{"id":2565,"job_id":5355,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5355, route 111 first look (step check): the Fouvry p.637 / BFI I re-read step is still open\n\n**Run:** `run-2026-10-08-fm`. **Job #5355**, type `explore`, stage `first_look`, route **111**, general mode,\nassignment 1 of 1. **Outcome: `promising`** — the held step, set by return #2294, is still open; it is\ncopied byte-for-byte from the served route `next_step` (`next_step.json`; canonical sorted-key compact\nUTF-8 sha256 `511d0e9831d211c02875b3a19f87c621bb2530507eef6b542767bd13d51290c1`).\n\nThis is a **served-record comparison only**. No experiment was run, no source was re-read, and no\npublished computation was reproduced (`cpu_hours = 0`). Nothing here bounds `G2`, `beta_2` or twin\nprimes; all scientific claims remain those of the cited returns at their recorded rungs.\n\n## Step identity\n\nServed route 111 is `active`, revision **15**, `last_return_id` **2521**, `parent_route_id` 110. Its\n`next_step`, return #2294's `research.next_step`, return #2521's `research.next_step` and the step\nembedded in this brief are the **same object** (canonical sha\n`511d0e9831d211c02875b3a19f87c621bb2530507eef6b542767bd13d51290c1`). Route-111 events (newest first)\nare `2521, 2294, 2290, 2168, 2166, 2161, 2156, 2084, 2046, 1982, 1818, 1418, 1414, 1351, 1340`: no\nroute-111 return exists after #2521.\n\nThe step (set by **#2294**, job #4767, route 111, outcome `progress`) is: read Fouvry 1987 p.637 at the\n**page image** to fix (a) the full `rho1..rho6(theta1,theta2)` formulas, (b) the exact `S` exponent in\nsection-VI case 3's `(C.2)` application at `R = x^theta1`, (c) re-read BFI I (Acta 156) Theorems 1-3;\nthen encode the band's actual exponent set (factor `d = [b^2,g]` exponent 0, mu-cofactor\n`theta2 = 11/60`, dust at order-k granularity), enumerate its positive M-partial-sums, and test `(C.2)`\nat each in `[eps, rho1+eps]`, validating against the known control `(1/3, 41/240)` with `check_ad.py`.\nPinned sources: `fouvry_1987_numdam`, `bfi_1986_acta156`; tool `python3`; budget 2 h.\n\n## Why the step is still open\n\n**Earlier step check #2521 (job #5296, reused).** #2521 already compared the record against this step\nand reported `promising` with the step copied exactly: the four pieces required by the step — the\nclosed-form `rho2..rho6` map, the exact VI case-3 `S` exponent at `R = x^theta1` re-read from the page\nimage, the BFI I Thms 1-3 re-read, and the band's encoded exponent set tested against `(C.2)` — are\nsupplied by **no** recorded return. #2294 read pp.636-639 only at the **OCR text layer** and recovered\n`rho1 = 2(theta1+theta2)-1` and the case-3 heading, leaving exactly those pieces unresolved (its own\nstated scoped obstacle). Its check `check_ad.py` (15/15) proves region membership and the `rho1`\nidentity, not the case-3 `(C.2)` input.\n\n**The two new candidates do not answer it.**\n\n- **Return #2550** (route **128**, job #5155, outcome `progress`, recorded, final_rung `recorded`).\n  It is the route-128 mirror-drift step check: it answers whether route 128's **12 serving revisions**\n  are `status: accepted` and whether the 12-cell classification survives a fresh generation — \"Leg (a)\n  passes\". It carries route 128's own step, and its report/evidence contains **none** of route 111's\n  step vocabulary (`Fouvry`, `rho2..rho6`, `p.637`, `C.2`, `M-partial`, `13/7980`, `11/60`, `check_ad`).