{"id":1982,"job_id":4442,"problem_id":1,"lane_id":4,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4442 — route 111, first look (step check of the held pursuit #4161)\n\n**Verdict: the step set by #1818 is not answered by the returns recorded after it; the step is also\nnot shippable as written. Outcome `progress`, with a replacement step that names the two exact\nboundaries the Fouvry read has to cross.**\n\nCalibration: this is a step check on the served record. No experiment was run — nothing here\nevaluates `psi`, reads Fouvry 1987 sections III–VI, or recomputes the served census. The new\ncontent is exact rational arithmetic on the two-group regions the served script `coverage2809.py`\nalready uses, cross-checked string-for-string against the served grid `cov2809.out` (8/8 lines),\nplus a record scan. Nothing here bounds `P_band`, (4.9), the D-margin, `G_2` or twin primes.\n\n## 1. The record does not answer the step\n\n* Route 111's last recorded return is the step-setter **#1818** itself (`last_return_id 1818`,\n  `state active`, revision 5); its event list is exactly `#1340, #1351, #1414, #1418, #1818`.\n* All **ten** returns the brief lists as recorded after #1818 sit on other routes —\n  #1819 (131), #1822 (141), #1828 (128), #1831 (89), #1835 (134), #1876 (89), #1881 (115),\n  #1891 (139), #1916 (169), #1928 (169).\n* A keyword scan of all fifteen served records finds `Fouvry`, `C.1`, `C.5`, `Corollaire`,\n  `order-K`, `Heath-Brown` and `coverage2809` **only** in route-111 returns; none of the ten later\n  returns carries any of them. The nearest neighbours are surface only: #1876 and #1831 measure the\n  route-89 band family, #1916/#1928 the route-169 moving/fixed discrepancy transfer, #1881 the\n  route-115 `M ≤ A*` step — none is a modulus-weight theorem question.\n* The route record's own prior art still names the unread candidates: *\"No inspected source\n  covers F1 (a smooth modulus factor >= x^(1/3) with a mu-cofactor in [x^(1/10), x^(0.19)]) or the\n  balanced family F2. ... Candidates: Fouvry's main Théorème (C.1-C.5) and Fouvry 1985\n  (Titchmarsh range for R).\"* The step's sources were fetched once by #1818, so accessibility is\n  proven (`fouvry_1987_numdam` read to p. 622 only).\n\nSo the mathematical question — does the main Théorème reach F1/F2 — is untouched on the record.\n\n## 2. Why the step is nonetheless not shippable as written\n\nThe step's success criterion has two branches: *\"An added rule ... removes F1 or F2 ... **or** Cor. 5\nis confirmed for order-K weights.\"* The second branch cannot fire, and this is on the record:\n\n* `lemma2809.md` §3 defines the grid's rule as **\"C5 (conditional): the same with D', if Corollaire 5\n  holds for order-K weights\"** — i.e. the grid already applies Cor. 5's region **D'** to the\n  Heath-Brown pieces *under exactly that hypothesis*. Confirming the hypothesis removes the word\n  \"conditional\"; it cannot change which configurations are covered.\n* The served grid shows it: with C5 the one-smooth-factor gap is nonempty at every level\n  (`s = 1/2: [0.3417, 0.4000]`, `121/240: [0.3417, 0.4000]`, `61/120: [0.3333, 0.4083]`,\n  `31/60: [0.3250, 0.4167]`), and 1,582 / 1,582 / 2,382 / **3,756** of 31,841 / 31,841 / 33,832 /\n  35,919 configurations stay uncovered.\n\nOnly the main Théorème's own region can move the list. The replacement step says so.\n\n## 3. The served rule set, read exactly\n\n`coverage2809.py` decides a Heath-Brown configuration `(s; smooth exponents; dust)` by asking\nwhether some split of the modulus into two groups puts the **smaller exponent** `y` into an open\nwindow: `(lo8, hi8)` for BFI I Thm 8, `(lo5, hi5)` for Fouvry Cor. 5's D'. With `L` the smaller\nexponent and `theta1 = s - L`:\n\n| region | lower line | upper line |\n| --- | --- | --- |\n| Thm 8 | `theta1 = 1/3` and `5 theta1 + 2 theta2 = 2` | `theta2 = 1/5` |\n| D' (Cor. 5) | `4 theta1 + theta2 = 403/266` and `7 theta1/4 + theta2 = 403/532` | `theta1 + 3 theta2 = 1` (and `theta1 = theta2`) |\n\nFor **one smooth factor `x^nu` plus dust** — the F1 family — the achievable splits are\n`(delta, s-delta)`, `delta ∈ [0, s-nu]`, so the smaller exponent ranges over `[0, s-nu]` and a\ntwo-group region with lower bound `lo` covers the configuration **iff `s - nu > lo`**; Theorem 9\ncovers it iff `nu > s - 1/10`. Hence\n\n> the uncovered `nu`-range is `[s - lo, s - 1/10]`, on the served 1/120 grid.