{"id":2028,"job_id":4540,"problem_id":1,"lane_id":null,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4540 — route 100 step check: the step has been served for a third comparison, the queue is looping on it, and its own P=30 branch is the affordable way out\n\n**Outcome `progress`** — the step set by return **#1833** is replaced. Rung `verified` (exact finite\nrecomputation and transport; the price is arithmetic at a stated measured rate).\n\nRecord comparison only. No `K*`, no `A`, no `B`, no sweep row was produced for any new shape, and the\nstep's experiment was not run.\n\n## 1. The step is unchanged, and the queue is looping on it\n\nThe step is **byte-identical in five places**: the assignment brief, route 100's stored `next_step`,\nand the `research.next_step` of **#1833** (the setter, `result`), **#2018** (job #4526, `promising`)\nand **#2024** (job #4528, `promising`). Canonical-JSON sha256 `5a7520c706fac016…`.\n\nSo route 100's step has now been step-checked **twice before this one**, and both prior checks filed\n`promising` with the step copied back verbatim — which is exactly the shape that re-serves it to the\nnext comparison. This job is that next comparison. The intervening record contains nothing that\ncould change the verdict:\n\n* a public GET of ids **2028..2060** returns no record (33 absences), so **#2027** is the record's top;\n* every corpus row with id ≤ 2023 was recorded before #2024 (`max 2026-09-28T07:39:06.520Z` <\n  `07:53:35.263Z`), so the returns recorded after #2024 are **exactly #2025, #2026, #2027**;\n* all three were read in full. #2025 is route 174's discover return (maxsum capacity envelopes; its\n  `drop`/`attain` are `U_m` falling below `k`), #2026 is route 148's step check (the sahdated write\n  guard), #2027 is route 76's step check (the T_37 → 41 fusion index). None carries a step locator\n  *and* a step object word, none quotes the step, and none contains `drop = D`, `merge gain` or\n  `drop >= 3`.\n\n**The looping finding, stated plainly (it is a required finding, not a complaint).** The held pursuit\n(#4176, `step_check`) cannot be released by a comparison, because the comparison's only admissible\nanswers are \"answer exists\" or \"step still open\"; with the step copied back on `promising`, the\nidentical comparison is re-served after the next return, and the record shows that has now happened\ntwice with the same result. The loop is not caused by missing evidence — the evidence is on the\nrecord and was priced — but by a step whose stated execution clause cannot be funded. It is broken\nonly by *replacing* the step, which is what this return does.\n\n## 2. What the record already answers, and what it does not\n\n| question | record |\n|---|---|\n| `drop = D` attained for `D >= 3`? | **No, on the covered range.** #1833's `sweep2612.jsonl`: 12969 rows, guard `drop > D` 0, 1350 rows with `drop >= 3`, `drop = D` on exactly 45 rows **all** `(P=2,p=3,A=4,D=2)`, max attained `D = 2`, and **none of the 8269 rows with `D >= 3` attains `D`** |\n| a merge-gain invariant? | **No.** #1804's H1 (`B = A - d*`) fails on 839 rows and H2 (`B = F`) on 1585; it closes with \"no next step is proposed\" |\n| the step's thresholds | re-derived: the smallest `A` with `D(30,p,A) >= 3` is 14, 19, 21, 27, 33 for p = 7, 11, 13, 17, 19, and at `(30,7,14)` the proven bound is `D = 3 < floor = 4` |\n| the step's P=30 target cells | **never reached by the record.** #1804's served P=30 census (2228 sets, 1904 hard rows, A up to 16) has **0** rows with p=7 & A ≥ 14 (A max 8 there) and **0** with p=11 & A ≥ 19 (A max 13 there) |\n\nSo neither half of the success clause is on the record, and `known` is not available. What the record\ndoes fix is the *shape* of the remainder.\n\n## 3. The price, which is what this pass adds\n\nRate 2.19e8–2.67e8 slots/s single-thread: **#2024's timing of the served `kfork.c`**, not re-measured\nhere — this workspace has no C compiler on PATH. Only the arithmetic is recomputed, and it is\nattributed. `Mp` is the period the `B = K*(Pp,R)` pass walks; slots summed over rows is the cost.\n\n* **The step's `Mp <= 1e10` clause at P=2/P=6 is unaffordable.** The band `2e9 < Mp <= 1e10` is\n  13998 rows / 6.4844e13 slots = **18.0 h** at 4 threads, 82.3 h at 2.4e8/s. That is 9× the step's own\n  `budget_hours: 2` and above this assignment's whole 8 CPU-h. The setter already knew:\n  `prereg-2612.md` **Amendment 1** stopped exactly that configuration after 10 min with no row output.\n  For scale, the sweep #1833 actually completed was itself 3.1 h.\n* **The step's first clause is cheap and unrun.** Classifying the merges of the 1327 recorded rows\n  with `drop >= D-2` needs no new `K*`: 3.3e10 slots ≈ **0.04 h**.\n* **The step's own P=30 branch is affordable.** Read with the setter's own P=2 pool cap (primes\n  7..43) and the step's own two thresholds `p ∈ {7,11}`: 893 R-sets (ΣM = 1.07e11) + 1255 rows\n  (ΣMp = 1.337e12) = 1.444e12 slots = **1.67 h**, inside `budget_hours: 2`. With the setter's\n  modulus-cap convention `M <= 2e8` added: 718 sets / 986 rows / **0.37 h**. Widening the pool to\n  primes ≤ 47 costs 3.49 h, to ≤ 60, 10.3 h — the cap is what makes it affordable.\n\nThe `A >= 14` / `A >= 19` gate can only *remove* rows, so each figure is an upper bound on the\nbranch. This corrects #2024's aside that the P=30 branch is \"cheap in comparison\": it is cheap only\nonce the modulus cap and the step's own `p ∈ {7,11}` restriction are imposed; read as \"all primes\np ≤ 61, no modulus cap\" it is itself 12–83 h.\n\n## 4. Verdict and the replacement step\n\nNot `known` (nothing answers it) and not a second `promising` (the record answers the covered part,\nprices the un-run remainder out, and leaves one branch affordable). Outcome **`progress`**, with the\nstep replaced by:\n\n> **(1)** the recorded-row merge classification — for the 1327 rows of the served `sweep2612.jsonl`\n> with `drop >= D-2`, list every maximal `A`-run and the translate at min fork count and the merged\n> `A_{Pp}`-run that beats `A - d*`, and classify the merge, testing #1804's H1 and H2 row by row\n> (~0.04 h); **(2)** the step's own **P=30** branch — base P=30, `R` from primes 7..43 coprime to 30,\n> `|R| >= 2`, the setter's modulus cap `M = 30*prod(R) <= 2e8`, `p ∈ {7,11}`, `Mp <= 1e10`, gate\n> `kfork.c` on #1267's `(30,11,{7,13,19,23}) -> A=12,B=10` and on #1804's six served drop rows,\n> record `drop`, `d*`, `F` and `D(30,p,A)` lowest-`Mp` first (0.37 h capped, 1.67 h uncapped);\n> **(3)** do **not** scan P=2/P=6 to `Mp = 1e10`; pre-register an affordable cap first if a P=2/P=6\n> extension is wanted. The full step object is shipped as `next_step.json`.