\n- **Return #2530** (route **67**, job #5115, outcome `result`, status **`pending`**, no `final_rung`).\n  It is a two-reading comparison at T29/T31 for route 67's loose census. It is not accepted/verified,\n  carries route 67's own step, and likewise contains none of route 111's step vocabulary.\n\n**Bounded window probe (returns 2522..2564, the record after #2521).** 42 return ids probed read-only\n(`probe_index.jsonl`); the only non-present ids are 2524 and 2565. **Zero** rows are on route 111 and\n**zero** rows carry route 111's step. The only token-bearing rows are other routes' objects and\nstep-checks that merely *name* `2294`/`2521` in their compared-returns lists — e.g. #2535 (route 128,\nits own mirror-drift step), #2529 (route 224, lag-1 statistic), #2541 (route 225, lag budget), and the\nsibling step checks #2555 (r196), #2557 (r189), #2558 (r42), #2561 (r15). An unchanged-step comparison\non another route is not new evidence.\n\n**Linked-route comparators (named in the brief).** #2421 (r128), #2399 (r67), #2309 (r67), #2308\n(r128), #2304/#2305 (unchanged-step comparisons naming `511d0e98…` as route 111's step), #2335 (r52,\nexplicitly a different exponent-window object), #2379 (r45, BFI I/II, no route-111 mention) all carry\ntheir own steps; none equals the route-111 step, and none supplies (a)-(c).\n\n## Scope and unresolved obligations\n\nThis is a **record comparison, not a global literature-absence claim** and not a theorem claim. Rungs:\nrouting and object-equality facts are **verified** from served JSON; the required source re-read is\n**not** performed here. Obligations still open (unchanged from the step): the page-image read of Fouvry\np.637, the BFI I Thms 1-3 windows, the band's encoded exponent set and its `(C.2)` test, and the\ndivisor-restricted BFI II lemma the route's contribution rests on (the decisive unproved assumption).\nThe step is handed on unchanged; the held pursuit goes out with this note.\n\nChecker `check_fm.py` (stdlib, offline, no producer import, no network; reads only this run's\n`work/served/**`, `probe_index.jsonl`, `next_step.json`, `brief_md.txt`): **49/49 PASS, exit 0**;\n`--corrupt` (4 planted mutations) **exit 1, 12 failures**. `depends_on`: 2294, 2521, 2550, 2530, 2290,\n2168, 2166.\n\n48 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_fm.py":"66d3f8211d32673049778bbb64cb40239dca80f045b08584cc14bc4cde8040c4","fetch_fm.py":"6e852eeb13246cdc8c8e9007ac2c3be12eda337304134b277bfa3a12413e7612","probe_fm.py":"aa3c78f977aac20db2909a13b7285e15ab98357d7f0c031e8da51194f97ee070","check_fm.out":"ac23e0b3de9cfd2d12f492e0948f8ab6137c3608c2a50516ddcc1a67ef9830dc","recipe_fm.md":"bdce6ddb3d35c4d382affd59a53aab066850ef74bd98662b53b2b2c14cff3796","redact_fm.py":"6743db60114d2d06c5f6e7d5895ac044db3cfb13983c4bc12add5389b00adb3e","report_fm.md":"b04ce93404a939fd5c72974489fb88e64dc2e47c71f5565e2091908644fa4c57","residual.out":"1cdc955d5920e4b9f59a6a08d43256136e6d49b5d0e5cf9b526295dd9c1b19fc","facts_fm.json":"077226d3ca111d8466c8677d4e5f3ea5e5f49cac1e24437f07102be0b7e863e7","evidence_fm.md":"8fe119d032acf7deb2aa361a99aa42d394730d17fb8d5050929a82e7c0f10631","next_step.json":"400330482fd1f03da4ef795a4541f3ae02b6eb9cdb248de38283bde6e8934256","prior_art_fm.md":"173cb088f79fbef59b6581011446093b35d0cae5ec6a8a642f118b21ce2f7a36","probe_index.jsonl":"699052bac059e0c37e01d5c4d1c7c65cdcb4e5e3aea0835f5f58ec874b7707be","served-board.json":"0e8e771e5a8bff8553ebf40c98930ebb1ae43d5756b18d2a3e8e94aa885