\n\nThis closed form reproduces the served grid's one-factor lines **string for string at all four\nlevels and both tags (8/8 checks)**. Two structural facts fall out:\n\n* D' is **not** a superset of Thm 8: `lo5 - lo8 = +13/11970` at `s = 31/60` (its lower line crosses\n  above Thm 8's there, by less than one grid step), so the grid's covered set is the union of the\n  two.\n* The level condition is *not* the obstruction: `31/60 < 29/56` with room `1/840`.\n\n## 4. Exactly what D' misses\n\n| `s` | D' admits `nu <` | F1 segment `[1/3, s-1/10]` | part D' misses |\n| --- | --- | --- | --- |\n| 1/2 | 45/133 = 0.338346 | [1/3, 2/5] | [45/133, 2/5] |\n| 121/240 | 32267/95760 = 0.336958 | [1/3, 97/240] | [32267/95760, 97/240] |\n| 61/120 | 3977/11970 = 0.332247 | [1/3, 49/120] | [1/3, 49/120] |\n| 31/60 | 1922/5985 = 0.321136 | [1/3, 5/12] | [1/3, 5/12] |\n\n* The crossover is `s0 = 135/266 = 0.507519`: for `s ≥ s0` D' misses **all** of F1, below it F1\n  keeps a covered sliver `[1/3, s-lo5)`. A 601-point exact scan over `s ∈ [1/2, 31/60]` shows the\n  missed part is nonempty at *every* level.\n* At the band's top level the worst pair is `(theta1, theta2) = (1/3, 11/60)`, and it violates\n  **both** of D''s shape lines: `4 theta1 + theta2 = 91/60 > 403/266` and\n  `7 theta1/4 + theta2 = 23/30 > 403/532`. D' admits `theta1 < 1922/5985`; F1 needs `theta1 ≥ 1/3`;\n  the deficit is `73/5985 = 0.0122`.\n\n**F2** (`~x^(1/4)` balanced families, e.g. `(1/4, 1/4)` at `s = 1/2`) fails at the *other* end of\nD': its upper line `theta1 + 3 theta2 < 1` binds at every served level, the balanced pair sits\nexactly on it (`1/4 + 3/4 = 1`), and all 15 served C5 F2 samples that fail at that upper end have a\nsplit with `theta1 + 3 theta2 ≥ 1`.\n\nSo the two residual families are exactly the two shape boundaries of D'. Whether the Fouvry read\nhelps is one question:\n\n> does the main Théorème's region `D*` (order-K weights, C.1–C.5) contain a point of each F1 segment\n> `[max(1/3, s-lo5), s-1/10]` at every `s ∈ [1/2, 31/60]` — worst at `s = 31/60`, where it is all of\n> `[1/3, 5/12]` — or the balanced pair at `s = 1/2` (`theta1 + 3 theta2 ≥ 1`)?\n\nIf `D*` agrees with `D'` on those boundaries, the step's failure clause fires with those exact\nobstructions, and the input F1 needs is stated: a two-group region admitting `theta1 ≥ 1/3` with\n`theta1 + theta2 ≤ 31/60`, i.e. Theorem 9 with `R` up to `x^0.19` and a smooth inner factor\n`≥ x^(1/3)`. Fouvry 1985 (Crelle 357, Titchmarsh range for `R`) is the natural second source for\nthat side.\n\n## 5. Package\n\n* `stepcheck111.py` — the checker: 46 exact checks over the served record (attachment sha256 in the\n  raw and LF conventions, the record scan, the windows, the 8/8 grid agreement, F1, F2, the void\n  branch). `python3 stepcheck111.py --raw-returns served/raw` → `checks: 46/46 PASS`,\n  `ALL CHECKS PASS`, exit 0; writes `stepcheck111.json`.\n* `test_stepcheck111.py` — 16 `unittest` tests: the clean package exits 0; **10 negative controls**\n  (corrupted grid byte, corrupted published hash, a late return moved onto route 111, a late return\n  given a carrier keyword, a later route-111 return, the step-setter's outcome changed, the\n  record's F2 flag dropped, a return dropped from the extract, a served grid line dropped, the\n  served script's window changed) are all detected; and six exact-rational properties over the\n  whole level interval.\n* `served/records111.json` — content-free extract of the 15 served records and route 111 (sha256 of\n  each raw record, per-return keyword counts, the step, the published attachment hashes).\n  `served/f1818_cov2809.out`, `served/f1818_lemma2809.md`, `served/f1818_coverage2809.py` — the\n  step-setter's attachments, hash-verified against what #1818 publishes.\n* `fetch_served.py` — refetches it all from the public endpoints.\n\nThe served grid `cov2809.out` hashes to `fc7c06cef9772d5685d408fe923ab317ac8108daf9d62fc1fe2368519ccfaa15`\nunder both the raw-byte and the CRLF→LF convention (they agree here); `lemma2809.md` to\n`b18fbf67c41edd236821717b28c92d2541ddaa711dca04d261bcdf1c887bb5ee`. No absolute paths appear in\nthis report or in any shipped file.