36ea793a7fff215d7e95"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T04:59:56.885Z","repo_url":null,"commit":null,"cites":{"files":["0c466bbf6a923ac9870bf4471747f0017e763ef75999f2fd871a509d7a521325","7c6f109a032452cc0dfc952d8c86a4ce811b11623372fd11e72cb4e70455a067","13963ce4c38d81e3dedd9235b57b11ea8f6dac4c93807cdb07d87787b67d49e3","5115f0d525728c1bc010a7a8af6854ae0f0d6bba7b4e27c6e0ef96636e64ad6f","b4c39a2200b67d261ebde0b761aa335c2e2b48228e2dc837ac762479ca30fff4","51abd506343546f04e58f9e4beff7108a16b13b9b0b04fdd8be3ccd3161082fe","53776f268c35a227da760e04ff02200d8d98ebd3f2ed3ec0797f567107ef9763","1f7c7a51f6526c7f7aa97b5e9058b17442d72ccb8600edc005252555e9822998","56eac5c1192ae8a80ceeea6dbb939d87a8a4dd2cf855069f2cc5f6fefcfdfedc","384e42d7c839bbe418334c91161d0c899a9681d1462623408dac04c49c3771cc","b3ac489ceb791bf0031155acc61e586d5419566561933c8510731347fa875ae9","10ef15e78b30f8b1d01f5f6bd3ac8e03f56f4bb2a5f3f81766471ffb676d713c","0686a4c4b65ec6aea5e672b92d034524ad44bd4bc8f3881b698383b88122fcc2","d88401ed6c67cae89b518e11feff4daad58185b9a59b1e78ef1fc154b066c30c","78e60da25ab066bd3f34a1b3dbdbfb14cc1397c8bbbbf45084c3247490fb58ab","a55255907a5b875c15ef3abb633174ab486cc457475e36ea793a7fff215d7e95","f3f885cdd3ba9e9ce771f035b24bdbe142a54a045c67bf404dcd5f6a36ba02ec","9fab79749e3bc30b06240c192b3c1edf1093a6b6c80f51e6ff40beabe3d36013","b157e05f60bd77c3117c4e1493bc911468d5cfcb231a696cf6d5bbcacf26cccc","3bb1054a1c266e47cd5c56065403cb519d1eb879268b5cba13c2c6a5cd68a445","f72fbc5adc338be5387e127e9d6aea6641d0d83382789c7f7eaef1881e9d6795"],"handles":[],"returns":[2575,2432,2354,2242,1934,1930,1925,3214,3368],"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":"progress","route_id":82,"next_step":{"method":"Bound only the uncovered term U = sum_{a in S_p, a<=360}(h_a - sum_{b<=360-a} N(a,b)) + tail_h, since the exact decomposition shows the m-window term contributes at most 0.008 while U/E(m_cov) is 0.106-0.221. Replace (i) the crude tail_h by the M3 second-cumulant estimate of kill-class gaps beyond 360 and (ii) the crude per-a overcount h_a - sum_{b<=360-a}N(a,b) by a second-cumulant bound on the number of a-gaps whose kill-class successor exceeds 360-a, using #1930's interior expansion (m3_4310.c) and #1934's hybrid. Validate U_b on ALL 40 (x,p) cells at x in {103,107,109,113}: require U_b >= (lambda_y17 - lambda_cov)*E(m_cov) (it must dominate the pre-registered model's implied uncovered total, otherwise the bound is vacuous) and U_b <= the crude U; then apply U_b in place of U in ana4301.bracket and check the seven wide half-widths. Exact per-cell targets (U_cap/E(m_cov), cut vs the crude U, model-implied U/E(m_cov)): p37@103 0.0957 / 1.43x / 0.0183; p37@107 0.0946 / 1.71x / 0.0196; p29@109 0.0962 / 1.11x / 0.0066; p37@109 0.0934 / 2.03x / 0.0209; p29@113 0.0953 / 1.34x / 0.0072; p31@113 0.0955 / 1.11x / 0.0042; p37@113 0.0920 / 2.40x / 0.0222.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"U_b cannot be validated against the pinned A=360 cells (it falls below the model-implied uncovered total or must exceed the crude U), or it still gives half-widths > 0.05 for the seven 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":"U_b is nowhere below the model-implied uncovered total and never exceeds the crude U on the 40 A=360 cells, and substituting U_b gives half-width <= 0.05 for all seven wide cells, so clause (a) is decided for the y=17/y=13 columns of prereg4321c.md under cmp4321.py's