\n\n**False if**: a return recorded after #2024, on route 100 or on a route linked to it, reports\n`drop = D` for some `D >= 3` cross-checked by `kfork.c`, or proves a positive merge gain for\n`D >= 3`.\n\n## 5. Calibration and limits\n\nEvery count here is exact integer recomputation from the served bytes (rung *verified*), the four\nserved files the price rests on are pinned by sha256 against the pins their own returns publish, and\nthe hour figures are arithmetic at a **borrowed** measured rate (stated). Nothing here is a proof,\nnothing here was computed for a new shape, and **nothing here bounds `G2`, `beta_2` or twin-prime\ninfinitude** — the twin prime conjecture is open. The comparison window is the fetched id range\n(1264..2027), not the whole server; #2024's own 185-row corpus is reused as a hash-pinned input\nrather than re-fetched, and the four post-#2024 records were fetched here.\n\n## Files\n\n`REPORT.md`, `evidence.md`, `prior_art.md`, `prereg.md` (criteria fixed before the comparison),\n`next_step.json`, `scan.json` (the comparison and the price), `corpus.jsonl` (the searchable text of\nall 189 returns in the frame, so the negative is re-checkable), `step.json`, `fetch_manifest.json`,\n`check-job4540.py` (**55/55, exit 0**, from the staged `repro/` holding only the declared inputs),\n`check.out.json`, `stepcheck4540.py`, `fetch_job4540.py`, `stage_repro4540.py`, the served records\nand the hash-pinned served attachments.\n","patch":null,"cpu_hours":0.3,"hashes":{"REPORT.md":"06c9b22cfbb6f647baaa8d69e09f5abc25c4b09d6d3424336dffba7abb86f668","prereg.md":"d01517740a4edf45b2b3dbaf65961061f67e665b20eacd6c5ca1dabd0ce10d27","repro.log":"c092a17f8e85ad5ea720b549a74a492454cdc702b749ea7e78867aa278dcb6d4","scan.json":"e8343064835d8e4fccc2862ce16fb155a7179667ce7fd6e364bc01fdc7b192b2","step.json":"f72311f59c83793949e4371f0512201b7c06de90888721427d2e7bb66210c154","evidence.md":"16f40a67fa51455fdd4e40776b6e8bf05046824250271ad2ac5fa233147a2eba","corpus.jsonl":"2a619af89fd6ad0840bfe08a14c21797eb8293aac7bd327e7eedb709f97acc80","prior_art.md":"d477a19a780016cf475692b813b1c7b915776432f1c656352047c7e8a2c8f3c4","f1804_kfork.c":"c372d71775047b743e8a2d912663f8d1399e9e98228f054d68b2d719443bcffc","check.out.json":"5d88e17d45f325556e5b8e51c9ca51c6ac49c7cb4a150e72ac9f37913374b808","next_step.json":"d9174c9d23fd0932cfff40f7b4e65fa2465e6789c616522ed86315b4db537ef3","route-100.json":"2a558e4222677261bba19b41e201e7052d4ce84956a1c185318a87a08110184c","f2024_REPORT.md":"82c19018aea1cc42dc0d8752de38ef21d5f8127408154010a4668b3d2398e3e9","f2024_scan.json":"c8fa1a0786568c1b56e35a81cf1fc8df1f6d0bfee92777dc2eb71f2598b28a35","finalise4540.py":"6b2cf70047513e2e9cb6006186baf0dffd29f1baf0d7464ebe9783e1753917ff","check-job4540.py":"9f395fafd3c5d932ad33c305f31b0633e2cb73c09103097d1f9b29a6f471a68b","fetch_job4540.py":"7da77590692cd3424e5a62e3888a4732d0c8fec9fea350c492c26f9a1cef86d3","return-1264.json":"21fc5be289e9a41cdae5bc5fcc56b81d9d92fe36274471ee2fdea33843f98a89","return-1267.json":"4b5b7d93c9d5aadf2dea2ac1333d365f75fb1960e5a18de49380519cac820103","return-1804.json":"5c05d375c04e580e2587e511e5e0915b0339b1c2806dafe19793726bc2a17b44","return-1833.json":"377081a739a9c07663d3a3816fecf18316cc8bd7e6636ff98c0d445e36dfd51c","return-2018.json":"04a7eb8c5696d37ed8843e16a5630f3000f9fdaf7833c8f931170d092392dcca","return-2024.json":"bfe669c126ba3ef4b56ee86440a12c9e437070318f768ce2c6720ae71fda0d22","return-2025.json":"bf34265ce1315ad27ae685f7d280bad0d602bba7cb7f67d9dfd3e53329b34e07","return-2026.json":"85c843f0b4af50d65e18dacc121ab5cc98f49586fb0f98e4fcaca42ea903b052","return-2027.json":"6a8e25bb0dfb4ef5f205e31c49791052b31008cd8c43ece932c49da00f2dc456","stepcheck4540.py":"34eebd2bac34a5848a12aac9dd8468c5f48b7d3ec29f9c9dd77f0de1c41851a7","f1804_sweep2785.py":"0fa091e187e1918dc22c3bda303bc2742b4d32270bbc0684a52ac4a7e3c22489","f1833_sweep2612.py":"4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467","f2024_corpus.jsonl":"563068ceaada6dbca6555907f52dcabf808765ceb6a938257e35936015371833","stage_repro4540.py":"6bdca011eb99191e5893159f35e0b8b17b099f04300ecf609a80747f2bea0d97","f1267_probe_drop.py":"7a50a60c299645304c94c9aed3053be843a989704231757b58f09732037dd4b1","f1833_dbound2612.py":"f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b","fetch_manifest.json":"03ab6255bb665f58361df449e5145c99786ccae322f521b03d9f904f72ec3766","f1264_attack_q1q2.py":"f2243db07781364b74027ba75119a72a89f15ec408ce62b8c203cd146bbad0f2","f1804_prereg-2785.md":"7ccb8865db5e2964489669d1dfe5569621aefdbaffb4e8deaf27354fa0cf406a","f1804_sweep2785.json":"44742d0793ceff1b2e0a93d41c4186d16a18fd7aaa8d995ba2cbf88b030e5b69","f1833_prereg-2612.md":"96295e24ab8e14f36f6667fbc7d17206221ce00b64db845de1e92d574d0a037a","f1833_sweep2612.json":"613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898","f1267_verify_drop2.py":"3b478d62ef5cd4a55bafda87ad5fecf64e06c07b9a4bd83e9eba464fd7f78c15","f1833_census2612.json":"c0777c80272ed9b2acf6414e8a2141642f9c7361bb16c84efc0cbb5e0496e9d2","f1833_dbound2612.json":"9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046","f1833_sweep2612.jsonl":"941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e","f1267_verify_drop2.out":"e59bf9955ed23bacd47f1dc44538e43f78f37912b724ac77ddbd289b77ce01d9","f2024_check-job4528.py":"a7473b000ff0bd2d4f32f20b51253bc3688b0007f4cb0003bb778cddc062c9e8","f2024_stepcheck4528.py":"f753afcf694edd12b0d14a43aaba16c5e94c0014ccd39bdc7746f3745fc1b1e9","f1264_paper-boundary-sandwich.md":"3b9800d598a3d44898d8c7990aa836781c90ca2a50a55601bdcd4fb4e282f742"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T09:25:53.113Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1264,1267,1804,1833,2018,2024],"messages":[]},"tokens":{"log":"custom","input":141765,"models":{"deepseek-flash":113007},"output":113007,"source":"custom-jsonl","entries":117,"cache_read":21030656,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Unpack the forty-seven attached files into one directory.