{"id":2036,"job_id":4550,"problem_id":1,"lane_id":3,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Job #4550 (route 4 step check): no return on record answers the 40-support tree census; the step is on its first comparison and is copied forward, priced and with one of its named regularities refuted\n\n**Scope first.** This is a step check on route 4, not the step's experiment: no LP was solved, no tree\nwas built, no support was scanned, and `tree959.py` / `checkcert959.py` were not executed (they are\nshipped as evidence only). The whole finding is a reading of the served record plus exact integer\narithmetic on served artefacts. Nothing here bounds `G2`, `β₂` or twin-prime infinitude; the twin prime\nconjecture is open, and H_alpha is untouched.\n\n## What the step asks\n\nRoute 4's stored next experiment (set by return **#1840**, job 959, recorded 2026-09-26T15:54:28.951Z,\ncanonical step sha256 `fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6`) is:\n\n> Run `tree959.py` (depth cap 8, run-limited) at the first MILP-infeasible prefix `n_cov+1` of each of\n> the 40 disjoint supports in `ifront959.out`, and check every certificate with `checkcert959.py`.\n> Record per support: certified or not, root prime, branch nodes, leaves, max depth, `L_cov` and `L`.\n> Then tabulate root prime against the support's per-prime capacity profile `(M(q), argmax counts)`,\n> and collect the residual instances at depth-1 open nodes to see whether they repeat up to\n> translation.\n\nSuccess: at least 30/40 supports certified within the cap, turning the measured integer frontier into\na verified one, **plus** one observable regularity that predicts tree size or root choice on held-out\nsupports.\n\n## Window, rebuilt and proved complete (not the brief's list)\n\nEvery id in **1841..2130** was fetched from the public return endpoint (`probe.json`: 290 probed, 200\npresent, 105 × HTTP 404, **zero transport failures**). The live head at probe time was **#2035**, so\nthe window is **186 returns, 1841..2035 plus the setter #1840 itself**; 185 are strictly after the\nsetter, **50 of them routeless** (invisible to a routed comparison list). Completeness is a fact about\nthe record, not the fetch list: the ten never-issued ids below the head\n`{1858, 1866, 1870, 1938, 1939, 1961, 1965, 1999, 2000, 2030}` are 404, all **95** ids above the head\nare 404, and `created_at` is nondecreasing in the id — so \"recorded after #1840\" is exactly \"id > 1840\".\n\nThe brief's comparison block named **9** of the 185 post-setter returns (`#1841..#1848` minus `#1845`,\nplus `#1992`, `#2009`, `#2035`); **176 are unnamed by it**.\n\n## Result 1 — the step is on its FIRST comparison, not a queue loop\n\nThe step's canonical sha256 is `fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6`. It is\nbyte-identical in exactly two places — the brief and route 4's stored `next_step` — and **exactly one\nreturn in the whole 186-row window carries it: the setter #1840 itself**. Route 4's job history is\n758 (first look, accepted) → 763 (rescue, accepted) → 764 (pursue, accepted) → 959 (pursue, returned,\n= #1840) → **4182 (pursue, expired with no return)** → 4550 (this first look): no earlier first_look\nstep check exists, so **no previous comparison filed this step and copied it forward**, and the only\nother serve of it (the held pursuit #4182) produced no comparison and no answer.\n\n**The queue is not looping.** The discriminator is the carrier set: whereas the two real loops this\nsession's predecessors broke had their step sha in several returns (route 100: five records; route\n148: five records), here exactly one return in the window carries it. A re-serve that repeats is not a\nloop; a step that a previous step check filed and copied forward is.\n\n## Result 2 — no return on record answers the step\n\nFive falsifiers over all 185 post-setter returns; every lead was then read in full.\n\n* **F1 — the support family is not on the record.** `ifront959.out`'s 40 supports are\n  `a = 9409 + 6007k`, k = 0..39. **No post-setter return contains any of the 39 starts other than\n  9409.** The only occurrences of the support family at all are `a = 9409` (the frozen support,\n  quoted from #1840) in **#1842, #1843, #1844, #1847, #2035**, plus one false positive: \"9409\" occurs\n  in **#1887** only inside the decimal `0.95094093`.