b437f","check_fm.control.out":"30c96b033ea07f6e7b8c39a9c71baf37c53c8c6c68a8aed172d22f3bfa9d444f","served-route_111.json":"24446817683520ebb5536241455789813006752920bf6a0c79af4ac59047d0c1","served-routes_all.json":"8b93961cfbd13be671c06931da3c2468d7da9b307fb5afd405f7e51d81fc320b","served-return_2166.json":"7a9d544bf43e9d83dcf9c9c70238246eba9857ea392e58b1a875c67b2aadb218","served-return_2168.json":"4040a925ec7b9717a7a78d91c9c86011c948a78f34bc57ba4628ae7367477fbe","served-return_2290.json":"1f9bc995e1735f0c0d1d64659ee1e8d415b9959afecd5664a2ddcf324dce68b0","served-return_2294.json":"eec96455bcbf4216a386ffe6005a5d1ab525ebc88a4b313d0e9f102ad62e7c99","served-return_2304.json":"083b16d8235e5bc429ff473ae05734a5a5f25d2419a03da4740cd9a84d33dc1e","served-return_2305.json":"2f392a72dda206e229ba4ce2311720d7299c4e10ca274c9524564056e4da3fbe","served-return_2308.json":"18197a0e58cdd8027e00868d0983c959af9a6b668413969beec5e814d1408a67","served-return_2309.json":"b58f5da6ffbb9ef28cb56d9cf6f6ba5330d9a8bbce913277aa59f4229076dd89","served-return_2335.json":"1d8cedb796ba615dd555ce83b019c738095ed403e362ade32f0cbb116b90ff9f","served-return_2379.json":"fdbccc4df6752ae4e53774de26171be024dea70d4f31cf2d794bb772d3c8efbe","served-return_2399.json":"31ecbe03c14a0cbc1ffd4363006941d1621465efeeac44d897040efbafc525c7","served-return_2421.json":"d508fb3cd618017df57e818e9fa694f6986605e91fc48407c2ca06ff7149fc2f","served-return_2521.json":"c275f3a3adbf4ddd769c4ce38941614c15f677c323981a5f5ee6c8566e5ef089","served-return_2530.json":"dd316422ad432fffdb40dde23d4750467b2b96abf5ce2b749355aed1a330177c","served-return_2550.json":"9909973a6f96362a6dc2689e9b2cf045e37d13ea816e811b3483e9a6b79f5287","served-protocol-api.json":"0fe6048fad5e73dedcd4fa02ba07f4189590c0fb3399a3e7e526ac41d9db75b5","served-protocol-evidence.json":"d2119899adf2cddfb81e830f52d3807fe0a7e0c0455a34f24ed2ccf5690697ce","served-research-protocol.json":"925c7cd9694d7ee41965f7086fada8f7ab7a9adc6429b42e4f0e039929957e29","served-protocol-framework.json":"e6108ce6a8711d3975d51d1dfbebb9b4383246947feefd1685b0d840820d848d","served-protocol-lifecycle.json":"45c40f1d4937e757128a5d230ceb89354f41f02fdc4ae1b679ae679675304edb","served-protocol-accounting.json":"93cc7304c3f05490afc8055f1e912127670cb00b76b4675db2181e3c846f1008","served-protocol-publication.json":"f2122dc2662f4f00ddb562d4147d35aa6c8b0dfbb6fc586653b07e53cb3b343c","served-protocol-publication_safety.json":"dc444ec3595c39510b4dcb5bceaef907d887a4cc2389f9fb938a9e14342f8387"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-08T23:25:52.096Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2294,2521,2550,2530,2290,2168,2166],"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 #5355 (route 111 first-look step check)\n\n## Reproduce this step check (offline, no network, no producer import)\n\n1. Ensure the served snapshots are present under this run's `work/served/` (fetched read-only by\n   `fetch_fm.py` through the shared tool's journaled client): `route_111.json`, `return_2294.json`,\n   `return_2521.json`, `return_2550.json`, `return_2530.json`, the comparator returns, plus\n   `probe_index.jsonl` (the 2522..2564 window facts, written by `probe_fm.py`), `next_step.json`\n   (byte-for-byte copy of the served route step) and `brief_md.txt` (this job's brief).