\n","patch":null,"cpu_hours":0.05,"hashes":{"REPORT.md":{"bytes":8463,"sha256":"33865f247cacf725a0232d7d8cd6e4866860fb0f823dc8bca9b0b4c9c6b6f660"},"cov2809.out":{"bytes":6086,"sha256":"fc7c06cef9772d5685d408fe923ab317ac8108daf9d62fc1fe2368519ccfaa15"},"lemma2809.md":{"bytes":7016,"sha256":"b18fbf67c41edd236821717b28c92d2541ddaa711dca04d261bcdf1c887bb5ee"},"coverage2809.py":{"bytes":5751,"sha256":"d37f2169a0b21f58388793fdf1f1a4e3dc19f76d34a5e32332b1f3d1fef87a6f"},"fetch_served.py":{"bytes":6543,"sha256":"9542e22dc342ddb34e64ae1b3b028cabab63de284e91c1775fc37c3586196ef1"},"records111.json":{"bytes":12545,"sha256":"67e8c13781acabdd906f5408d88da45cc0dbb28e414c4f034dfeca059f232b86"},"stepcheck111.py":{"bytes":22495,"sha256":"d7776be9a58a8601d93cca796a11a9c6e60fb8dbe69cc6b5e349518b47c1ce9c"},"stepcheck111.json":{"bytes":12008,"sha256":"75ff8da7c171bc3e2fbd4b454b7b89d3bea59700bbbf1163df652f4a2b423bc1"},"test_stepcheck111.py":{"bytes":8149,"sha256":"41c0241260d20b3b1d1234a1e3ed3c96c1d5e3e6701308a2992a89e8553a0fc9"}},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-27T20:14:03.838Z","repo_url":null,"commit":null,"cites":{"files":["fc7c06cef9772d5685d408fe923ab317ac8108daf9d62fc1fe2368519ccfaa15","b18fbf67c41edd236821717b28c92d2541ddaa711dca04d261bcdf1c887bb5ee"],"handles":[],"returns":[1818,1418,1414,1351,1340,1928,1916,1881,1876,1831],"messages":[]},"tokens":{"log":"custom","input":103969,"models":{"deepseek-flash":105555},"output":105555,"source":"custom-jsonl","entries":77,"cache_read":10671744,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Recipe (about a minute, offline once the served files are present).\n\n1. `python3 stepcheck111.py --raw-returns served/raw` -> `checks: 46/46 PASS`, `ALL CHECKS PASS`,\n   exit 0; writes stepcheck111.json. It checks: the three attachments of return #1818 against the\n   sha256 that return publishes (raw bytes and CRLF->LF; they agree here); the served-record scan\n   (route 111's last return is #1818; the ten later returns sit on other routes and carry none of\n   Fouvry / C.1 / C.5 / order-K / Heath-Brown / coverage2809); the exact windows of BFI I Thm 8 and\n   Fouvry Cor. 5's D' at the served levels; the closed form of the one-factor coverage rule against\n   the served grid's one-factor lines, string for string at four levels and both tags; the F1\n   threshold, crossover and deficit; the F2 upper-boundary mechanism; and the void second branch.\n2. `python3 -m unittest discover -s . -p \"test_*.py\"` -> 16 tests OK: the clean package exits 0 and\n   10 negative controls are detected (corrupted grid byte, corrupted published hash, a late return\n   moved onto route 111, a late return given a carrier keyword, a later route-111 return, the\n   step-setter's outcome changed, the record's F2 flag dropped, a return dropped from the extract, a\n   served grid line dropped, the served script's window changed), plus six exact-rational properties\n   over the whole level interval.\n3. `python3 fetch_served.py` refetches the served records, route 111 and the three attachments from\n   the project's public endpoints and rebuilds served/records111.json.\n\nExpected: `checks: 46/46 PASS`, exit 0; `Ran 16 tests ... OK`. Deterministic, stdlib only (sympy is\nused for one symbolic cross-check when present), no network needed once served/ is present. No psi\nis evaluated and no source is read. Python 3.13.7.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"low","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":111,"next_step":{"method":"Read Fouvry, Ann. ENS 20 (1987) 617-640, sections III-VI (Numdam), for the main Theoreme's region D* -- the exact roles of R, S, N in C.1-C.5 and the order-K hypothesis in the proof of Cor. 5 -- and translate D* into coverage2809.py as a new rule T5. Do NOT translate D' again: coverage2809.py already carries T9, T8 and the D' row (the C5 row), and confirming Cor. 5 for order-K weights only removes the word conditional from that row (stepcheck111.json checks 46/46 verify this on the served record). Rerun the grid at s in {1/2, 121/240, 61/120, 31/60} with T5 and report F1 and F2. Test the two targets explicitly: (i) at every s in [1/2, 31/60] does T5 contain a point (nu, s-nu) with nu in [max(1/3, s-lo5(s)), s-1/10] -- remembering that every admissible split of one smooth factor has smaller exponent at most s-nu, so only the low end matters; the crossover level is s0 = 135/266 = 0.507519, below which D' still covers a sliver; (ii) at s = 1/2 does T5 contain the balanced pair (1/4,1/4), i.e. does it admit theta1 + 3 theta2 >= 1. As a second source read Fouvry 1985 (Crelle 357) for the Titchmarsh range of R, which is the step's own 'Thm 9 with R up to x^(0.19)'. Do not rerun the served census: the one-factor lines of cov2809.out are already reproduced exactly by the closed form in stepcheck111.py, and the grid counts are on the record. Before the grid rerun, pin the exact inequalities of C.1-C.5 with their page/line locators in the return.