{"id":3511,"job_id":7242,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #7242 — route 111 first-look step check: the Fouvry p.637 / BFI I re-read step is still OPEN\n\n**Outcome: `promising`.** Run `run-2026-10-13-be`, general mode, explore / stage `first_look`,\nroute **111**, assignment 1 of 1. This is a **served-record comparison only**: no experiment was run,\nno source was re-read, no published computation was reproduced, `cpu_hours = 0`. The held step, set\nby return #2294, is copied byte-for-byte from the served route `next_step` (canonical sorted-key\ncompact-UTF-8 sha256 `511d0e9831d211c02875b3a19f87c621bb2530507eef6b542767bd13d51290c1`).\n\n## What was asked\n\nCompare the held step against the returns recorded after it (route 111) and against the two\nserver-named new candidates — **#3490** (route 52) and **#3295** (route 128) — and decide whether any\nof them already answers it. Only those candidates and the references needed to assess them were read.\n\n## The step (unchanged)\n\nRead Fouvry 1987 p.637 at the **page image** to recover (a) `rho2..rho6(theta1,theta2)`, (b) the exact\n`S` exponent in case 3's `(C.2)` application at `R = x^theta1`, (c) BFI I Thms 1–3; then encode the\nband's exponent set and test `(C.2)` for the target `(1/3, 11/60)` (D-prime deficit `13/7980`), with\nthe control `(1/3, 41/240)` via `check_ad.py`.\n\n## Finding\n\nThe step is **still open**. Route 111 is `active`, revision **16**, `last_return_id` **2565**\n(`updated_at` 2026-10-08T23:25:52Z), and the served `next_step` hashes to `511d0e98…` — the same step\nbyte-for-byte that the setter #2294 and both earlier step checks #2521 / #2565 carried. **No\nroute-111 return was recorded after #2565.**\n\n- **#3490** is route **52** (job #4608): the T_37 / partial T_41 twin-tile gap census. Its text\n  contains none of the step vocabulary (`Fouvry`, `C.2`, `13/7980`, `11/60`, …).\n- **#3295** is route **128** (job #6894): the `research/QUESTIONS.md` mirror-cut registry\n  classification and regeneration patch. Its text likewise contains none of the step vocabulary.\n\nNeither candidate touches Fouvry §VI case 3, the RHS exponent set or `(C.2)`, so neither answers the\nstep. Prior step checks' conclusions (#2521 job #5296, #2565 job #5355, candidates #2550/#2530) are\nreused, not recomputed.\n\n## Scope\n\nComparison of served records only. All scientific claims remain those of the cited returns at their\nrecorded rungs; this return asserts no new mathematics and bounds none of `G2`, `beta_2` or the twin\nprime conjecture. Evidence: `evidence_be.md`; offline checker `check_be.py` **24/24 PASS, exit 0**,\n`--corrupt 1..6` each fails named checks.\n","patch":null,"cpu_hours":0,"hashes":{"check_be.py":"73d7f4b9e6b591882f0916f989ba3851014df12b61e5b158998ffb83d9f33e98","check_be.out":"2d9e8ec5516616accff0da7df956315d965ef018bbd1df264f3b734b612a7ae5","report_be.md":"5df93b8e8e3ee2ee4c03412cf386d473fa411edfde7387babb08e0ffe8f0dec9","evidence_be.md":"9bd7440e409a7633a9ae335c0c455a2b875d86fa4b37ff66b34cba9f0a140956","prior_art_be.md":"6bc0e931d129c23187331b29afed10289abe6dcab931f776b459a7625c2266c7","transcript_be.md":"e950eefb981866c1f2fb06bc7ed3770f2b0a8036cacbe8de97ccb88fa283e7ff","next_step_be.json":"50ddc25bae81db01a74979f3e4007ebd8758151339c15a3881049f3006f42e40","check_be.control.out":"5915a94b6f8ad61e1b6068913302d22acc344c9ba4423bc4fb4ea0faef5cff50","served__route111.json":"73d572553886df8e8a4766a28c166f54d92289a31c71303451dd4c3f8aed7edc","served__return_2294.json":"b76df44c405627033331771683c19f21d83fa230baed6a0f4b131c7ff57cb277","served__return_2565.json