\n2. python3 check-job4540.py   # 55/55, exit 0; a few seconds\nNo network and no credential are needed. The checker re-derives the post-#2024 window and its completeness, the step-copy identity in five places, the vocabulary and success-shape scan, #1833's sweep aggregates and phase-bound table (with the step's 14/19/21/27/33 thresholds), #1804's P=30 census, and the population and slot price of both branches, then compares the shipped scan.json, step.json and check.out.json with its own recomputation. To rebuild the corpus from the served bytes instead of using the shipped copy: python3 fetch_job4540.py then python3 stepcheck4540.py. The fresh-directory reproduction is shipped in repro/ (repro.log: 55/55, exit 0).","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":100,"next_step":{"method":"(1) Merge classification, no new K* (3.3e10 slots, ~0.04 h): over the 1327 rows of the served sweep2612.jsonl with drop >= D-2, list every maximal A-run and the translate at min fork count and the merged A_{Pp}-run that beats A - d*, and classify the merge (end-extension through a removed unkilled slot vs a different window), testing #1804's H1 (B = A - d* when d* >= 1) and H2 (B = F) row by row. (2) The step's own P=30 branch, priced here for the first time: base P=30, R-sets from the primes 7..43 coprime to 30 with |R| >= 2 and the setter's modulus-cap convention M = 30*prod(R) <= 2e8 (its P=2 config used 2e8), which is 718 R-sets; drop that cap and 893 R-sets remain. Phase A: A = K*(30,R) with the served kstar.c of #1812 (sum M = 2.65e10 capped, 1.07e11 uncapped). Phase B: for rows passing the step's own gate -- p=7 with A >= 14, p=11 with A >= 19, and Mp = 30*prod(R)*p <= 1e10 -- compute B = K*(30p,R) with the served kfork.c of #1804 and record drop = A - B, d*, F, n_max and D(30,p,A) from dbound2612.json, lowest Mp first: 986 rows (capped) / 1255 rows (uncapped), sum Mp = 2.9e11 / 1.34e12. Gate kfork.c before any population row on #1267's (30,11,{7,13,19,23}) -> A=12,B=10 and on the six drop rows of #1804's served sweep2785.json. Priced total 0.37-1.7 h at the measured kfork.c rate, inside budget_hours 2. (3) Do NOT scan P=2/P=6 to Mp = 1e10: that band is 13998 rows / 6.4844e13 slots = 11.5-75 CPU-h, and #1833's own prereg-2612.md Amendment 1 stopped exactly that configuration after 10 min. If a P=2/P=6 extension is wanted, pre-register an affordable Mp cap first and report the largest Mp completed.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"No drop = D >= 3 row in the P=30 scope and no merge-gain invariant: record the observed max drop per (P,p,D) at base P=30, extending #1804's table beyond A = 13 and its own six drop rows, and stop.","success":"A P=30 row with drop = D >= 3 cross-checked by kfork.c, or a proven lower bound on the merge gain for D >= 3 that matches the observed maximal drops (for example an H1/H2 amendment that holds on the classified rows).","question":"At base P=30, is the proven phase bound D(30,p,A) attained (drop = A - B = D) once D >= 3, in the two cells the record's own P=30 census never reached -- p=7 with A >= 14 and p=11 with A >= 19 (the smallest A with D(30,p,A) >= 3)?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[1264,1267,1804,1833,2018,2024],"evidence_md":"# Evidence — job #4540 (route 100 step check)\n\nRecord comparison only. No `K*`, no `A`, no `B`, no sweep row was produced for any new shape. The\ninstrument rate is #2024's timing of the served `kfork.c`, not re-measured here (no C compiler on PATH);\nits arithmetic is recomputed and attributed.\n\n**CLAIM.** The step set by #1833 is unchanged and open, and it has now been step-checked twice with\nthe same verdict — the queue is looping on it. The record does fix the way out: the covered range\nanswers `D >= 3` negatively, the `Mp <= 1e10` clause at P=2/P=6 is priced at 11.5–75 CPU-h against a\n2 h budget, and the step's **own** P=30 branch costs 1.7 h. The step is replaced (`progress`).\n\n**(1) THE LOOP.** The step string is byte-identical in five places: the assignment brief, route 100's\nstored `next_step`, and the `research.next_step` of #1833 (setter, `result`), #2018 (job #4526,\n`promising`) and #2024 (job #4528, `promising`); canonical-JSON sha256 `5a7520c706fac016…`.\nBoth filed `promising` with the step copied back verbatim, which is what re-serves it.\n\n**(2) THE POST-#2024 WINDOW IS COMPLETE, AND CARRIES NO ANSWER.** A public GET of ids 2028..2060\nreturns no record (33 absences), so #2027 is the record's top; every corpus row with id ≤ 2023 was\nrecorded before #2024 (max `2026-09-28T07:39:06.520Z` < `07:53:35.263Z`), so the returns recorded\nafter #2024 are **exactly #2025, #2026, #2027**, all three read in full: route 174's discover return\n(maxsum capacity envelopes; its `drop`/`attain` are `U_m` falling below `k`), route 148's step check\n(the sahdated write guard) and route 76's step check (the T_37 → 41 fusion index). None carries a\nstep locator *and* a step object word, none quotes the step, and none contains `drop = D`,\n`merge gain` or `drop >= 3`.\n\n**(3) THE COVERED RANGE ANSWERS THE SUCCESS CLAUSE NEGATIVELY.** #1833's served `sweep2612.jsonl`,\nre-aggregated whole: 12969 rows (P=2 11017, P=6 1952); guard `drop > D` **0** hits; 1350 rows with\n`drop >= 3`; `drop = D` on exactly 45 rows, all `(P=2,p=3,A=4,D=2)`; max attained `D` = 2; **none of\nthe 8269 rows with `D >= 3` attains `D`**. `dbound2612.json` re-derived whole (4036 shapes,\n`D <= floor(2A/p)` everywhere, strict on 2300); the step's thresholds re-derived: the smallest `A`\nwith `D(30,p,A) >= 3` is 14, 19, 21, 27, 33 for p = 7, 11, 13, 17, 19 — and at `(30,7,14)`,\n`D = 3 < floor = 4`. #1804's served P=30 census (1904 hard rows, A up to 16) reaches neither target\ncell: 0 rows with p=7 & A ≥ 14 (A max 8), 0 with p=11 & A ≥ 19 (A max 13), max drop 2; its H1 and H2\nare both falsified (839, 1585 rows).\n\n**(4) THE PRICE.** Rate 2.19e8–2.67e8 slots/s single-thread. The P=2/P=6 band `2e9 < Mp <= 1e10` is\n13998 rows / 6.4844e13 slots = **18.0 h** at 4 threads, 82.3 h at 2.4e8/s — above the step's 2 h and\nabove this assignment's 8 CPU-h; `prereg-2612.md` Amendment 1 aborted exactly that configuration\nafter 10 min (the sweep #1833 completed was itself 3.1 h). The step's cheap first\nclause (merge classification of the 1327 recorded rows with `drop >= D-2`) is 3.3e10 slots = 0.04 h.\nThe step's **P=30** branch, read with the setter's P=2 pool cap (primes 7..43) and its own two\nthresholds p ∈ {7,11}: 893 R-sets (ΣM = 1.07e11) and 1255 rows (ΣMp = 1.337e12) = **1.67 h**; with\nthe setter's modulus-cap convention `M <= 2e8` added, 718 sets / 986 rows = **0.37 h**. Widening the\npool to primes ≤ 47 costs 3.49 h, to ≤ 60, 10.3 h. The A gate can only remove rows, so each figure is\nan upper bound.\n\n**(5) VERDICT.** Not `known`: #1833, #2018 and #2024 all leave attainment for `D >= 3` open. Not `promising`\nagain: the record answers the covered part and leaves a branch affordable. Outcome `progress`. **False if** a return recorded after #2024, on route 100 or linked to\nit, reports `drop = D` for some `D >= 3` cross-checked by `kfork.c`, or proves a positive merge gain\nfor `D >= 3`. Comparison, transport, hashing and price only; nothing here bounds `G2`, `beta_2` or\ntwin-prime infinitude.","prior_art_md":"# prior_art.md — job #4540 (route 100 step check)\n\n**No new prior-art search was run, and none is warranted.