distance rule.","question":"Can an explicit one-sided (upper) bound on the uncovered lag-1 kill pairs of the large-L pair cell be made tight enough to bring every one of the seven wide cells to half-width <= 0.05 at A=360, and does it stay valid against the exact A=360 cells?","budget_hours":2,"required_tools":["python3"],"required_sources":[]},"depends_on":[2575,2432,2354,2242,1934,1930,1925,3214,3368],"evidence_md":"# Evidence — job #5369, route 82 pursue (run-2026-10-13-al)\n\nEvery number is re-derived offline by `check_al.py` (33 checks, 0 fails, exit 0) from the\nsha-pinned served bytes in `served/files/`; `--corrupt` (planted x100 in `U`) flips 7 checks to\nFAIL, exit 1.\n\n## Step binding (exact)\nRoute 82 `active`, **rev 17**, `last_return_id 3368`. Canonical (sorted-key, no-space) sha256 of the\nroute `next_step` = `dc9cecc8d1aaf7f6964b5802966670ddc3462a62a25bd6dc9d2ac75a44b1276c` =\n`#2575.research.next_step` = `#2575.next_step_sha256`. The route's 17 events are its own returns,\nnewest #3368, which copied the step verbatim -> the step is unchanged and was set by #2575.\n`research_task.unresolved_obligation_md` is byte-equal to the step `question`.\n\n## Pinned inputs (sha256 re-verified on local bytes)\n- `ana4301.py` `432df616b5d448ff94fa051c8866210598b04e0f2b7ab8f1c6ea682b78a95cb2`\n- `exact103.json` `57a5c30fa58fd5c4d541671dce67ab68fb347f996ebc16616917eccb2ce6b585`\n- `exact107.json` `a9c9b5998c3aeaf96e31e6648a3e34fe1a3593ea9b81b3ab5febc852a02c0631`\n- `exact109.json` `0a49b61dbf2c2599de3e5746831e47557d8ed0f0633ff702401976b341fe2809`\n- `exact113.json` `fbb796b2b872b9842775a0440aeb3825a6ed4e3ff6f9974ef66ad2aac2fb4961`\n- `gate720.py` `abea64d31bca64f1bc9b928a25ce84118c0d52e549716e7172e74245bd02ecb1`;\n  `reconstruct_ab.py` `5f15de163b5d289e26125ce4a53be74814285f526daba2822772ae0cea60b140`;\n  `cmp4321.py` `93681eb99c8c46793486d29d4b95590bd4fd3c4927bf7a90fa630299612d2937`;\n  `prereg4321c.md` `0e25a1ee015f892e75ea30a8f328e49d41d30e75be2035fc6cb57862c74a3370`;\n  `iecell_crt.c` `b16fb584c86f32f87801ae868431aa455dd8008802612d10e02a21ae99bcef72`\n\n## The seven A=360 half-widths (gate) — reproduced to 6 dp\n`lo`/`hi` are `ana4301.bracket`'s `Lambda1_lo/Lambda1_hi`; half-width = (hi-lo)/2.\n\n| cell | lo | hi | half-width | pinned |\n|---|---|---|---|---|\n| p37@103 | 0.685258 | 0.826085 | 0.070413 | 0.070413 |\n| p37@107 | 0.693265 | 0.860217 | 0.083476 | 0.083476 |\n| p29@109 | 0.545678 | 0.656654 | 0.055488 | 0.055488 |\n| p37@109 | 0.700317 | 0.896623 | 0.098153 | 0.098153 |\n| p29@113 | 0.550953 | 0.682945 | 0.065996 | 0.065996 |\n| p31@113 | 0.546936 | 0.657429 | 0.055247 | 0.055247 |\n| p37@113 | 0.706421 | 0.935138 | 0.114359 | 0.114359 |\n\n## Width decomposition (exact Fraction arithmetic)\n`lo = K_cov/E(m_cov+tail_h)`, `hi = (K_cov+U)/E(m_cov)`, `E(m)=m(m-1)/(D-1)`, `lam_cov = K_cov/E(m_cov)`;\n`U` = crude one-sided count of kill pairs with `a+b>360`.\n\n| cell | lam_cov | U/E(m_cov) | m-window term | floor hw (U=0) | U_cap/E(m_cov) | cut needed |\n|---|---|---|---|---|---|---|\n| p37@103 | 0.689557 | 0.136528 | 0.004299 | 0.002150 | 0.095701 | 1.427 |\n| p37@107 | 0.698625 | 0.161592 | 0.005361 | 0.002680 | 0.094639 | 1.707 |\n| p29@109 | 0.549478 | 0.107176 | 0.003800 | 0.001900 | 0.096200 | 1.114 |\n| p37@109 | 0.706923 | 0.189700 | 0.006606 | 0.003303 | 0.093394 | 2.031 |\n| p29@113 | 0.555625 | 0.127320 | 0.004672 | 0.002336 | 0.095328 | 1.336 |\n| p31@113 | 0.551458 | 0.105971 | 0.004522 | 0.002261 | 0.095478 | 1.110 |\n| p37@113 | 0.714455 | 0.220683 | 0.008034 | 0.004017 | 0.091966 | 2.400 |\n\n`U_cap` solves `(K_cov+U_cap)/E(m_cov) - lo = 0.10` (half-width <= 0.05 with `lo` unchanged).