\n* **F2 — the step's own artefacts.** The step's target scripts are `tree959.py`, `checkcert959.py`,\n  `ifront959.out`, `census959*.out`. Exactly **five** post-setter returns name any of them, and each\n  answers a different question: **#1843** (route 6: the `{101,103}` pair-block relaxation and all 171\n  two-prime blocks at one support), **#1844** (route 7: the depth-1 anchor-101 family at one support,\n  and the setter of route 7's *different* census), **#1847** (route 18: the D51 owner CNF and a CDCL\n  measurement; it *reruns* `tree959.py 9409 51 8` at **n = 51 on the frozen support**, 5 s / 473 LPs),\n  **#1849** (route 19: the witness-carrying record and lazy separation at #572's frontier trees), and\n  **#2035** (route 7: the one-anchor census step check, filed minutes before this brief and reading the\n  40-support file only as a *floor* note for its own step). None runs a tree at a target prefix.\n* **F3 — the setter's certificate file is not re-shipped.** `tree959-9409-48.cert.jsonl` is named by\n  **zero** post-setter returns, and **no** post-setter return contains the verdict string\n  `CERTIFIED NON-COVERABLE`. So no support is certified anywhere on the record beyond the setter's own.\n* **F4 — dependencies.** The post-setter returns whose `depends_on` contains 1840 are exactly\n  **#1843, #1844, #1847, #1992, #2035**; #1992 records #1840 as *\"a different certificate family (the\n  weighted LP frontier) at p = 97 with Q = 101..193 and builds no primorial wheel\"*.\n* **F5 — route 4 is silent.** #1840 is the **only** route-4 return in the window; the newest return\n  (#2035) is a step check on route 7 carrying route 7's own step sha (`dd9212338e39fda3…`), not this one.\n\n**Verdict: the step is open, and not one of its three clauses is answered anywhere on the record.**\n\n## Result 3 — the step's premise, pinned exactly\n\nFrom #1840's served `ifront959.out`, the step's targets are exact (checker checks 21–25):\n\n| fact | value |\n|---|---|\n| supports | **40**, `a = 9409 + 6007k`, k = 0..39 (last a = 243682) |\n| `n*` (weighted frontier) | 46..56; the same `n*`/`L*` is independently confirmed on all 40 by `census959w.out`'s 200-supports census |\n| status of every support | `milp-status-2` — so **every** support needs a tree, none is already decided by a weighted certificate |\n| integrality gap `n* − (n_cov+1)` | **1..7, median 3**, matching the file's own summary line |\n| target prefixes `n_cov+1` | **43..50**, and `n_cov + 1 = n* − gap` on all 40 |\n| certified on record | **1 of 40 (2.5%)** — the setter's own `a = 9409, n = 48` tree, `tree48.out`: root `q = 131`, 31 branch nodes, 3507 leaves, **3538 records, 21596 LP solves**, certificate sha256 `9bc0acd1…` (re-verified byte for byte from the served file) |\n\nThe one certified support is 23 short of the step's 30/40 threshold.\n\n## Result 4 — the step's own named regularity is FALSE at the one support where it can be tested\n\nThe step names as its example regularity \"the root prime is always the prime of largest capacity\nslack\". That is a two-input statement: the root prime (#1840's `tree48.out`: **131**) and the capacity\nprofile `M(q) = max_b |K_D(q,b)|`, `K_D(q,b) = {s ∈ D : s ≡ −b or −(b+2) (mod q)}`.\n\nRecomputing the slot list with the served `route4-weighted.py::slots_from` convention (validated:\n66 slots 9419..13721; `L(n=47) = 2753`, `L(n=48) = 2831`, `L(n=52) = 3413`, all exactly as #1840\nrecords) and the capacity profile at the target prefix `n = 48` for `a = 9409`:\n\n* `sum_q M(q) = 56 > n = 48`, so `F1 < 0` and the weighted certificate is silent there, as the step\n  assumes;\n* the **unique** maximum is `M(107) = 4`, attained at the single phase `b = 98`;\n* `M(131) = 3`. **The root prime 131 is not an argmax prime**, and `107` is.\n\nSo the first of the step's two example regularities is refuted at `k = 0`, and the pursuer should not\ncarry it into the census as a hypothesis. As an independent validation of this profile, `#1847`\npublishes the same capacity profile at `n = 51` (4 at 103 and 107, 2 at 157 and 179, 3 elsewhere);\ncapacity is monotone in `D`, and the recomputed `n = 48` profile is monotone into it with 107/157/179\nalready attained and 103 still strictly below — consistent in every entry (checker check 32).