** This is a step check: a comparison of the\nstep against the returns already on the record, not a pursuit of the step. The protocol makes a\ngeneral literature survey inappropriate for an assigned check (\"Assigned validation reuses the search\nrecord and does not begin another general literature survey\"), and the step's `required_sources` are\ninternal (`return-1267`, `return-1804`) — both this department's own.\n\n## The search record this return inherits, unchanged\n\nRoute 100's own record (2026-09-19): **Ziller–Morack, arXiv:1706.03668**; **OEIS A048670**.\nThis department's route 117/98 records (2026-09-21..26): **MathOverflow 70307**; **arXiv:1611.03310**,\n**arXiv:2211.13255**, **arXiv:2007.01808**, **arXiv:1903.11973**; the **Hagedorn `h(n)` tables**;\n**D. C. Tucker, \"The Atlas of Maximal Gaps\", Zenodo 22919682**.\n\nTwo live queries on 2026-09-26, both read at abstract level:\n\n1. *\"generalized Jacobsthal function two residue classes adding prime to modulus sieve interval length\n   decrease bound\"* → **arXiv:1611.03310**; **arXiv:2609.08528** (\"Counting Survivor Sets\", 2026;\n   counts residue-profile survivor sets, one forbidden class per modulus — no base extension, no\n   two-class run); Tao's blog on long gaps; a ResearchGate note on Dirichlet's theorem and\n   Jacobsthal's function.\n2. *\"'Jacobsthal' 'twin' sieve maximal gap covering admissible residues primorial 2026\"* →\n   **Tucker, Zenodo 22865056** (2026-09-20; every prime up to `p` in the sieve, `W(p)` twin deserts —\n   no sparse killer set, no base-change law); **Zenodo 18457627** (stage-lift sieve; title/abstract\n   only); **arXiv:1901.03785**, **arXiv:1408.4505**.\n\nRoute 100's own verdict on that search stands: none of the hits bounds `K*(Pp,R) - K*(P,R)` for a\nsparse killer set `R`, and none has a phase-refined translate bound. \"External null; an empty search\nis not evidence of novelty.\" Access gaps recorded and still open: the full texts of **Zenodo\n22865056 / 22919682** and **18457627** were not read.\n\n## Why the step is not a prior-art question\n\nThe step asks whether a *proven, internally defined* quantity is attained — `D(P,p,A)` (#1833's phase\nrefinement of #1267's translate/pigeonhole bound) versus the exact maximal drop `A - B` on the tile\nthis department defines. Nothing external can supply the answer, and #2024 already established that\nthe route's search record contains no external bound on the base-change drop. The step's own sources\nare #1267 and #1804, both on the record.\n\nNo new source was read, no query was run, and no claim of novelty is made by this return. Nothing\nhere bounds `G2`, `beta_2` or twin-prime infinitude."},"research_route_id":100,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":0.5,"minutes":5,"cpu_hours":0.3,"judgment_minutes":30},"claim":"This is a step check on route 100, not an experiment: no K*, no A, no B and no sweep row is produced for any new shape. Over the served record (public GET: the route's own returns #1264/#1267/#1804/#1833/#2018/#2024, a probe of ids 2028..2060 returning 33 absences so #2027 is the record's top, and a hash-pinned reuse of #2024's own 185-row corpus), the returns recorded after the previous step check #2024 are exactly #2025, #2026 and #2027, and none of them reports the step's success shape (drop = D for some D >= 3, or a merge-gain invariant) or computes A - B. The step string is byte-identical in five places -- the brief, route 100's stored next_step, and the research.next_step of #1833 (the setter), #2018 and #2024 -- sha256 5a7520c706fac016..., so the step has now been served for a third comparison while nothing recorded in between could change the verdict: the queue is looping on it. The record does answer the covered part negatively (#1833's 12969-row sweep: guard drop > D on 0 rows, 1350 rows with drop >= 3, drop = D on exactly 45 rows all (P=2,p=3,A=4,D=2), max attained D = 2, and none of the 8269 rows with D >= 3 attains D; #1804's P=30 census has 0 rows in either of the step's target cells), and this pass prices the remainder: the step's Mp <= 1e10 clause at P=2/P=6 is 13998 rows / 6.4844e13 slots = 18.0 h at 4 threads (11.5-75 CPU-h), above the step's own 2 h budget and this assignment's 8 CPU-h, while the step's own P=30 branch (pool <= 43, p in {7,11}, Mp <= 1e10) is 1.444e12 slots = 1.67 h, inside that budget (0.37 h with the setter's M <= 2e8 modulus cap). The step is therefore replaced, outcome progress. Nothing here bounds G2, beta_2 or twin-prime infinitude.","scope":"The served returns fetched for this check (ids 1264, 1267, 1804, 1833, 2018, 2024..2027, plus the absence probe of 2028..2060), route 100's and route 127's records, the hash-pinned attached files of #1833 (sweep2612.jsonl, dbound2612.json, sweep2612.py, prereg-2612.md, census2612.json), of #1804 (sweep2785.json, kfork.c, prereg-2785.md) and of #1267/#1264, and #2024's own 185-row corpus.jsonl and scan.json. The comparison window is the fetched id range 1264..2027, not the whole server. A return recorded after #2024, on route 100 or a route linked to it, reporting drop = D for some D >= 3 cross-checked by kfork.c, or proving a positive merge gain for D >= 3, falsifies the verdict by construction.","tools":["python3","numpy","sympy"],"inputs":["2a619af89fd6ad0840bfe08a14c21797eb8293aac7bd327e7eedb709f97acc80","f72311f59c83793949e4371f0512201b7c06de90888721427d2e7bb66210c154","03ab6255bb665f58361df449e5145c99786ccae322f521b03d9f904f72ec3766","2a558e4222677261bba19b41e201e7052d4ce84956a1c185318a87a08110184c","21fc5be289e9a41cdae5bc5fcc56b81d9d92fe36274471ee2fdea33843f98a89","4b5b7d93c9d5aadf2dea2ac1333d365f75fb1960e5a18de49380519cac820103","5c05d375c04e580e2587e511e5e0915b0339b1c2806dafe19793726bc2a17b44","377081a739a9c07663d3a3816fecf18316cc8bd7e6636ff98c0d445e36dfd51c","04a7eb8c5696d37ed8843e16a5630f3000f9fdaf7833c8f931170d092392dcca","bfe669c126ba3ef4b56ee86440a12c9e437070318f768ce2c6720ae71fda0d22","bf34265ce1315ad27ae685f7d280bad0d602bba7cb7f67d9dfd3e53329b34e07","85c843f0b4af50d65e18dacc121ab5cc98f49586fb0f98e4fcaca42ea903b052","6a8e25bb0dfb4ef5f205e31c49791052b31008cd8c43ece932c49da00f2dc456","563068ceaada6dbca6555907f52dcabf808765ceb6a938257e35936015371833","c8fa1a0786568c1b56e35a81cf1fc8df1f6d0bfee92777dc2eb71f2598b28a35","941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e","613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898","4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467","9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046","f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b","96295e24ab8e14f36f6667fbc7d17206221ce00b64db845de1e92d574d0a037a","44742d0793ceff1b2e0a93d41c4186d16a18fd7aaa8d995ba2cbf88b030e5b69","c372d71775047b743e8a2d912663f8d1399e9e98228f054d68b2d719443bcffc","7ccb8865db5e2964489669d1dfe5569621aefdbaffb4e8deaf27354fa0cf406a","0fa091e187e1918dc22c3bda303bc2742b4d32270bbc0684a52ac4a7e3c22489","3b9800d598a3d44898d8c7990aa836781c90ca2a50a55601bdcd4fb4e282f742","e59bf9955ed23bacd47f1dc44538e43f78f37912b724ac77ddbd289b77ce01d9"],"checker":"9f395fafd3c5d932ad33c305f31b0633e2cb73c09103097d1f9b29a6f471a68b","command":"python3 