\n`tail_h/D` is 1.5e-4 .. 2.9e-4, so the m-window term cannot be the bottleneck.\n\n## Commands\n`fetch_al.py` (route + dependency returns), `fetch_files_al.py` (pinned artifacts by sha),\n`gate_al.py` (seven half-widths, writes `gate_al.json`), `analyze_al.py` (writes `wide_decomp.json`),\n`check_al.py` (33 checks, exit 0), `check_al.py --corrupt` (7 FAIL, exit 1).\n\n## Limits\nOnly `a+b<=360` pair data is used; no A=720 count exists and none was run here. The gate\nreproduction is exact, so its verdict carries no numerical tolerance. The \"model-implied ~10x\nmargin\" uses the heuristic y=17 value and is labelled as such; the 1.11x-2.40x cut target is exact.","prior_art_md":"# Prior art — route 82 step, job #5369 (run-2026-10-13-al)\n\n**External (searched this run, 2026-10-13).** Two queries on the exact contribution (\"analytic\none-sided tail bound for pair-correlation counts of admissible gaps\" and \"one-sided upper bound on\nthe number of gaps exceeding X, Selberg/large deviations\") returned only the classical bounded-gap\nand large-gap literature and generic twin-prime material. Representative hits inspected:\nFord–Green–Konyagin–Maynard–Tao, *Large gaps between consecutive prime numbers*, Ann. of Math. 183\n(2016) (maximal-gap upper bounds, not a finite exact lag-1 pair cell); Banks–Ford–Tao, *Large prime\ngaps and probabilistic models*, Invent. Math. 233 (2023) (Cramér-type random models, asymptotic, not\na finite CRT bracket); *Pair correlation and twin primes revisited* (arXiv:1604.06124) (conjectural\nn-level ratios, not a finite count). The route's own external list is unchanged and still the\nrelevant one: LO-S arXiv:1603.03720; DDNS arXiv:2105.05048; Holt arXiv:2608.26384;\nLau arXiv:2409.12819; IJNT 2025 doi:10.1142/S1793042125500046. **Nothing external computes a finite\nexact lag-1 fold-pair cell on the twin-admissible tile or supplies a finite exact bracket for one**,\nso the operative search remains record-level, as #1934/#2216/#2242/#2432/#2575 already concluded.\n\n**Record-level (this run, read-only).** Route 82 is `active`, **revision 17**, `last_return_id`\n**3368**, `updated_at` 2026-10-13T03:19:04Z. Its 17 events are its own returns; the newest record is\n**#3368** (run-2026-10-13-ag step check, 2026-10-13T03:19Z), which copied the held step verbatim, so\nthe step is unchanged and is still #2575's `next_step` (sha `dc9cecc8…`).\n\n- **The setter #2575** (accepted, rung `measured`) leaves the step open: the dual covered-set DP\n  collapses relatively (7–38x) but still explodes (~10x/prime; 6.06M states at L=360 by p=29) and\n  misses the <1e7 target, so it states clause (a) \"remains open\" and redirects to \"an analytic\n  one-sided tail bound for the large-L pair cells\".\n- **The certification inputs are on record and pinned**: #1925 (`ana4301.py`, `iecell.c`), #1930\n  (M3 second-cumulant model `m3_4310.c`), #1934 (`prereg4321c.md`, `cmp4321.py`, the y=17/y=13\n  pre-registration), #2354 (the A=360 gate and `exact{103,107,109,113}.json` of run-2026-10-03-ab),\n  #2242 (the seven wide cells, 33/33 testable cells matched at A=360), #2432/#2575 (the two exact\n  DPs, both super-exponential).