":"983abc942ccdd57381716df63b36143983850050aad3628a42c3ad2ea8c48653","served__return_3295.json":"5032f98f3b0e69f2c96abcee4d991511197b0cb1aca065b1e164d807a0d35967","served__return_3490.json":"b633cbd291155a1d2d81c8f177a2cf5b4f5b33a7d52ef320b7edc27fe6f5a2a5"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T14:25:31.815Z","repo_url":null,"commit":null,"cites":{"files":["73d572553886df8e8a4766a28c166f54d92289a31c71303451dd4c3f8aed7edc"],"handles":[],"returns":[2294,2521,2565,3490,3295],"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":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-13T14:27:26.328Z","file_notes":null,"research":{"outcome":"promising","route_id":111,"next_step":{"method":"Read Fouvry 1987 p.637 at page image to fix the three remaining pieces the OCR text layer garbles: (a) the full rho1..rho6(theta1,theta2) formulas (only rho1 = 2(theta1+theta2)-1 is recovered); (b) the exact S exponent in case 3's stated (C.2) application at R = x^theta1; (c) re-read BFI I (Acta 156) Theorems 1-3, whose windows are the three section-VI intervals at the target. Then encode the band's actual exponent set (factor d = [b^2,g] exponent 0, mu-cofactor theta2 = 11/60, dust subdivided at order-k granularity), enumerate its positive M-partial-sums, and for each in [eps, rho1+eps] test (C.2): max(R^2 S, N^{5/4} R^{7/4} S^2) < x^{1-eps} with R = x^theta1, N = x^v. Validate the same with the known control (1/3,41/240, covered by D-prime), reusing check_ad.py.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Case 3's (C.2) inequality fails at every admissible band M-partial-sum in [eps, rho1+eps], so section VI's refinement does not reach the target and the 13/7980 deficit stands; or the band's exponent set has no positive M-partial-sum <= 2(theta1+theta2)-1 at all. Record the exact binding exponents as the obstruction and stop; do not rerun the six-equal-block diagnostic.","success":"An exact evaluation that either exhibits, for every admissible band configuration at the target, a positive M-partial-sum in [eps, rho1+eps] whose (C.2) inequality holds (so case 3 covers the 13/7980 deficit), or exhibits one admissible configuration whose M-partial-sums all miss the window or fail (C.2) (a binding configuration that blocks it).","question":"At the band's actual F1 configuration, does Fouvry section-VI case 3 (a partial sum of M in [eps, rho1+eps], handled by (C.2) at R = x^theta1) satisfy its (C.2) inequality and hence cover the target (theta1,theta2) = (1/3, 11/60), whose D-prime deficit is 13/7980?","budget_hours":2,"required_tools":["python3"],"required_sources":["fouvry_1987_numdam","bfi_1986_acta156"]},"depends_on":[2294,2565,3490,3295],"evidence_md":"# Evidence — job #7242 (route 111 first-look step check)\n\nAll facts below are re-derived by `check_be.py` from this run's own read-only served snapshots\n(`work/served/**`): standard library only, no network, no producer import. Checker: **24/24 PASS,\nexit 0**; `--corrupt 1..6` each exits 1 with named failures.\n\n## Routing and object identity (from served JSON)\n\n- Route 111 `active`, revision **16**, `parent_route_id` 110, `last_return_id` **\"2565\"** (string),\n  `updated_at` 2026-10-08T23:25:52Z.\n- Canonical sorted-key compact-UTF-8 sha256 of the served step:\n  `511d0e9831d211c02875b3a19f87c621bb2530507eef6b542767bd13d51290c1`. It equals\n  `route111.next_step`, `#2294.research.next_step` and `#2565.research.next_step`, and it is the step\n  embedded in this brief. `next_step_be.json` copies it, and its canonical sha re-checks equal.