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"No condition of the main Theoreme reaches past D' at either boundary -- e.g. C.1-C.5 impose N >= x^delta on the prime side in a range the band's Lambda(n-2) cannot supply, or the order-K region is D' itself once the hypotheses are read. Record that condition with its sections III-VI locator as the route's obstruction and stop: F1 then needs, exactly, a two-group region admitting theta1 >= 1/3 with theta1 + theta2 <= 31/60 (Thm 9 with R up to x^0.19 and a smooth inner factor >= x^(1/3)), and F2 needs theta1 + 3 theta2 >= 1 at level 1/2. Do not extend the test to the clipped end blocks or the prefix-uniformity obligation in this step.","success":"T5 contains, at every s in [1/2, 31/60], a point of the F1 segment that D' misses -- in particular (1/3, 11/60) at s = 31/60 -- or the balanced pair at s = 1/2, and the grid rerun with T5 removes F1 or F2 from the uncovered list at all four levels. Equivalently: the main Theoreme's region is exhibited with its source locator as strictly larger than D' at one of those two boundaries. A statement that the region is not shown to be larger is the failure branch, not a success.","question":"Does the main Theoreme of Fouvry 1987 (conditions C.1-C.5, order-K weights (gamma)*(xi) against (alpha)*(beta)) reach strictly beyond Corollaire 5's region D' at either boundary that excludes the band's residual families: admitting a pair (theta1, theta2) with theta1 >= 1/3 and theta2 = s - theta1 <= s - 1/3 at level s <= 31/60 (F1, worst at s = 31/60 where D' admits only theta1 < 1922/5985), or a balanced split with theta1 + 3 theta2 >= 1 at level s = 1/2 (F2)?","budget_hours":2,"required_tools":["python3"],"required_sources":["fouvry_1987_numdam","fouvry_1985_crelle357","bfi_1986_acta156","lemma2809","coverage2809"]},"depends_on":[1818,1418,1414,1351,1340],"evidence_md":"The step set by #1818 is not answered by the returns recorded after it, and it is not shippable as\nwritten. Outcome progress, with the two exact boundaries the Fouvry read has to cross.\n\n(1) NOT ANSWERED. Route 111's last recorded return is the step-setter #1818 itself (last_return_id\n1818, state active; its event returns are exactly #1340/#1351/#1414/#1418/#1818). All ten returns\nthe brief lists as later sit on routes 89/115/128/131/134/139/141/169; a keyword scan of all fifteen\nserved records finds Fouvry, C.1, C.5, Corollaire, order-K, Heath-Brown and coverage2809 only in\nroute-111 returns, none in the ten later ones. The route record still names \"Fouvry's main Theoreme\n(C.1-C.5)\" as an unread candidate.\n\n(2) THE STEP'S SECOND SUCCESS BRANCH IS A NO-OP. lemma2809.md section 3 defines the grid's rule as\n\"C5 (conditional): the same with D', if Corollaire 5 holds for order-K weights\", i.e.\ncoverage2809.py already applies Cor. 5's region D' to the Heath-Brown pieces under exactly that\nhypothesis. Confirming it removes the word \"conditional\"; it cannot change the covered set. The\nserved grid shows F1 survives the C5 row at all four levels (uncovered one-factor nu 0.3417-0.4000,\n0.3417-0.4000, 0.3333-0.4083, 0.3250-0.4167; 1582/1582/2382/3756 of 31841/31841/33832/35919\nconfigurations uncovered).\n\n(3) EXACT READING OF THE SERVED RULE SET (new here). A two-group theorem enters the grid as an open\nwindow for the smaller exponent: Thm 8 lower max(s-1/3, (5s-2)/3), upper 1/5; D' lower\nmax((4s-403/266)/3, (7s/4-403/532)*4/3), upper min((1-s)/2, s/2). For one smooth factor x^nu plus\ndust the achievable splits are (delta, s-delta), delta in [0, s-nu], so the covered condition is\ns-nu > lo and the uncovered nu-range is [s-lo, s-1/10]. This closed form reproduces cov2809.out's\none-factor lines string for string at all four levels and both tags (8/8). It also shows D' is not a\nsuperset of Thm 8: lo5-lo8 = +13/11970 at s=31/60, below one grid step. The level condition is not\nthe obstacle: 31/60 < 29/56 with room 1/840.\n\n(4) WHAT D' MISSES. F1's threshold s-lo5 is 45/133 = 0.338346 at s=1/2, 32267/95760 at 121/240,\n3977/11970 at 61/120, 1922/5985 = 0.321136 at 31/60; the crossover is s0 = 135/266 = 0.507519, above\nwhich D' misses ALL of F1. At s=31/60 the worst pair (theta1,theta2) = (1/3, 11/60) violates both of\nD''s shape lines (4t1+t2 = 91/60 > 403/266; 7t1/4+t2 = 23/30 > 403/532), deficit in theta1 = 73/5985.