\n2. Run `python3 check_fm.py` — expect **49/49 PASS, exit 0**. It re-derives: route 111 state/revision/\n   `last_return_id`; the step's canonical sha `511d0e9831…` and its equality across route, #2294,\n   #2521, `next_step.json` and the brief; that #2294 is the setter and #2521 the earlier open step\n   check; that #2550/#2530 are on routes 128/67 and carry none of the step vocabulary; that no probe\n   row is on route 111 or carries the step; and the step's pinned sources/tool/budget.\n3. Run `python3 check_fm.py --corrupt` — expect a non-zero exit with the planted mutations detected\n   (`state=closed`, altered `budget_hours`, a faked step carrier in #2550, a faked route-111 probe\n   row): **exit 1, 12 failures**.\n\n## Run the handed-on step (when the pursuit is spent)\n\nThe step is copied exactly into `next_step.json`. It is a **source-reading plus exact-arithmetic**\ntask, budget 2 h, tool `python3`, pinned sources `fouvry_1987_numdam` and `bfi_1986_acta156`, reusing\n`check_ad.py` (served with return #2294) for the control `(1/3, 41/240)`:\n\n1. Read Fouvry 1987 **p.637 at the page image** (the Numdam PDF, sha256\n   `13dec04a3f215c0b5809dcefe77cd11fcad8a8982ddb9c471f1b6b08fad61c7f`) and transcribe the full\n   `rho1..rho6(theta1,theta2)` formulas and the exact `S` exponent of the case-3 `(C.2)` application at\n   `R = x^theta1`. Re-read BFI I (Acta 156) Thms 1-3 windows (the three section-VI intervals).\n2. Encode the band's actual exponent set (factor `d = [b^2,g]` exponent 0, mu-cofactor\n   `theta2 = 11/60`, dust subdivided at order-k granularity); enumerate its positive M-partial-sums.\n3. For each sum in `[eps, rho1+eps]`, test `max(R^2 S, N^{5/4} R^{7/4} S^2) < x^{1-eps}` with\n   `R = x^theta1`, `N = x^v`; validate the same at the known control `(1/3, 41/240)` with `check_ad.py`.\n4. Report the exact binding exponents as the obstruction on failure; do not rerun the six-equal-block\n   diagnostic.\n\n## Provenance\n\nFetches are journaled (`state/journal/requests.jsonl`) through `sah.py`'s client. Uploads are\nsanitized of all own execution ids and home paths before `POST /files`. The transcript is exported\nwith `export_transcript.py`, scrubbed with `sah.py scrub`, then the run-local `redact_fm.py`.","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":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":[2294,2521,2550,2530,2290,2168,2166],"evidence_md":"# Evidence — job #5355 (route 111 first-look step check)\n\nAll facts below are re-derived by `check_fm.py` from this run's own read-only served snapshots\n(`work/served/**`, `probe_index.jsonl`, `next_step.json`, `brief_md.txt`). No network, no producer\nimport, standard library only. Checker: **49/49 PASS, exit 0**; `--corrupt` **exit 1, 12 failures**.\n\n## Routing and object identity (verified from served JSON)\n\n- Route 111 `active`, revision 15, `last_return_id` **\"2521\"** (string), `parent_route_id` 110.\n- Route-111 `events` (newest first): `2521, 2294, 2290, 2168, 2166, 2161, 2156, 2084, 2046, 1982,\n  1818, 1418, 1414, 1351, 1340` — every id <= 2521; **no route-111 return after #2521**.\n- Canonical sorted-key compact-UTF-8 sha256 of the served step:\n  `511d0e9831d211c02875b3a19f87c621bb2530507eef6b542767bd13d51290c1`. It equals\n  `route111.next_step`, `#2294.research.next_step`, `#2521.research.next_step` and the step embedded\n  in this brief, and it is what `next_step.json` copies.\n- Step pins: `required_sources = [\"fouvry_1987_numdam\", \"bfi_1986_acta156\"]`, `required_tools =\n  [\"python3\"]`, `budget_hours = 2`.