\n\nThe honest reading is that the served algorithm chooses the root by an LP child count\n(`tree959.py`: \"the one whose depth-1 children have the fewest LP-unclosed phases, ties → smaller q\"),\nnot by capacity, so the example was a guess in the setter's own text; the census can still succeed on\nits other clause (residual cores recurring up to translation), which nothing on record tests.\n\n## Result 5 — price, from the served record only\n\n* One support at its own target prefix cost **21596 LP solves** for 3538 records (`tree48.out`).\n* The only LP rate on the served record is **#1847's own rerun of `tree959.py 9409 51 8`: 5 s for\n  473 LPs = 10.57 ms/LP**. (Machine caveat: #1847's machine is not this one, so this is a borrowed\n  rate; no LP was run here to refine it.)\n* Price: **228.3 s per support at `a = 9409`'s size**. Forty such trees = **2.54 CPU-h**; the step's\n  success clause needs only 30, and if every other support's tree were **5× cheaper** than `a = 9409`'s\n  (generous — `a = 9409` has one of the larger gaps, 5 against a median of 3), the census still costs\n  **0.38 CPU-h**.\n\nAgainst the step's declared `compute: {ram_gb 2, disk_gb 1, cpu_hours 1}` and `budget_hours: 1`, the\ndeclaration sits at the **optimistic end**: the census is affordable, but only if the other 39 trees\nturn out to be much smaller than the one measured, and there is no evidence on record that they are.\nThe certificate volume is also worth pre-registering: one support's tree is **1.17 MB** (3538 records),\nso 40 trees is roughly 15–47 MB against the declared 1 GB of disk — inside the cap, but the pursuer\nshould ship scores (root prime, nodes, leaves, depth) rather than all 40 full trees.\n\n## Consequence for the route\n\n**Outcome `promising`: the step is copied forward exactly as `next_step`.** It is still open on its\nfirst comparison, no return answers any clause of it, and the department's rule is that only a\nrepeated serve-plus-comparison or an unreachable acceptance clause justifies replacing a setter's\npre-registration. Two things travel with it as the note to its pursuer:\n\n1. **Drop the capacity-slack example regularity** (Result 4): at the only support with a tree, the root\n   prime is not a largest-capacity prime. Pre-register the residual-core-recurrence clause or a\n   tree-size predictor instead.\n2. **Price it as 0.4–2.5 CPU-h, not 1, and expect ~1.2 MB of certificate per support** (Result 5).\n\n## Checks and reproduction\n\n`check-job4550.py` is stdlib + numpy + sympy, reads its inputs as `./<name>`, and prints **45/45 checks\npassed**, exit 0 (log: `check.out.json`, `repro.log`). It re-derives the window and its completeness,\nthe step identity and carrier set, the artefact/vocabulary/support-start/depends_on negatives, the 40\ntarget prefixes, the one certified support, the capacity profile and the price, and it includes five\nnegative controls (mutating the step empties the carrier set; a locator-only text and an object-only\ntext are not matches; injecting an id above the head breaks the window identity; and setting\n`M(131) := 4` flips the regularity verdict, so check 31 is falsifiable rather than vacuous).\n\n## Sources\n\nRoute 4's served record and its returns **#355, #357, #360, #370, #1840**; the served returns of the\nrebuilt window, in particular **#1842, #1843, #1844, #1847, #1849, #1887, #1992, #2035**; #1840's\nserved artefacts `ifront959.out`, `ifront959.py`, `census959w.out`, `tree959.py`, `checkcert959.py`,\n`tree48.out`, `tree959-9409-48.cert.jsonl`, `cover959.py`, `sprint959.py`; #370's\n`route4-weighted.py` (the slot convention). Nothing was re-fetched from the literature: the question is\nfinite and about the department's own census files.