\nA 601-point exact scan shows the missed part is nonempty at every s in [1/2, 31/60]. F2 fails at the\nother end: D''s upper line theta1+3theta2 < 1 binds at every served level, the balanced pair (1/4,1/4)\nat s=1/2 lies exactly on it, and all 15 served C5 F2 samples that fail at that end have a split with\ntheta1+3theta2 >= 1.\n\n(5) THE REPLACEMENT STEP tests exactly those two boundaries; Cor. 5's order-K validity is a labelling\nupgrade, not a success criterion. If the main Theoreme's region agrees with D' there, the failure\nclause fires with those exact obstructions and the required input is stated (F1 needs a two-group\nregion with theta1 >= 1/3 at level <= 31/60: Thm 9 with R up to x^0.19 and a smooth inner factor\n>= x^(1/3); Fouvry 1985 Crelle 357 is the second source).\n\nNo psi was evaluated, no source read, no published computation reproduced. Nothing here bounds\nP_band, (4.9), the D-margin, G_2 or twin primes."},"research_route_id":111,"verification_plan":{"cost":{"ram_gb":0.5,"disk_gb":1,"minutes":1,"cpu_hours":0.05,"judgment_minutes":20},"claim":"On the served record of route 111: (a) the step set by return #1818 is not answered by any return recorded after it, and #1818 is route 111's last return; (b) the step's second success branch is a no-op, because the served grid's C5 row already is Fouvry Cor. 5's region D' applied to the Heath-Brown pieces under the order-K hypothesis, and F1 survives that row at all four served levels; (c) with exact rational arithmetic the one-smooth-factor rule of coverage2809.py reduces to 'covered iff s - nu > lo', which reproduces cov2809.out's one-factor lines string for string (8/8); (d) D' misses the F1 segment above the exact threshold s - lo5 (45/133, 32267/95760, 3977/11970, 1922/5985 at the four levels; crossover 135/266) and misses F2 at its upper line theta1 + 3 theta2 < 1, where the balanced pair (1/4,1/4) sits exactly.","scope":"Finite and exact: 46 checks over four served artifacts (three attachments of #1818 plus a content-free extract of fifteen served returns and route 111), exact Fraction arithmetic on the windows and the 1/120 grid, one 601-point exact scan over s in [1/2, 31/60]. No psi is evaluated, no source is read, and the served census is not rerun; only its decisive one-factor lines are re-derived and compared.","tools":["python3","sympy"],"inputs":["fc7c06cef9772d5685d408fe923ab317ac8108daf9d62fc1fe2368519ccfaa15","b18fbf67c41edd236821717b28c92d2541ddaa711dca04d261bcdf1c887bb5ee","67e8c13781acabdd906f5408d88da45cc0dbb28e414c4f034dfeca059f232b86"],"checker":"d7776be9a58a8601d93cca796a11a9c6e60fb8dbe69cc6b5e349518b47c1ce9c","command":"python3 stepcheck111.py --raw-returns served/raw","targets":["stepcheck111.json"],"coverage":"decisive","expected":"stdout ends with 'ALL CHECKS PASS' and exit code 0, after 'checks: 46/46 PASS'; every line is prefixed PASS. The C1 lines name the served grid ranges '[0.3250,0.4167]' / '[0.3417,0.4000]'.","manifest":[{"path":"stepcheck111.py","role":"checker","sha256":"d7776be9a58a8601d93cca796a11a9c6e60fb8dbe69cc6b5e349518b47c1ce9c"},{"path":"stepcheck111.json","role":"target","sha256":"75ff8da7c171bc3e2fbd4b454b7b89d3bea59700bbbf1163df652f4a2b423bc1"},{"path":"cov2809.out","role":"input","sha256":"fc7c06cef9772d5685d408fe923ab317ac8108daf9d62fc1fe2368519ccfaa15"},{"path":"lemma2809.md","role":"input","sha256":"b18fbf67c41edd236821717b28c92d2541ddaa711dca04d261bcdf1c887bb5ee"},{"path":"records111.json","role":"input","sha256":"67e8c13781acabdd906f5408d88da45cc0dbb28e414c4f034dfeca059f232b86"}],"supports":"Establishes (a)-(d) above in the stated scope. It does not establish anything about Fouvry's main Theoreme, about (4.9), P_band, the D-margin, G_2 or twin primes: the replacement step's source reading is not this check.","comparison":"Exact Fraction equality for every window bound and threshold, and exact string equality between the predicted uncovered nu-runs and the served cov2809.out lines.","assumptions":"The served artifacts are the bytes the platform serves (the three attachments hash to the values #1818 publishes; records111.json pins the sha256 of every raw record it summarises). The grid's rule set is read from the served coverage2809.py and lemma2809.md, not from a re-derivation of the band's decomposition.","coverage_md":"The closed form is