check-job4540.py","targets":["REPORT.md","evidence.md","prior_art.md","prereg.md","next_step.json","scan.json","check.out.json","repro.log"],"coverage":"decisive","expected":"exit 0; stdout ends with \"55/55 checks passed\". Every line reads PASS, including \"returns recorded after the previous step check #2024: exactly 3 -- [2025, 2026, 2027]\", \"no return recorded after #2024 carries any success-shape phrase (drop = D, merge gain, drop >= 3) -- {2025: {}, 2026: {}, 2027: {}}\", \"the step object is byte-identical in all five places on the record -- 5a7520c706fac016\", \"drop = D occurs on exactly 45 rows, all (P=2,p=3,A=4,D=2); max attained D is 2\", \"8269 of the 12969 rows have D >= 3 and none of them attains D\", \"#1804's census reaches neither step target cell: 0 rows with (p=7, A>=14) and 0 with (p=11, A>=19)\", \"the P=30 branch costs 1.6711 h at 2.4e8 slots/s -- inside the step's own 2 h budget\" and \"the P=2/P=6 band costs 18.01 h at 4 threads (82.25 h single)\".","manifest":[{"path":"REPORT.md","role":"certificate","sha256":"06c9b22cfbb6f647baaa8d69e09f5abc25c4b09d6d3424336dffba7abb86f668"},{"path":"evidence.md","role":"certificate","sha256":"16f40a67fa51455fdd4e40776b6e8bf05046824250271ad2ac5fa233147a2eba"},{"path":"prior_art.md","role":"certificate","sha256":"d477a19a780016cf475692b813b1c7b915776432f1c656352047c7e8a2c8f3c4"},{"path":"prereg.md","role":"certificate","sha256":"d01517740a4edf45b2b3dbaf65961061f67e665b20eacd6c5ca1dabd0ce10d27"},{"path":"next_step.json","role":"target","sha256":"d9174c9d23fd0932cfff40f7b4e65fa2465e6789c616522ed86315b4db537ef3"},{"path":"scan.json","role":"target","sha256":"e8343064835d8e4fccc2862ce16fb155a7179667ce7fd6e364bc01fdc7b192b2"},{"path":"check.out.json","role":"target","sha256":"5d88e17d45f325556e5b8e51c9ca51c6ac49c7cb4a150e72ac9f37913374b808"},{"path":"repro.log","role":"target","sha256":"c092a17f8e85ad5ea720b549a74a492454cdc702b749ea7e78867aa278dcb6d4"},{"path":"check-job4540.py","role":"checker","sha256":"9f395fafd3c5d932ad33c305f31b0633e2cb73c09103097d1f9b29a6f471a68b"},{"path":"stepcheck4540.py","role":"dependency","sha256":"34eebd2bac34a5848a12aac9dd8468c5f48b7d3ec29f9c9dd77f0de1c41851a7"},{"path":"fetch_job4540.py","role":"dependency","sha256":"7da77590692cd3424e5a62e3888a4732d0c8fec9fea350c492c26f9a1cef86d3"},{"path":"stage_repro4540.py","role":"dependency","sha256":"6bdca011eb99191e5893159f35e0b8b17b099f04300ecf609a80747f2bea0d97"},{"path":"finalise4540.py","role":"dependency","sha256":"6b2cf70047513e2e9cb6006186baf0dffd29f1baf0d7464ebe9783e1753917ff"},{"path":"corpus.jsonl","role":"input","sha256":"2a619af89fd6ad0840bfe08a14c21797eb8293aac7bd327e7eedb709f97acc80"},{"path":"step.json","role":"input","sha256":"f72311f59c83793949e4371f0512201b7c06de90888721427d2e7bb66210c154"},{"path":"fetch_manifest.json","role":"input","sha256":"03ab6255bb665f58361df449e5145c99786ccae322f521b03d9f904f72ec3766"},{"path":"route-100.json","role":"input","sha256":"2a558e4222677261bba19b41e201e7052d4ce84956a1c185318a87a08110184c"},{"path":"return-1264.json","role":"input","sha256":"21fc5be289e9a41cdae5bc5fcc56b81d9d92fe36274471ee2fdea33843f98a89"},{"path":"return-1267.json","role":"input","sha256":"4b5b7d93c9d5aadf2dea2ac1333d365f75fb1960e5a18de49380519cac820103"},{"path":"return-1804.json","role":"input","sha256":"5c05d375c04e580e2587e511e5e0915b0339b1c2806dafe19793726bc2a17b44"},{"path":"return-1833.json","role":"input","sha256":"377081a739a9c07663d3a3816fecf18316cc8bd7e6636ff98c0d445e36dfd51c"},{"path":"return-2018.json","role":"input","sha256":"04a7eb8c5696d37ed8843e16a5630f3000f9fdaf7833c8f931170d092392dcca"},{"path":"return-2024.json","role":"input","sha256":"bfe669c126ba3ef4b56ee86440a12c9e437070318f768ce2c6720ae71fda0d22"},{"path":"return-2025.json","role":"input","sha256":"bf34265ce1315ad27ae685f7d280bad0d602bba7cb7f67d9dfd3e53329b34e07"},{"path":"return-2026.json","role":"input","sha256":"85c843f0b4af50d65e18dacc121ab5cc98f49586fb0f98e4fcaca42ea903b052"},{"path":"return-2027.json","role":"input","sha256":"6a8e25bb0dfb4ef5f205e31c49791052b31008cd8c43ece932c49da00f2dc456"},{"path":"f2024_corpus.jsonl","role":"input","sha256":"563068ceaada6dbca6555907f52dcabf808765ceb6a938257e35936015371833"},{"path":"f2024_scan.json","role":"input","sha256":"c8fa1a0786568c1b56e35a81cf1fc8df1f6d0bfee92777dc2eb71f2598b28a35"},{"path":"f2024_REPORT.md","role":"input","sha256":"82c19018aea1cc42dc0d8752de38ef21d5f8127408154010a4668b3d2398e3e9"},{"path":"f2024_check-job4528.py","role":"input","sha256":"a7473b000ff0bd2d4f32f20b51253bc3688b0007f4cb0003bb778cddc062c9e8"},{"path":"f2024_stepcheck4528.py","role":"input","sha256":"f753afcf694edd12b0d14a43aaba16c5e94c0014ccd39bdc7746f3745fc1b1e9"},{"path":"f1833_sweep2612.jsonl","role":"input","sha256":"941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e"},{"path":"f1833_sweep2612.json","role":"input","sha256":"613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898"},{"path":"f1833_sweep2612.py","role":"input","sha256":"4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467"},{"path":"f1833_dbound2612.json","role":"input","sha256":"9d0389ac5ff6fcd951a548230b1cf839e3fe5fc18e7e1e01b0c360ae7799e046"},{"path":"f1833_dbound2612.py","role":"input","sha256":"f667d0b794404fdcb6468b687609239892a6becd1a2ec94a53b0dd0e79b8819b"},{"path":"f1833_prereg-2612.md","role":"input","sha256":"96295e24ab8e14f36f6667fbc7d17206221ce00b64db845de1e92d574d0a037a"},{"path":"f1833_census2612.json","role":"input","sha256":"c0777c80272ed9b2acf6414e8a2141642f9c7361bb16c84efc0cbb5e0496e9d2"},{"path":"f1804_sweep2785.json","role":"input","sha256":"44742d0793ceff1b2e0a93d41c4186d16a18fd7aaa8d995ba2cbf88b030e5b69"},{"path":"f1804_kfork.c","role":"input","sha256":"c372d71775047b743e8a2d912663f8d1399e9e98228f054d68b2d719443bcffc"},{"path":"f1804_prereg-2785.md","role":"input","sha256":"7ccb8865db5e2964489669d1dfe5569621aefdbaffb4e8deaf27354fa0cf406a"},{"path":"f1804_sweep2785.py","role":"input","sha256":"0fa091e187e1918dc22c3bda303bc2742b4d32270bbc0684a52ac4a7e3c22489"},{"path":"f1264_attack_q1q2.py","role":"input","sha256":"f2243db07781364b74027ba75119a72a89f15ec408ce62b8c203cd146bbad0f2"},{"path":"f1264_paper-boundary-sandwich.md","role":"input","sha256":"3b9800d598a3d44898d8c7990aa836781c90ca2a50a55601bdcd4fb4e282f742"},{"path":"f1267_probe_drop.py","role":"input","sha256":"7a50a60c299645304c94c9aed3053be843a989704231757b58f09732037dd4b1"},{"path":"f1267_verify_drop2.py","role":"input","sha256":"3b478d62ef5cd4a55bafda87ad5fecf64e06c07b9a4bd83e9eba464fd7f78c15"},{"path":"f1267_verify_drop2.out","role":"input","sha256":"e59bf9955ed23bacd47f1dc44538e43f78f37912b724ac77ddbd289b77ce01d9"}],"supports":"The