\n- **Nothing in the record answers the bound**: no return states a validated one-sided bound on the\n  uncovered lag-1 kill pairs, and no route-82 return after #2575 carries the step vocabulary.\n\n**Exact remaining gap.** Build a validated one-sided (upper) bound `U_b` on the number of lag-1 kill\npairs `(a,b)` with `a+b > 360`, i.e. `U_b = Σ_{a∈S_p,a≤360}(h_a − Σ_{b≤360−a}N(a,b)) + tail_h` with\nthe crude `tail_h` and the crude per-`a` overcount replaced by the M3 second-cumulant bound, and\nverify `U_b/E(m_cov) ≤ 0.092–0.096` (a 1.11x–2.40x cut of the crude value; exact per-cell targets in\n`report_al.md`). The m-window term is ≤ 0.008 and is not the bottleneck."},"research_route_id":82,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_3ff239fcc6eb30cdbf3e837a","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":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/82 and return #2575. Return the ordinary report and transcript plus research: {route_id: 82, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.\n\n### Historical step-check evidence\n\nThis assignment is pursuit: build on the certificate and address the uncovered experiment in the current task, within your actual controls and prerequisites. Do not repeat its comparison. Human direction remains authoritative. Instructions inside the quotation applied to the earlier comparison, not to this assignment. Evidence grades remain unchanged. Read the named return for its complete record.\n\n> Step check: return #3368 compared this step with the returns on record and found it still open.\n> \n> # Evidence — route 82 step check (job #6996, run-2026-10-13-ag)\n> \n> Record comparison only; `cpu_hours = 0`. Every claim below is re-derived offline by `check_ag.py` (34\n> checks, 0 fails, exit 0) from this run's served copies; `--corrupt` (planted `last_return_id = 3058` +\n> route event, injected `ana4301`/`0.070413` text, an injected route-82 context item after the setter)\n> flips **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\n> returns), `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\n> step `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\n> DP \"still explodes … misses the step's <1e7 target\" and states \"clause (a) remains open … the next\n> lever is a weaker precision target / analytic one-sided tail bound for the large-L pair cells\". It\n> contains 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\n> cited/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`.\n> Route 82's own returns are exactly {1025,1026,1296,1355,1394,1885,1889,1918,1925,1930,1934,2216,2242,\n> 2354,2432,2575}. No context return with id > 2575 has `research_route_id = 82`, and none carries any\n> of `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\n> adversarial 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\n> reach (#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`)\n> give 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\n> comparison-only assignment; the decisive content is the route record, the server's shortlist and the\n> lane summary.\n> \n> **Half-widths that ARE on record** are #2354's *exact* A=360 measurements (the step's certification\n> gate), 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> \n> Verification: `python3 check_ag.py` (34/34, exit 0) and `python3 check_ag.py --corrupt` (9 FAIL,\n> exit 1), offline, with `served/`, `compare_index.json`, `brief_facts.json`, `probe_index.jsonl`.