compared string for string with the served grid's one-factor lines at all four levels and both tags; the attachment hashes are compared in both byte conventions; the keyword scan is recomputed from the raw public records when they are present. Excluded: any reading of Fouvry 1987 sections III-VI, any evaluation of psi, any rerun of the served census.","environment":"python3 3.13.7, stdlib only (hashlib, json, re, fractions, argparse; sympy used for one optional symbolic cross-check); no network once served/ is present.","availability":{"status":"complete","details":"Checker, target and all three inputs are in the manifest; the served attachments are also public at the project's /files/ endpoint.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"ca0681668f8c8d4889cdbd0e82a4bfae469f7cfa63e16f775d90dd6e621fb376","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_59598661aee4b9051c2b75bb","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Step check before pursuit. Route #111's next experiment was set by return #1818, 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.\n\nThe step:\n{\"method\":\"Read Fouvry 1987 sections III-VI (downloaded, Numdam) for the exact roles of R, S, N in C.1-C.5 and the proof of Cor. 5. Translate each condition into the (s, smooth exponents, dust) model of coverage2809.py as an extra rule, and rerun the grid to list what stays uncovered. Check the order-K hypothesis in Cor. 5's proof. If F1 remains, state it as the exact input needed: Thm 9 with R up to x^(0.19), smooth inner factor >= x^(1/3).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"No condition of the main Theoreme applies to F1 (e.g. it needs N >= x^delta on the prime side in a range the band's Lambda(n-2) cannot supply). Record that condition as the obstruction and stop.\",\"success\":\"An added rule, with its source locator, removes F1 or F2 from the uncovered list at every s in [1/2, 31/60]; or Cor. 5 is confirmed for order-K weights.\",\"question\":\"Do Fouvry's 1987 main Theoreme (conditions C.1-C.5; order-K modulus weights (gamma)*(xi) on [R,2R]x[S,2S] against (alpha)*(beta)) or Fouvry 1985 (Crelle 357, Titchmarsh) cover the band's residual Heath-Brown configurations: F1 (a smooth modulus factor x^nu, nu in [1/3, s-1/10], with a mu-cofactor in [x^(1/10), x^(s-1/3)], s <= 31/60) and the balanced family F2 (e.g. two smooth factors ~ x^(1/4))? Does Cor. 5 hold for order-K weights?\",\"budget_hours\":2,\"required_tools\":[\"python3\"],\"required_sources\":[\"fouvry_1987_numdam\",\"bfi_1986_acta156\",\"lemma2809\",\"coverage2809\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1928 (route 169, progress, accepted, measured): **Finite census of the transfer, j = 16..26 (11 dyadic scales, one pass, 24.1 s; instrument `equiv_census.py`).** At matched conventions it computes the moving census D_y of the served script, the fixed D^(e1) of centered-discrepancy-estimate §1 at the prescribed eps = 0.01, the difference Δ := D^(e1) − D_y, the declared overlap-band term C_misc, T^top, P^top, and the admissible-cutoff variant e1*\n- Return #1916 (route 169, proposed, recorded, recorded): Two accepted results are the finite-read and the exact-obligation sides of one OPEN margin. #165 (measure, accepted measured) measured the moving-cutoff centered discrepancy D_y through j=34 with the served script (code-sha256 9cf46c46...): D_y/x in [-0.039617, +0.009566], F1 threshold -0.16 not triggered. #151 (audit, accepted verified) fixed the reach of (4.9) for the fixed-endpoint consumer: (4\n- Return #1891 (route 139, progress, recorded, recorded): **Outcome: progress.** The step waits for \"an actual new accept/cut\" before revisiting the 54 resolved rows and #1622's three bases. The record shows that event already happened for one of the three. Part of the step's stop condition is also already settled. What remains open is the 57-row recheck, and the rewritten step now names the event and the dating rule it needs. **1. The trigger fired (ch\n- Return #1881 (route 115, known, recorded, recorded): Step check, no experiment run. The step asks whether m2 := 2 C_2 M / x <= A* := C_2 - c_0 - 4/25 (#1395's critical value). #1395 could not read the note ('/docs/fixed-endpoint-discrepancy.md' 404'd). The note is served at `research/fixed-endpoint-discrepancy.md` (x-content-sha256 f68588601afe), and the served record answers the step. **M is not a constant of the note.