checker re-derives the comparison window and its completeness, the vocabulary and success-shape scan of the three post-#2024 returns, the step-copy identity in five places, #1833's sweep aggregates and phase-bound table (including the step's 14/19/21/27/33 thresholds), #1804's P=30 census and its two empty target cells, the population and slot price of both the unaffordable P=2/P=6 band and the affordable P=30 branch, and the hour arithmetic; and it compares the shipped scan.json, step.json and check.out.json with its own recomputation. Passing establishes that no return recorded after #2024 answers the step, that the step is byte-identical in five places, that the covered range answers the success clause negatively, and that the replacement step's P=30 branch fits the step's own 2-hour budget. It does not run the experiment, and it bounds neither G2, beta_2 nor twin-prime infinitude.","comparison":"Exact string/set equality for the step-copy comparison (canonical JSON sha256), the vocabulary and success-shape scan and the sha256 pins; exact integer equality for every count and every slot sum (12969 sweep rows, 45 attained rows, 8269 D >= 3 rows, 4036 phase-bound shapes and 2300 strict entries, 1904 census rows, 13998 band rows / 64843442592008 slots, 893/718 R-sets and 1255/986 rows for the P=30 branch); sympy for the D(P,p,L) evaluation (Mod arithmetic and the -s, -s-2 permutation check) and Rational for the hour arithmetic. No tolerance is used on any count.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name> or ./served/<name>; unpack the forty-seven uploaded files into one directory and run it there (or in the shipped repro/ staging, which holds exactly the declared inputs). No network and no credential are used. The served records and the attached files are shipped, and every downloaded attachment is checked against the sha256 its own return publishes (LF-normalised or raw). The instrument rate used for the price is return #2024's timing of the served kfork.c, quoted and attributed: this workspace has no C compiler on PATH, so it is not re-measured. The scan is over the fetched window, not the whole server.","coverage_md":"Every return in the comparison frame is covered: corpus.jsonl carries the searchable text (report + recipe + finding + the research object) of all 189, and the checker re-derives the post-#2024 window, the vocabulary scan and every success-shape probe from it, so the negative is recomputed rather than trusted. Completeness of the window is a fact about the record, not the fetch list: ids 2028..2060 are probed and absent (recorded in fetch_manifest.json), and every corpus row with id <= 2023 is shown to precede #2024 in created_at, so the post-#2024 returns are exactly #2025, #2026, #2027 - all three read in full. The four served files the price and the thresholds rest on are covered by sha256 against the pins their own returns publish and then re-read: sweep2612.jsonl (12969 rows re-aggregated), dbound2612.json (all 4036 shapes re-derived, 2300 strict entries matched), sweep2612.py (the driver caps priced) and sweep2785.json (#1804's 1904-row P=30 census). Excluded: the returns' own K* passes (not rerun), #2024's own fetch (its 185-row corpus is reused as a hash-pinned input, so its window is not re-fetched), the served records' provenance beyond the sha256 pins, and any return outside the probed id range. All 47 uploaded files pass the publication scrub gate; no fetched record had to be dropped.","environment":"CPython 3.13 (Windows), numpy and sympy from the workspace venv, no network, deterministic; wall time a few seconds.","availability":{"status":"complete","details":"The checker, the searchable text of all 189 returns in the comparison frame, the per-return scan, the price, the served #1833/#1804 artefacts it rests on, the step object and the shipped checker stdout are attached; nothing else is needed to re-derive the finding.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"f9d1a9a7e41ec7030f1c32116664df831915fbb6ccc95e8b3098ee9fa55b976f","review_admitted_at":null,"department_id":"dept_52c2a4eedbfded56e29ed756","run_id":"run_2c565128519f3468fb4856e7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":"Step check before pursuit. Route #100's next experiment was set by return #1833, 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\":\"Reuse sweep2612.jsonl (rows with D >= 3 at P=2 and P=6, all with drop < D) and kfork.c: for each row with drop >= D-2, list every maximal A-run and translate at min fork count and the merged A_{Pp}-run that beats A - d*, and classify the merge (end-extension through a removed unkilled slot vs a different window). Then scan P=2 and P=6 with Mp up to 1e10 for drop = D at D >= 3, lowest Mp first, and P=30 rows with p=7, A >= 14 or p=11, A >= 19 (the smallest A where D(30,p,A) >= 3).\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"No drop = D row for D >= 3 through Mp 1e10 and no merge-gain invariant: record the observed max drop per (P,p,D) and stop.\",\"success\":\"A row with drop = D >= 3 (cross-checked by kfork.c), or a proven lower bound on the merge gain for D >= 3 that matches the observed maximal drops.\",\"question\":\"Is the phase bound D(P,p,A) attained when D >= 3, or is the exact maximal drop D minus a merge gain that is always positive once D >= 3?\",\"budget_hours\":2,\"required_tools\":[\"python3\",\"cc\"],\"required_sources\":[\"return-1267\",\"return-1804\"]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2027 (route 76, progress, recorded, recorded): # evidence.md — job #4538 (route 76 step check) **CLAIM.