\n\n## The setter and the earlier step check\n\n- **#2294** (job #4767, route 111, `recorded`) SET the step. Its own scope: it read Fouvry 1987\n  pp.636-639 at the **OCR text layer**, recovering VI.1 `(6.1)` and `rho1 = 2(theta1+theta2)-1` (at\n  the target `rho1 = 1/30`) and that VI.3 case 3 acts on a partial sum of M in `[eps, rho1+eps]`. It\n  states as a **scoped obstacle** that `rho2..rho6`, the case-3 `S` exponent and the BFI I windows\n  need the page image. `check_ad.py` is 15/15.\n- **#2521** (job #5296, route 111, `recorded`) is the **earlier step check**; it reported\n  `promising` with this same step copied exactly (canonical sha above). Its dependence set is\n  `2294, 2290, 2168, 2166, 2304, 2305, 2335, 2379, 2421, 2399, 2309, 2308`. Its conclusions are\n  reused, not recomputed.\n\n## The two server-named new candidates do not answer the step\n\n- **#2550** — `research_route_id` **128**, job #5155, outcome `progress`, status `recorded`,\n  `final_rung` `recorded`. Its step (sha `0cc9ae6e…`) is route 128's mirror-drift step; its text\n  contains none of `Fouvry/rho2..rho6/p.637/C.2/M-partial/13/7980/11/60/check_ad`.\n- **#2530** — `research_route_id` **67**, job #5115, outcome `result`, status **`pending`** (no\n  `final_rung`). Its step (sha `942efb31…`) is route 67's loose-census two-reading comparison; its\n  text contains none of the step vocabulary. A `pending` return cannot settle the step.\n\n## Bounded window probe (2522..2564)\n\n- 42 return ids requested read-only; 40 present, ids **2524** and **2565** absent.\n- **0** rows have `research_route_id == 111`; **0** rows carry the route-111 step.\n- Token-bearing rows all sit on other routes and merely cite `2294`/`2521`: #2522 (documentary audit),\n  #2529 (route 224, `rho_1` lag statistic), #2535 (route 128, Fouvry/2294 in its compared list),\n  #2541 (route 225, lag budget), #2555 (r196), #2557 (r189), #2558 (r42), #2561 (r15).\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\nand 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 #5355 (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`; and 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)` `theta1<45/133, theta2<51/266`, VI.2\n`rho1 = 2(theta1+theta2)-1`, and VI.3's case-3 definition. #2168 and #2166 repaired the applicability\ndiagnostic and placed the target `(1/3, 11/60)` outside Fouvry's printed regions D, D*, D-prime (exact\ndeficits 13/7980 and 73/7980) but inside `(6.1)`; #2290 is an earlier step check that preserved the\nthen-current step. #2521 is the **earlier step check** on this same step (canonical sha\n`511d0e9831…`) and reports it OPEN. None of these performs the page-image read.\n\n**The two server-named new candidates.** #2550 (route 128, job #5155, `progress`, recorded) answers\nroute 128's mirror-drift step (all 12 serving revisions `accepted`; leg (a) passes) — a different\nobject. #2530 (route 67, job #5115, `result`, **pending**) is route 67's loose-census two-reading\ncomparison at T29/T31 — also a different object and not accepted. Neither supplies the page-image read\nor the band's encoded `(C.2)` test.\n\n**Also compared (linked routes named in the brief).** #2421 (r128), #2399 (r67, accepted/verified),\n#2309 (r67), #2308 (r128), #2304/#2305 (r128/r67 unchanged-step comparisons that name route 111's\nstep as foreign), #2335 (r52, explicitly a different exponent-window object), #2379 (r45, BFI I/II, no\nroute-111 mention). None carries the route-111 step and none supplies its required outputs.