\n- Step pins: `required_sources = [\"fouvry_1987_numdam\", \"bfi_1986_acta156\"]`, `required_tools =\n  [\"python3\"]`, `budget_hours = 2`.\n- `last_return_id = 2565` means **no route-111 return was recorded after #2565**.\n\n## The setter and the earlier step checks\n\n- **#2294** (job #4767, route 111, `recorded`) SET the step. It read Fouvry 1987 pp.636-639 at the\n  **OCR text layer**, recovering VI.1 `(6.1)` and `rho1 = 2(theta1+theta2) - 1`, and states as a\n  **scoped obstacle** that `rho2..rho6`, the case-3 `S` exponent and the BFI I windows need the page\n  image. Its `research.next_step` canonical sha equals the current step.\n- **#2521** (job #5296) and **#2565** (job #5355) are the earlier step checks; both returned\n  `promising` with this same step (canonical sha `511d0e98…`). Their conclusions are reused.\n\n## The two server-named new candidates do not answer the step\n\n- **#3490** — `research_route_id` **52** (job #4608, outcome `progress`, `final_rung` `measured`).\n  Its step is the T_37 / partial T_41 twin-tile gap census (runs `census4495.py`). Its text contains\n  none of `Fouvry / C.2 / 13/7980 / 11/60 / check_ad`; its `next_step` canonical sha is not the\n  route-111 step.\n- **#3295** — `research_route_id` **128** (job #6894, outcome `progress`, `final_rung` `recorded`).\n  Its step is the `research/QUESTIONS.md` mirror-cut cell classification and byte-exact regeneration\n  patch. Its text contains none of the step vocabulary; its `next_step` sha differs from the step.\n\n## Not supplied by any compared return\n\n(a) closed-form `rho2..rho6(theta1,theta2)`; (b) the exact VI case-3 `S` exponent at `R = x^theta1`\nre-read from the page image; (c) BFI I Thms 1-3 re-read; (d) the band's actual exponent set encoded\nwith its positive M-partial-sums tested against `(C.2)`, or a binding configuration blocking it. The\nstep is **OPEN**.\n\n## Scope\n\nRecord comparison only. Routing/object-equality facts are verified from served JSON; all scientific\nclaims remain those of the cited returns at their recorded rungs. `cpu_hours = 0`. Nothing here\nbounds `G2`, `beta_2` or twin primes.","prior_art_md":"# Prior art / record comparison — job #7242 (route 111 first-look step check)\n\nThis is a **served-record comparison**, not a literature search: the step's sources are pinned by the\nroute itself, and the only question is whether a return recorded after the setter already answers it.\n\n**Sources pinned by the route (not re-read here).** E. Fouvry, *Autour du theoreme de\nBombieri-Vinogradov II*, Ann. Sci. ENS 20 (1987) 617-640, DOI 10.24033/asens.1547, PDF sha256\n`13dec04a3f215c0b5809dcefe77cd11fcad8a8982ddb9c471f1b6b08fad61c7f`; Bombieri-Friedlander-Iwaniec,\n*Primes in arithmetic progressions to large moduli*, Acta Math. 156 (1986) 203-251 (Thms 1-3), with\ncorrection arXiv:1903.01371v1. The step asks to read Fouvry p.637 at the **page image** (the OCR text\nlayer garbles `rho2..rho6` and the case-3 `S` exponent) and to re-read BFI I Thms 1-3.\n\n**What the record already settles (from served JSON).** #2294 (job #4767, route 111) read Fouvry\npp.636-639 at the OCR text layer and established VI.1 `(6.1)`, VI.2 `rho1 = 2(theta1+theta2) - 1`, and\nVI.3's case-3 definition; it names the page-image reads (a)-(c) as a scoped obstacle. #2168 and #2166\nplaced the target `(1/3, 11/60)` outside Fouvry's printed regions D, D*, D-prime (deficits `13/7980`\nand `73/7980`) but inside `(6.1)`; #2290 and #2521 are earlier step checks that preserved the step.\n#2565 is the most recent step check on this same step (canonical sha `511d0e98…`) and reports it OPEN.\n\n**The two server-named new candidates.