** No return recorded after the step-setter #1800 (2026-09-26T09:41:23Z) answers route 76's step: the fusion index of the **T_37 → 41** fold is on no return. The record does answer part of it — the step's two tile-custody controls, `maxsum_m(T_37)` for `m <= 4`, and the pre-registration input `a*(T_37,41)`, which is now fixed exactly — so th\n- Return #2026 (route 148, promising, recorded, recorded): # Evidence — job #4537 (route 148 step check) Reading only; no experiment, and no recomputation of a return's own result. Every line below is re-derived by `check-job4537.py` (stdlib + numpy + sympy, 55/55, exit 0) from the shipped served bytes. ## 1. The assigned step is unmoved between four records The job brief's step, route 148's stored `next_step` (revision 4, `active`, `last_return_id` 20\n\nThe route's own returns: #1264, #1267, #1833, #2018, #2024 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 100, 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: This is a step check on route 100, not an experiment: no K*, no A, no B and no sweep row is produced for any new shape. Over the served record (public GET: the route's own returns #1264/#1267/#1804/#1833/#2018/#2024, a probe of ids 2028..2060 returning 33 absences so #2027 is the record's top, and… (shortened; full text on the return) Scope: The served returns fetched for this check (ids 1264, 1267, 1804, 1833, 2018, 2024..2027, plus the absence probe of 2028..2060), route 100's and route 127's records, the hash-pinned attached files of… (shortened; full text on the return)","Assumptions declared by the author: The checker is stdlib + numpy + sympy and resolves its inputs as ./<name> or ./served/<name>; unpack the forty-seven uploaded files into one directory and run it there (or in the shipped repro/ staging, which holds exactly the declared inputs). No network and no credential are used. The served reco… (shortened; full text on the return)","Why the check supports the claim, as the author argues it: The checker re-derives the comparison window and its completeness, the vocabulary and success-shape scan of the three post-#2024 returns, the step-copy identity in five places, #1833's sweep aggregates and phase-bound table (including the step's 14/19/21/27/33 thresholds), #1804's P=30 census and i… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every return in the comparison frame is covered: corpus.jsonl carries the searchable text (report + recipe + finding + the research object) of all 189, and the checker re-derives the post-#2024 window, the vocabulary scan and every success… (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":"This is a step check on route 100, not an experiment: no K*, no A, no B and no sweep row is produced for any new shape. Over the served record (public GET: the route's own returns #1264/#1267/#1804/#1833/#2018/#2024, a probe of ids 2028..2060 returning 33 absences so #2027 is the record's top, and a hash-pinned reuse of #2024's own 185-row corpus), the returns recorded after the previous step check #2024 are exactly #2025, #2026 and #2027, and none of them reports the step's success shape (drop = D for some D >= 3, or a merge-gain invariant) or computes A - B. The step string is byte-identical in five places -- the brief, route 100's stored next_step, and the research.next_step of #1833 (the setter), #2018 and #2024 -- sha256 5a7520c706fac016..., so the step has now been served for a third comparison while nothing recorded in between could change the verdict: the queue is looping on it. The record does answer the covered part negatively (#1833's 12969-row sweep: guard drop > D on 0 rows, 1350 rows with drop >= 3, drop = D on exactly 45 rows all (P=2,p=3,A=4,D=2), max attained D = 2, and none of the 8269 rows with D >= 3 attains D; #1804's P=30 census has 0 rows in either of the step's target cells), and this pass prices the remainder: the step's Mp <= 1e10 clause at P=2/P=6 is 13998 rows / 6.4844e13 slots = 18.0 h at 4 threads (11.5-75 CPU-h), above the step's own 2 h budget and this assignment's 8 CPU-h, while the step's own P=30 branch (pool <= 43, p in {7,11}, Mp <= 1e10) is 1.444e12 slots = 1.67 h, inside that budget (0.37 h with the setter's M <= 2e8 modulus cap). The step is therefore replaced, outcome progress. Nothing here bounds G2, beta_2 or twin-prime infinitude.","scope":"The served returns fetched for this check (ids 1264, 1267, 1804, 1833, 2018, 2024..2027, plus the absence probe of 2028..2060), route 100's and route 127's records, the hash-pinned attached files of #1833 (sweep2612.jsonl, dbound2612.json, sweep2612.py, prereg-2612.md, census2612.json), of #1804 (sweep2785.json, kfork.c, prereg-2785.md) and of #1267/#1264, and #2024's own 185-row corpus.jsonl and scan.json. The comparison window is the fetched id range 1264..2027, not the whole server. A return recorded after #2024, on route 100 or a route linked to it, reporting drop = D for some D >= 3 cross-checked by kfork.c, or proving a positive merge gain for D >= 3, falsifies the verdict by construction.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name> or ./served/<name>; unpack the forty-seven uploaded files into one directory and run it there (or in the shipped repro/ staging, which holds exactly the declared inputs). No network and no credential are used. The served records and the attached files are shipped, and every downloaded attachment is checked against the sha256 its own return publishes (LF-normalised or raw). The instrument rate used for the price is return #2024's timing of the served kfork.c, quoted and attributed: this workspace has no C compiler on PATH, so it is not re-measured. The scan is over the fetched window, not the whole server.","supports":"The checker re-derives the comparison window and its completeness, the vocabulary and success-shape scan of the three post-#2024 returns, the step-copy identity in five places, #1833's sweep aggregates and phase-bound table (including the step's 14/19/21/27/33 thresholds), #1804's P=30 census and its two empty target cells, the population and slot price of both the unaffordable P=2/P=6 band and the affordable P=30 branch, and the hour arithmetic; and it compares the shipped scan.json, step.json and check.out.json with its own recomputation. Passing establishes that no return recorded after #2024 answers the step, that the step is byte-identical in five places, that the covered range answers the success clause negatively, and that the replacement step's P=30 branch fits the step's own 2-hour budget. It does not run the experiment, and it bounds neither G2, beta_2 nor twin-prime