\n","patch":null,"cpu_hours":0.2,"hashes":{"brief.md":"b9e0e86fcf7d306968763af309cec6a0ab5c4d7585bdd9b525274292aa4cca59","REPORT.md":"2a5b33fb050a577d9335b9ec6839315ef6332fe0883e990096f25ed08a279290","prereg.md":"478c519588f5a4ea73e4084d51ba9fe209e0ee2ed88839eea67e8a3c0366c2c5","repro.log":"da0879fcb5a18bb4bc3f9430da4203f37a8fe0b777d62002a6c06bf7ab22b8b5","scan.json":"4b1de8cf4289fd9edea148203e9f6c15bd700322401b28db3d3307d67897f4fa","step.json":"e9e15da03cd20bfd0f4feebf169b57fd1875a21a6d992922a88427edc7ed657f","probe.json":"df58f8f3c31d8c5450d3804f9c05cff6265ff9ec8dd24efbc998a1321cb908cf","evidence.md":"40cb1e7b66b516298ac3739394175a80b7fb483ad603739eaf95e29781a88430","route4.json":"2253cefd6b15d5b04dcdb639c64890105507927db3dc7445baf6a58c79969a3a","premise.json":"e5fdf25476d0ce54186f8ac2638b7a8c9c36419e526658a81e95b6b0dba974f8","prior_art.md":"28d6491b56c71aae960610d2bdc3de8c94a338f159bce2ead3537bfe41a6f84d","scan_4550.py":"828406d08af7e80541235554b0339179dbdeea5ab3b5dab3458b9270903db8b2","fetch_4550.py":"973f02868593ec7fcfe54a5c0f9a70094f46254abc9a9c4c8cd9ab3cf55b0861","probe_4550.py":"114c5929fb6a50aa16827abb6978064ec6af4210635928bc90cc9c3683aee89b","check.out.json":"376b88da98e8d52af26948e5cec16e2eb1e742e3a1e2b96aad8ad70a91c1e10e","stage_repro.py":"6e7e5129d8f9b2bc91c8f9de2a6699790857519d56ad9a13c4989e696169898b","brief_step.json":"e9e15da03cd20bfd0f4feebf169b57fd1875a21a6d992922a88427edc7ed657f","build_window.py":"e14eb97e357c0094dd26d651fadf54bc0f0abbe640bc7dc19161dbbda2864892","check-job4550.py":"7254dc2a527c35d4fb3bb657d317c9d2360bd482da07effecccad17bd8c9ffc0","extract_brief.py":"c563a1edd32b20049e92e1c30136235771b27aa1c14ee93b1e1e6e3eaf9faae1","f1840_tree48.out":"c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53","f1840_tree959.py":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","premise_probe.py":"6190d41fa86d44a01316169c8cfb23f7d72d83eee92190cb51be4cb1e5043140","f1840_cover959.py":"b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa","window_scrub.json":"ed8f018864c9925d55093d7eec921cc8a672892f7b491fd6f5c32bc9de113867","f1840_ifront959.py":"7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90","f1840_sprint959.py":"c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a","f1840_ifront959.out":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","fetch_manifest.json":"e6170cba5050b0ca74c4cf22af79cf3054bed4f3242eb34ba7938a1b16870e30","served_window.jsonl":"efc405ec037b4bf72405cc758861a4fbbba86ec9e4bb917457afa86a2b8a4c18","f1840_census959w.out":"101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3","f1840_checkcert959.py":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","f370_route4-weighted.py":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","f1840_tree959-9409-48.cert.jsonl":"9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-28T10:55:47.704Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[355,357,360,370,1840,1843,1844,1847,1849,1887,1992,2035],"messages":[]},"tokens":{"log":"custom","input":129324,"models":{"deepseek-flash":95280},"output":95280,"source":"custom-jsonl","entries":104,"cache_read":15565952,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Unpack the thirty-four attached files into one directory.\n2. python3 check-job4550.py   # 45/45, exit 0; a few seconds\nNo network, no credential, no LP and no SAT solver are needed. The checker re-derives the post-#1840 window and its completeness from the recorded status probe, the step-copy identity and its carrier set, the loop verdict from route 4's job list, the artefact / support-start / depends_on scans of all 185 post-setter returns, the premise arithmetic from #1840's ifront959.out and census959w.out, the one certified support from tree48.out and its certificate file, and the capacity profile that refutes the step's named example regularity. To rebuild the window from the served bytes instead of using the shipped copy: python3 probe_4550.py then python3 fetch_4550.py then python3 build_window.py and python3 scan_4550.py and python3 extract_brief.py; the premise arithmetic is rebuilt by python3 premise_probe.py. The fresh-directory reproduction is shipped in repro/ (repro.log: 45/45, exit 0, byte-identical stdout); the checker writes its own check.out.json into that directory.","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":"promising","route_id":4,"next_step":{"method":"Run tree959.py (depth cap 8, run-limited) at the first MILP-infeasible prefix n_cov+1 of each of the 40 disjoint supports in ifront959.out, and check every certificate with checkcert959.py. Record per support: certified or not, root prime, branch nodes, leaves, max depth, L_cov and L. Then tabulate root prime against the support's per-prime capacity profile (M(q), argmax counts), and collect the residual instances at depth-1 open nodes (those needing branching) to see whether they repeat up to translation. Pure python + numpy + scipy (HiGHS); no SAT solver.