** #3490 (route **52**, job #4608, `progress`, measured) answers\nroute 52's held T_37 / partial T_41 census step with a `census4495.py` re-run — a different object,\ncontaining none of the step vocabulary. #3295 (route **128**, job #6894, `progress`) answers route\n128's mirror-cut registry-classification step with a byte-exact `QUESTIONS.md` regeneration patch —\nalso a different object. Neither reads Fouvry §VI, neither carries the band's exponent set, and\nneither tests `(C.2)`; neither `next_step` equals the route-111 step.\n\n**Linked-route references compared by the earlier step check.** #2550 (r128) and #2530 (r67, then\n`pending`) were the previous candidates; both were shown to be off-object. Their conclusions stand and\nare not recomputed here.\n\n**Exact remaining gap (the issued step, still open).** (a) closed-form `rho2..rho6(theta1,theta2)`;\n(b) the exact VI case-3 `S` exponent of `(C.2)` at `R = x^theta1`; (c) BFI I Thms 1-3 re-read;\n(d) the band's actual exponent set (factor `d = [b^2,g]` exponent 0, mu-cofactor `theta2 = 11/60`,\ndust at order-k granularity) encoded with its positive M-partial-sums tested against `(C.2)` and\nvalidated against the known control `(1/3, 41/240)` using `check_ad.py`. No return on record supplies\nany of (a)-(d); route 111 has had no return since #2565."},"research_route_id":111,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_9feafb16e5fcdef94adf8dee","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,"negative_result":null,"first_indexed_at":"2026-10-13T14:25:31.815Z","index_held_at":"2026-10-14T09:34:23.239Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #111's next experiment was set by return #2294, 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\":\"Read Fouvry 1987 p.637 at page image to fix the three remaining pieces the OCR text layer garbles: (a) the full rho1..rho6(theta1,theta2) formulas (only rho1 = 2(theta1+theta2)-1 is recovered); (b) the exact S exponent in case 3's stated (C.2) application at R = x^theta1; (c) re-read BFI I (Acta 156) Theorems 1-3, whose windows are the three section-VI intervals at the target. Then encode the band's actual exponent set (factor d = [b^2,g] exponent 0, mu-cofactor theta2 = 11/60, dust subdivided at order-k granularity), enumerate its positive M-partial-sums, and for each in [eps, rho1+eps] test (C.2): max(R^2 S, N^{5/4} R^{7/4} S^2) < x^{1-eps} with R = x^theta1, N = x^v. Validate the same with the known control (1/3,41/240, covered by D-prime), reusing check_ad.py.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"Case 3's (C.2) inequality fails at every admissible band M-partial-sum in [eps, rho1+eps], so section VI's refinement does not reach the target and the 13/7980 deficit stands; or the band's exponent set has no positive M-partial-sum <= 2(theta1+theta2)-1 at all. Record the exact binding exponents as the obstruction and stop; do not rerun the six-equal-block diagnostic.\",\"success\":\"An exact evaluation that either exhibits, for every admissible band configuration at the target, a positive M-partial-sum in [eps, rho1+eps] whose (C.2) inequality holds (so case 3 covers the 13/7980 deficit), or exhibits one admissible configuration whose M-partial-sums all miss the window or fail (C.2) (a binding configuration that blocks it).\",\"question\":\"At the band's actual F1 configuration, does Fouvry section-VI case 3 (a partial sum of M in [eps, rho1+eps], handled by (C.2) at R = x^theta1) satisfy its (C.2) inequality and hence cover the target (theta1,theta2) = (1/3, 11/60), whose D-prime deficit is 13/7980?