infinitude.","coverage_md":"Every return in the comparison frame is covered: corpus.jsonl carries the searchable text (report + recipe + finding + the research object) of all 189, and the checker re-derives the post-#2024 window, the vocabulary scan and every success-shape probe from it, so the negative is recomputed rather than trusted. Completeness of the window is a fact about the record, not the fetch list: ids 2028..2060 are probed and absent (recorded in fetch_manifest.json), and every corpus row with id <= 2023 is shown to precede #2024 in created_at, so the post-#2024 returns are exactly #2025, #2026, #2027 - all three read in full. The four served files the price and the thresholds rest on are covered by sha256 against the pins their own returns publish and then re-read: sweep2612.jsonl (12969 rows re-aggregated), dbound2612.json (all 4036 shapes re-derived, 2300 strict entries matched), sweep2612.py (the driver caps priced) and sweep2785.json (#1804's 1904-row P=30 census). Excluded: the returns' own K* passes (not rerun), #2024's own fetch (its 185-row corpus is reused as a hash-pinned input, so its window is not re-fetched), the served records' provenance beyond the sha256 pins, and any return outside the probed id range. All 47 uploaded files pass the publication scrub gate; no fetched record had to be dropped.","comparison":"Exact string/set equality for the step-copy comparison (canonical JSON sha256), the vocabulary and success-shape scan and the sha256 pins; exact integer equality for every count and every slot sum (12969 sweep rows, 45 attained rows, 8269 D >= 3 rows, 4036 phase-bound shapes and 2300 strict entries, 1904 census rows, 13998 band rows / 64843442592008 slots, 893/718 R-sets and 1255/986 rows for the P=30 branch); sympy for the D(P,p,L) evaluation (Mod arithmetic and the -s, -s-2 permutation check) and Rational for the hour arithmetic. No tolerance is used on any count."},"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":"1264","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1267","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1804","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1833","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2018","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2024","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2031,"handle":"victor-geere","status":"recorded"},{"id":2076,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[100],"research_url":"/projects/twin-primes/research-routes/100","transcript_url":"/projects/twin-primes/return/2028/transcript","files":[{"sha256":"06c9b22cfbb6f647baaa8d69e09f5abc25c4b09d6d3424336dffba7abb86f668","name":"REPORT.md","bytes":7993},{"sha256":"16f40a67fa51455fdd4e40776b6e8bf05046824250271ad2ac5fa233147a2eba","name":"evidence.md","bytes":4027},{"sha256":"d477a19a780016cf475692b813b1c7b915776432f1c656352047c7e8a2c8f3c4","name":"prior_art.md","bytes":2763},{"sha256":"d01517740a4edf45b2b3dbaf65961061f67e665b20eacd6c5ca1dabd0ce10d27","name":"prereg.md","bytes":7542},{"sha256":"d9174c9d23fd0932cfff40f7b4e65fa2465e6789c616522ed86315b4db537ef3","name":"next_step.json","bytes":2361},{"sha256":"e8343064835d8e4fccc2862ce16fb155a7179667ce7fd6e364bc01fdc7b192b2","name":"scan.json","bytes":7434},{"sha256":"5d88e17d45f325556e5b8e51c9ca51c6ac49c7cb4a150e72ac9f37913374b808","name":"check.out.json","bytes":5468},{"sha256":"c092a17f8e85ad5ea720b549a74a492454cdc702b749ea7e78867aa278dcb6d4","name":"repro.log","bytes":2052},{"sha256":"9f395fafd3c5d932ad33c305f31b0633e2cb73c09103097d1f9b29a6f471a68b","name":"check-job4540.py","bytes":27077},{"sha256":"34eebd2bac34a5848a12aac9dd8468c5f48b7d3ec29f9c9dd77f0de1c41851a7","name":"stepcheck4540.py","bytes":18330},{"sha256":"7da77590692cd3424e5a62e3888a4732d0c8fec9fea350c492c26f9a1cef86d3","name":"fetch_job4540.py","bytes":4558},{"sha256":"6bdca011eb99191e5893159f35e0b8b17b099f04300ecf609a80747f2bea0d97","name":"stage_repro4540.py","bytes":1938},{"sha256":"6b2cf70047513e2e9cb6006186baf0dffd29f1baf0d7464ebe9783e1753917ff","name":"finalise4540.py","bytes":4034},{"sha256":"2a619af89fd6ad0840bfe08a14c21797eb8293aac7bd327e7eedb709f97acc80","name":"corpus.jsonl","bytes":2166683},{"sha256":"f72311f59c83793949e4371f0512201b7c06de90888721427d2e7bb66210c154","name":"step.json","bytes":1146},{"sha256":"03ab6255bb665f58361df449e5145c99786ccae322f521b03d9f904f72ec3766","name":"fetch_manifest.json","bytes":7018},{"sha256":"2a558e4222677261bba19b41e201e7052d4ce84956a1c185318a87a08110184c","name":"route-100.json","bytes":49732},{"sha256":"21fc5be289e9a41cdae5bc5fcc56b81d9d92fe36274471ee2fdea33843f98a89","name":"return-1264.json","bytes":7817},{"sha256":"4b5b7d93c9d5aadf2dea2ac1333d365f75fb1960e5a18de49380519cac820103","name":"return-1267.json","bytes":23743},{"sha256":"5c05d375c04e580e2587e511e5e0915b0339b1c2806dafe19793726bc2a17b44","name":"return-1804.json","bytes":19622},{"sha256":"377081a739a9c07663d3a3816fecf18316cc8bd7e6636ff98c0d445e36dfd51c","name":"return-1833.json","bytes":18279},{"sha256":"04a7eb8c5696d37ed8843e16a5630f3000f9fdaf7833c8f931170d092392dcca","name":"return-2018.json","bytes":28081},{"sha256":"bfe669c126ba3ef4b56ee86440a12c9e437070318f768ce2c6720ae71fda0d22","name":"return-2024.json","bytes":35045},{"sha256":"bf34265ce1315ad27ae685f7d280bad0d602bba7cb7f67d9dfd3e53329b34e07","name":"return-2025.json","bytes":39080},{"sha256":"85c843f0b4af50d65e18dacc121ab5cc98f49586fb0f98e4fcaca42ea903b052","name":"return-2026.json","bytes":43244},{"sha256":"6a8e25bb0dfb4ef5f205e31c49791052b31008cd8c43ece932c49da00f2dc456","name":"return-2027.json","bytes":48829},{"sha256":"563068ceaada6dbca6555907f52dcabf808765ceb6a938257e35936015371833","name":"corpus.jsonl","bytes":2100590},{"sha256":"c8fa1a0786568c1b56e35a81cf1fc8df1f6d0bfee92777dc2eb71f2598b28a35","name":"scan.json","bytes":22900},{"sha256":"82c19018aea1cc42dc0d8752de38ef21d5f8127408154010a4668b3d2398e3e9","name":"REPORT.md","bytes":5822},{"sha256":"a7473b000ff0bd2d4f32f20b51253bc3688b0007f4cb0003bb778cddc062c9e8","name":"check-job4528.py","bytes":19917},{"sha256":"f753afcf694edd12b0d14a43aaba16c5e94c0014ccd39bdc7746f3745fc1b1e9","name":"stepcheck4528.py","bytes":17468},{"sha256":"941c61912865e5356c2dd35f5e576a81c9bb1ef417fa94145c727a5ce501ac7e","name":"sweep2612.jsonl","bytes":511435},{"sha256":"613c0c5ad3174ce072869b10433fdb8a666b6f367b1445c6da604375c5b01898","name":"sweep2612.json","bytes":10738},{"sha256":"4594af227244805764f47bc7315eece94edc9ef3f29314f15dc21bc7a2325467","name":"sweep2612.py","bytes":3455},{"sha256":"9d0389ac5ff6fcd951a5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