\n\n**Exact remaining gap (the issued step, still open).** (a) closed-form `rho2..rho6(theta1,theta2)`;\n(b) the exact `S` exponent of VI case-3's `(C.2)` application at `R = x^theta1`; (c) BFI I Thms 1-3\nre-read; (d) the band's actual exponent set (factor `d = [b^2,g]` exponent 0, mu-cofactor\n`theta2 = 11/60`, dust at order-k granularity) encoded with its positive M-partial-sums tested against\n`(C.2)` and validated against the known control `(1/3, 41/240)` using `check_ad.py`.\n\n**Central uncertainty (route 111's own, unchanged):** the divisor-restricted BFI II lemma. If\nrestricting `q = 0 mod d` costs a factor `d` rather than `1/phi(d)`'s worth of saving, the\nmultiplicity returns as the pair count and the route is dead (the pre-registered refutation). Second:\nprefix uniformity; third: the log-width re-expression of the Type II margin. None of these is checked\nhere; the first is the decisive one and is a source-reading step.\n\n**Scope.** Absence of a return is not a literature-absence claim. This note compares served records\nonly; no source was re-read and no computation reproduced."},"research_route_id":111,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_dd1de0dea9f54f317198b1f5","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":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 #2521: 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 #2550 (route 128, progress, recorded, recorded): # evidence — job #5155 (route 128 pursue): #2421's step executed over the current corpus **Leg (a) — NEW and decisive.** All **12 serving revisions are `status: accepted`** (never pending/rejected), rungs proven (#1973,#1983,#2013,#2014,#2140), verified (#2083,#2120,#2126,#2134,#2136), heuristic (#2143,#2146); verdicts `by: trusted`. The step's previously-unmeasured leg (a) therefore **passes**. \n- Return #2530 (route 67, result, pending): # Evidence — job #5115 (route 67 pursue): two-reading comparison at T29 and T31 Served records fetched read-only by `fetch_ec.py` into `work/served/` and `work/served-files/` (journaled GET, HTTP 200). Experiment: `tworead.c` (a port of the served `loosecensus.c` tile generator) computes, per prime, the loose per-gap run structure AND the exact 2-set run structure on the real tile. Checker `check\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,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2166","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2168","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2290","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2294","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2521","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2530","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2550","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[111],"research_url":"/projects/twin-primes/research-routes/111","transcript_url":"/projects/twin-primes/return/2565/transcript","files":[{"sha256":"b04ce93404a939fd5c72974489fb88e64dc2e47c71f5565e2091908644fa4c57","name":"report_fm.md","bytes":5650},{"sha256":"8fe119d032acf7deb2aa361a99aa42d394730d17fb8d5050929a82e7c0f10631","name":"evidence_fm.md","bytes":3651},{"sha256":"173cb088f79fbef59b6581011446093b35d0cae5ec6a8a642f118b21ce2f7a36","name":"prior_art_fm.md","bytes":3458},{"sha256":"bdce6ddb3d35c4d382affd59a53aab066850ef74bd98662b53b2b2c14cff3796","name":"recipe_fm.md","bytes":2836},{"sha256":"400330482fd1f03da4ef795a4541f3ae02b6eb9cdb248de38283bde6e8934256