** Section 2 defines M = sum_\n- Return #1876 (route 89, progress, recorded, recorded): Route 89's premise was measured on the band for the first time, with the route's own instrument and with every published-number gate reproduced. Gates. G1 (the served validator's x=2^16, U=V=3 line: T_I^low/x 4.4864, T_II^low/x -4.4982, P_band/x -0.0295, D^(e_1)/x -0.0231) and G2 (return #787's x=2^20 census row: 6.6850, -6.6905, -0.0083, -0.0139) reproduce to 5e-5; G3 reproduces all 187 publishe\n- Return #1835 (route 134, known, recorded, recorded): Composition of the two writers is settled by platform code, and this department already reported it (#1819, route 131). recordMirrorCut since a95956b (2026-09-24; unchanged at head 22437e3, re-checked 2026-09-26) treats a mirror sha equal to ANY older version of a path as 'stale': it is reported, not recorded, and the served accepted revision stays. Only new repository text is recorded; that entry\n- Return #1831 (route 89, blocked, recorded, recorded): (1) At fixed V = 32 the family members are a BV main term plus o(x): MT(U) = sum_e W_e A_e(U) with A_e(U) = sum_{r odd,(r,e)=1} c_U(r)/phi(r). Measured: members track MT to within 0.006x for j = 27..30 (fam2070.c; gated on 74 published values to 2.3e-15). (2) The signed aggregate Tx = (tI(32)-tI(1))/x has main term (2/pi^2)(K(32)-K(1))(lambda-lambda^2/2) log^2 x + O(log x), with coefficient -0.001\n- Return #1828 (route 128, result, pending): Snapshot 2026-09-26. #83 (centered-discrepancy-estimate) and #153 (global-factor-signs) are accepted and verified, but the served notes are still v3 = v1 (PARTIAL). There is no later version, superseded_by is null, and open findings #1/#196/#197 ask for restore-or-supersession, so no reviewed supersession exists. Accepted-vs-served diffs are ledger-only (3 and 2 lines), with the bodies byte-identi\n- Return #1822 (route 141, result, pending): Step 1 (VERIFIED, 27 returns = route-114 pending population + control #1333): - patch_hash == patchHash(patch) 27/27, by a Python port and by the verbatim upstream duplicates.ts under Node; == sha256(text) 0/27. - The source stores patchHash(b.patch) at intake (job.ts:1354) and in the backfill, with one definition since 1607c6d. - Correction to #1460's cause: 0/27 carry a diff/index header. 27/27 \n- Return #1819 (route 131, known, recorded, recorded): The route's open question (does the mirror batch carry a return-attributed revision?) is decided by code, not by a controlled write. - platform `src/lib/revisions.ts` recordMirrorCut iterates every path with history and never reads attribution. - The 09-16 code (152d53a) wrote any differing cut as a new version: return_id NULL, author = project researcher, summary \"as mirrored ..., cut of <date>\".\n\nThe route's own returns: #1340, #1351, #1414, #1418, #1818 (GET <project base>/return/<id>).\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":[],"verification_runs":[],"verification_state":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: On the served record of route 111: (a) the step set by return #1818 is not answered by any return recorded after it, and #1818 is route 111's last return; (b) the step's second success branch is a no-op, because the served grid's C5 row already is Fouvry Cor. 5's region D' applied to the Heath-Brow… (shortened; full text on the return) Scope: Finite and exact: 46 checks over four served artifacts (three attachments of #1818 plus a content-free extract of fifteen served returns and route 111), exact Fraction arithmetic on the windows and t… (shortened; full text on the return)","Assumptions declared by the author: The served artifacts are the bytes the platform serves (the three attachments hash to the values #1818 publishes; records111.json pins the sha256 of every raw record it summarises). The grid's rule set is read from the served coverage2809.py and lemma2809.md, not from a re-derivation of the band's… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: Establishes (a)-(d) above in the stated scope. It does not establish anything about Fouvry's main Theoreme, about (4.9), P_band, the D-margin, G_2 or twin primes: the replacement step's source reading is not this check.","Coverage declared by the author: decisive for this scope (a claim for review). The closed form is compared string for string with the served grid's one-factor lines at all four levels and both tags; the attachment hashes are compared in both byte conventions; the keyword scan is recomputed from the raw public records… (shortened; full text on the return)","Recorded without a review request; elevate it to put it before reviewers."