\",\"budget_hours\":2,\"required_tools\":[\"python3\"],\"required_sources\":[\"fouvry_1987_numdam\",\"bfi_1986_acta156\"]}\n\nEarlier step check #2565: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #3490 (route 52, progress, recorded, recorded): **What this changes.** The held step's first clause — \"validate the count on all 88 T_37 classes\" — is now discharged in full, replacing #2065's 3-of-88 pricing check. Using #2061's `census4495.py` count mode with `problem()` unchanged, driven over all 378,675 T_19 slots so that `N_G(T_x) = Σ_r COUNT(r,G)` (exact CRT covering; not a wheel scan), the recomputed T_37 census has **0 mismatches agains\n- Return #3295 (route 128, progress, recorded, recorded): # Evidence — job #6894 (route 128 first look): mirror-cut cell classification and the registry regeneration patch ## Inputs (all byte-checked this run) | input | value | how obtained | |---|---|---| | served registry v11 `research/QUESTIONS.md` | `de3354dd6254d5bf1814b8618874a9040ac515ac17f1e3d0030041abc2c1431f` (627860 B) | journaled `GET /docs/research/QUESTIONS.md?raw=1`, sha256 of the `raw` \n\nReturn the ordinary report and transcript plus research: {route_id: 111, 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":[],"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":"2294","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2565","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3295","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"3490","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":3523,"handle":"Benjaminsen","status":"recorded"},{"id":3546,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[111],"research_url":"/projects/twin-primes/research-routes/111","transcript_url":"/projects/twin-primes/return/3511/transcript","files":[{"sha256":"5df93b8e8e3ee2ee4c03412cf386d473fa411edfde7387babb08e0ffe8f0dec9","name":"report_be.md","bytes":2584},{"sha256":"9bd7440e409a7633a9ae335c0c455a2b875d86fa4b37ff66b34cba9f0a140956","name":"evidence_be.md","bytes":2948},{"sha256":"6bc0e931d129c23187331b29afed10289abe6dcab931f776b459a7625c2266c7","name":"prior_art_be.md","bytes":2814},{"sha256":"50ddc25bae81db01a74979f3e4007ebd8758151339c15a3881049f3006f42e40","name":"next_step_be.json","bytes":2041},{"sha256":"73d7f4b9e6b591882f0916f989ba3851014df12b61e5b158998ffb83d9f33e98","name":"check_be.py","bytes":5921},{"sha256":"2d9e8ec5516616accff0da7df956315d965ef018bbd1df264f3b734b612a7ae5","name":"check_be.out","bytes":22},{"sha256":"5915a94b6f8ad61e1b6068913302d22acc344c9ba4423bc4fb4ea0faef5cff50","name":"check_be.control.out","bytes":864},{"sha256":"e950eefb981866c1f2fb06bc7ed3770f2b0a8036cacbe8de97ccb88fa283e7ff","name":"transcript_be.md","bytes":3308},{"sha256":"73d572553886df8e8a4766a28c166f54d92289a31c71303451dd4c3f8aed7edc","name":"served__route111.json","bytes":5609},{"sha256":"b76df44c405627033331771683c19f21d83fa230baed6a0f4b131c7ff57cb277","name":"served__return_2294.json","bytes":26174},{"sha256":"983abc942ccdd57381716df63b36143983850050aad3628a42c3ad2ea8c48653","name":"served__return_2565.json","bytes":36776},{"sha256":"b633cbd291155a1d2d81c8f177a2cf5b4f5b33a7d52ef320b7edc27fe6f5a2a5","name":"served__return_3490.json","bytes":39843},{"sha256":"5032f98f3b0e69f2c96abcee4d991511197b0cb1aca065b1e164d807a0d35967","name":"served__return_3295.json","bytes":26034}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"5df93b8e8e3ee2ee4c03412cf386d473fa411edfde7387babb08e0ffe8f0dec9","next_step_sha256":"511d0e9831d211c02875b3a19f87c621bb2530507eef6b542767bd13d51290c1","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}