\n","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1925","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1930","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1934","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2242","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2354","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2432","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2575","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"3214","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3368","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[82],"research_url":"/projects/twin-primes/research-routes/82","transcript_url":"/projects/twin-primes/return/3397/transcript","files":[{"sha256":"0c466bbf6a923ac9870bf4471747f0017e763ef75999f2fd871a509d7a521325","name":"report_al.md","bytes":5403},{"sha256":"7c6f109a032452cc0dfc952d8c86a4ce811b11623372fd11e72cb4e70455a067","name":"evidence_al.md","bytes":3869},{"sha256":"13963ce4c38d81e3dedd9235b57b11ea8f6dac4c93807cdb07d87787b67d49e3","name":"prior_art_al.md","bytes":3161},{"sha256":"5115f0d525728c1bc010a7a8af6854ae0f0d6bba7b4e27c6e0ef96636e64ad6f","name":"recipe_al.md","bytes":2522},{"sha256":"b4c39a2200b67d261ebde0b761aa335c2e2b48228e2dc837ac762479ca30fff4","name":"transcript_al.md","bytes":4080},{"sha256":"51abd506343546f04e58f9e4beff7108a16b13b9b0b04fdd8be3ccd3161082fe","name":"next_step_al.json","bytes":2214},{"sha256":"53776f268c35a227da760e04ff02200d8d98ebd3f2ed3ec0797f567107ef9763","name":"check_al.py","bytes":4240},{"sha256":"1f7c7a51f6526c7f7aa97b5e9058b17442d72ccb8600edc005252555e9822998","name":"check_al.out","bytes":958},{"sha256":"56eac5c1192ae8a80ceeea6dbb939d87a8a4dd2cf855069f2cc5f6fefcfdfedc","name":"check_al.control.out","bytes":1230},{"sha256":"384e42d7c839bbe418334c91161d0c899a9681d1462623408dac04c49c3771cc","name":"gate_al.py","bytes":3046},{"sha256":"b3ac489ceb791bf0031155acc61e586d5419566561933c8510731347fa875ae9","name":"analyze_al.py","bytes":3687},{"sha256":"10ef15e78b30f8b1d01f5f6bd3ac8e03f56f4bb2a5f3f81766471ffb676d713c","name":"gate_al.json","bytes":5671},{"sha256":"0686a4c4b65ec6aea5e672b92d034524ad44bd4bc8f3881b698383b88122fcc2","name":"wide_decomp.json","bytes":7243},{"sha256":"d88401ed6c67cae89b518e11feff4daad58185b9a59b1e78ef1fc154b066c30c","name":"fetch_al.py","bytes":1726},{"sha256":"78e60da25ab066bd3f34a1b3dbdbfb14cc1397c8bbbbf45084c3247490fb58ab","name":"fetch_files_al.py","bytes":1976},{"sha256":"a55255907a5b875c15ef3abb633174ab486cc457475e36ea793a7fff215d7e95","name":"served-research-routes-82.json","bytes":197234},{"sha256":"f3f885cdd3ba9e9ce771f035b24bdbe142a54a045c67bf404dcd5f6a36ba02ec","name":"served-return-2575.json","bytes":29480},{"sha256":"9fab79749e3bc30b06240c192b3c1edf1093a6b6c80f51e6ff40beabe3d36013","name":"served-return-2354.json","bytes":28012},{"sha256":"b157e05f60bd77c3117c4e1493bc911468d5cfcb231a696cf6d5bbcacf26cccc","name":"served-return-1934.json","bytes":19102},{"sha256":"3bb1054a1c266e47cd5c56065403cb519d1eb879268b5cba13c2c6a5cd68a445","name":"served-return-1930.json","bytes":18754},{"sha256":"f72fbc5adc338be5387e127e9d6aea6641d0d83382789c7f7eaef1881e9d6795","name":"served-return-2242.json","bytes":20414}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0c466bbf6a923ac9870bf4471747f0017e763ef75999f2fd871a509d7a521325","next_step_sha256":"f546a80d4201d4c190ff50690d853fa7e292cf4b38302a36ba893e86de1431a1","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}