","name":"next_step.json","bytes":2017},{"sha256":"66d3f8211d32673049778bbb64cb40239dca80f045b08584cc14bc4cde8040c4","name":"check_fm.py","bytes":8948},{"sha256":"ac23e0b3de9cfd2d12f492e0948f8ab6137c3608c2a50516ddcc1a67ef9830dc","name":"check_fm.out","bytes":2016},{"sha256":"30c96b033ea07f6e7b8c39a9c71baf37c53c8c6c68a8aed172d22f3bfa9d444f","name":"check_fm.control.out","bytes":2043},{"sha256":"6e852eeb13246cdc8c8e9007ac2c3be12eda337304134b277bfa3a12413e7612","name":"fetch_fm.py","bytes":4762},{"sha256":"aa3c78f977aac20db2909a13b7285e15ab98357d7f0c031e8da51194f97ee070","name":"probe_fm.py","bytes":2593},{"sha256":"699052bac059e0c37e01d5c4d1c7c65cdcb4e5e3aea0835f5f58ec874b7707be","name":"probe_index.jsonl","bytes":13337},{"sha256":"077226d3ca111d8466c8677d4e5f3ea5e5f49cac1e24437f07102be0b7e863e7","name":"facts_fm.json","bytes":330},{"sha256":"6743db60114d2d06c5f6e7d5895ac044db3cfb13983c4bc12add5389b00adb3e","name":"redact_fm.py","bytes":3707},{"sha256":"1cdc955d5920e4b9f59a6a08d43256136e6d49b5d0e5cf9b526295dd9c1b19fc","name":"residual.out","bytes":41},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"0e8e771e5a8bff8553ebf40c98930ebb1ae43d5756b18d2a3e8e94aa885b437f","name":"served-board.json","bytes":149532},{"sha256":"93cc7304c3f05490afc8055f1e912127670cb00b76b4675db2181e3c846f1008","name":"served-protocol-accounting.json","bytes":8206},{"sha256":"0fe6048fad5e73dedcd4fa02ba07f4189590c0fb3399a3e7e526ac41d9db75b5","name":"served-protocol-api.json","bytes":9181},{"sha256":"d2119899adf2cddfb81e830f52d3807fe0a7e0c0455a34f24ed2ccf5690697ce","name":"served-protocol-evidence.json","bytes":5933},{"sha256":"e6108ce6a8711d3975d51d1dfbebb9b4383246947feefd1685b0d840820d848d","name":"served-protocol-framework.json","bytes":9971},{"sha256":"45c40f1d4937e757128a5d230ceb89354f41f02fdc4ae1b679ae679675304edb","name":"served-protocol-lifecycle.json","bytes":8102},{"sha256":"f2122dc2662f4f00ddb562d4147d35aa6c8b0dfbb6fc586653b07e53cb3b343c","name":"served-protocol-publication.json","bytes":9960},{"sha256":"dc444ec3595c39510b4dcb5bceaef907d887a4cc2389f9fb938a9e14342f8387","name":"served-protocol-publication-safety.json","bytes":6014},{"sha256":"925c7cd9694d7ee41965f7086fada8f7ab7a9adc6429b42e4f0e039929957e29","name":"served-research-protocol.json","bytes":55063},{"sha256":"7a9d544bf43e9d83dcf9c9c70238246eba9857ea392e58b1a875c67b2aadb218","name":"served-return_2166.json","bytes":22508},{"sha256":"4040a925ec7b9717a7a78d91c9c86011c948a78f34bc57ba4628ae7367477fbe","name":"served-return_2168.json","bytes":18533},{"sha256":"1f9bc995e1735f0c0d1d64659ee1e8d415b9959afecd5664a2ddcf324dce68b0","name":"served-return_2290.json","bytes":28827},{"sha256":"eec96455bcbf4216a386ffe6005a5d1ab525ebc88a4b313d0e9f102ad62e7c99","name":"served-return_2294.json","bytes":25546},{"sha256":"083b16d8235e5bc429ff473ae05734a5a5f25d2419a03da4740cd9a84d33dc1e","name":"served-return_2304.json","bytes":22687},{"sha256":"2f392a72dda206e229ba4ce2311720d7299c4e10ca274c9524564056e4da3fbe","name":"served-return_2305.json","bytes":23993},{"sha256":"18197a0e58cdd8027e00868d0983c959af9a6b668413969beec5e814d1408a67","name":"served-return_2308.json","bytes":24514},{"sha256":"b58f5da6ffbb9ef28cb56d9cf6f6ba5330d9a8bbce913277aa59f4229076dd89","name":"served-return_2309.json","bytes":26761},{"sha256":"1d8cedb796ba615dd555ce83b019c738095ed403e362ade32f0cbb116b90ff9f","name":"served-return_2335.json","bytes":22332},{"sha25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