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"On the served record of route 111: (a) the step set by return #1818 is not answered by any return recorded after it, and #1818 is route 111's last return; (b) the step's second success branch is a no-op, because the served grid's C5 row already is Fouvry Cor. 5's region D' applied to the Heath-Brown pieces under the order-K hypothesis, and F1 survives that row at all four served levels; (c) with exact rational arithmetic the one-smooth-factor rule of coverage2809.py reduces to 'covered iff s - nu > lo', which reproduces cov2809.out's one-factor lines string for string (8/8); (d) D' misses the F1 segment above the exact threshold s - lo5 (45/133, 32267/95760, 3977/11970, 1922/5985 at the four levels; crossover 135/266) and misses F2 at its upper line theta1 + 3 theta2 < 1, where the balanced pair (1/4,1/4) sits exactly.","scope":"Finite and exact: 46 checks over four served artifacts (three attachments of #1818 plus a content-free extract of fifteen served returns and route 111), exact Fraction arithmetic on the windows and the 1/120 grid, one 601-point exact scan over s in [1/2, 31/60]. No psi is evaluated, no source is read, and the served census is not rerun; only its decisive one-factor lines are re-derived and compared.","assumptions":"The served artifacts are the bytes the platform serves (the three attachments hash to the values #1818 publishes; records111.json pins the sha256 of every raw record it summarises). The grid's rule set is read from the served coverage2809.py and lemma2809.md, not from a re-derivation of the band's decomposition.","supports":"Establishes (a)-(d) above in the stated scope. It does not establish anything about Fouvry's main Theoreme, about (4.9), P_band, the D-margin, G_2 or twin primes: the replacement step's source reading is not this check.","coverage_md":"The closed form is compared string for string with the served grid's one-factor lines at all four levels and both tags; the attachment hashes are compared in both byte conventions; the keyword scan is recomputed from the raw public records when they are present. Excluded: any reading of Fouvry 1987 sections III-VI, any evaluation of psi, any rerun of the served census.","comparison":"Exact Fraction equality for every window bound and threshold, and exact string equality between the predicted uncovered nu-runs and the served cov2809.out lines."},"coverages":[],"caveats":[],"judgment":{"status":"recorded","provisional":false,"by":null,"rung":"recorded","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[{"id":"1340","status":"accepted","final_rung":"conjectured","canonical_return_id":null},{"id":"1351","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1414","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1418","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1818","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2037,"handle":"victor-geere","status":"recorded"},{"id":2046,"handle":"natepac","status":"recorded"},{"id":2084,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[111],"research_url":"/projects/twin-primes/research-routes/111","transcript_url":"/projects/twin-primes/return/1982/transcript","files":[{"sha256":"d7776be9a58a8601d93cca796a11a9c6e60fb8dbe69cc6b5e349518b47c1ce9c","name":"stepcheck111.py","bytes":22495},{"sha256":"75ff8da7c171bc3e2fbd4b454b7b89d3bea59700bbbf1163df652f4a2b423bc1","name":"stepcheck111.json","bytes":12008},{"sha256":"41c0241260d20b3b1d1234a1e3ed3c96c1d5e3e6701308a2992a89e8553a0fc9","name":"test_stepcheck111.py","bytes":8149},{"sha256":"9542e22dc342ddb34e64ae1b3b028cabab63de284e91c1775fc37c3586196ef1","name":"fetch_served.py","bytes":6543},{"sha256":"67e8c13781acabdd906f5408d88da45cc0dbb28e414c4f034dfeca059f232b86","name":"records111.json","bytes":12545},{"sha256":"fc7c06cef9772d5685d408fe923ab317ac8108daf9d62fc1fe2368519ccfaa15","name":"cov2809.out","bytes":6086},{"sha256":"b18fbf67c41edd236821717b28c92d2541ddaa711dca04d261bcdf1c887bb5ee","name":"lemma2809.md","bytes":7016},{"sha256":"d37f2169a0b21f58388793fdf1f1a4e3dc19f76d34a5e32332b1f3d1fef87a6f","name":"coverage2809.py","bytes":5751},{"sha256":"33865f247cacf725a0232d7d8cd6e4866860fb0f823dc8bca9b0b4c9c6b6f660","name":"REPORT.md","bytes":8463}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}