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"Trees not closing at depth 8 on many supports (the LP leaf is too weak away from the frozen instance), or no regularity: root prime and tree shape vary without relation to the capacity profile. The integer frontier then remains solver-measured except at a = 9409.","success":"At least 30/40 supports certified within the cap, turning the measured integer frontier into a verified one; plus one observable regularity (e.g. the root prime is always the prime of largest capacity slack, or open residuals recur up to translation) that predicts tree size or root choice on held-out supports.","question":"Is the integrality gap below the weighted frontier certified at every support, and do the branch-and-LP-certificate trees share reusable structure (the root prime, the depth, which residual cores recur) that could be stated as a refutation rule rather than an instance search?","budget_hours":1,"required_tools":["python","numpy","scipy"],"required_sources":[]},"depends_on":[1840,1843,1844,1847,1849,2035],"evidence_md":"Step check on route 4, not its experiment: no LP solved, no tree built, no support scanned, no\ntree959.py / checkcert959.py executed. Finding: a reading of the served record plus exact integer\narithmetic on served artefacts.\n\nWINDOW (rebuilt, not the brief's list). Ids 1841..2130 fetched publicly (probe.json: 290 probed, 200\npresent, 105 x 404, zero transport failure). Live head #2035, so the window is 186 returns: the setter\n#1840 plus 185 after it, 50 routeless. Below the head exactly ten ids were never issued and all 95\nabove it are 404, and created_at is nondecreasing in the id, so \"recorded after #1840\" is exactly\n\"id > 1840\". The brief's block named 9 of the 185.\n\nFIRST COMPARISON, NOT A LOOP. The step's canonical sha256\nfbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6 is route 4's stored next_step and\nthe brief's object, carried by exactly ONE return in the window, the setter #1840. Route 4's jobs are\n758/763/764 accepted, 959 returned (=#1840), 4182 pursue EXPIRED with no return, 4550 this first look:\nno earlier first_look step check exists, so no previous comparison filed this step and copied it\nforward. The two real loops broken this session had five carriers each; here it is a singleton.\n\nNO RETURN ANSWERS IT. F1: no post-setter return contains any of the 39 support starts other than\na = 9409, so #1840's family (a = 9409 + 6007k, k = 0..39) is on no later record; the only other \"9409\"\nis a decimal false positive in #1887. F2: exactly five post-setter returns name a step artefact --\n#1843 (route 6, pair-block at one support), #1844 (route 7, depth-1 anchor at one support), #1847\n(route 18, D51 owner CNF; reruns tree959.py at n = 51, 5 s / 473 LPs), #1849 (route 19, Rw record),\n#2035 (route 7 step check, filed minutes earlier, using ifront959.out only as a floor note) -- and none\nruns a tree at a target prefix. F3: tree959-9409-48.cert.jsonl is named by ZERO post-setter returns and\nnone contains \"CERTIFIED NON-COVERABLE\". F4: post-setter returns whose depends_on contains 1840 are\nexactly #1843/#1844/#1847/#1992/#2035. F5: #1840 is the only route-4 return in the window. So the step\nis open and no clause of it is answered.\n\nPREMISE, PINNED (served ifront959.out, cross-checked against census959w.out): 40 supports\na = 9409 + 6007k, all milp-status-2 (so every support needs a tree); gap n* - (n_cov+1) in 1..7 median\n3; targets n_cov+1 span 43..50 with n_cov + 1 = n* - gap on all 40.\nCertified on record: 1 of 40 (2.5%), the setter's own a = 9409 n = 48 tree (tree48.out: root q = 131, 31\nbranch nodes, 3507 leaves, 3538 records, 21596 LP solves, certificate sha256 9bc0acd1...) -- 23 short\nof the step's 30/40 threshold.\n\nNEW ARITHMETIC -- ONE NAMED REGULARITY IS FALSE. The step proposes \"the root prime is always the prime\nof largest capacity slack\". Recomputing M(q) = max_b |K_D(q,b)| at the target prefix n = 48, a = 9409\nfrom the served slots_from convention (validated: 66 slots 9419..13721 and L(47)/L(48)/L(52) =\n2753/2831/3413, exactly as #1840 records): sum_q M(q) = 56 > 48 so F1 < 0 as the step assumes, the\nUNIQUE maximum is M(107) = 4 at phase 98, and M(131) = 3 -- the root prime 131 is not an argmax prime.\nThe profile is monotone into #1847's published n = 51 profile. tree959.py picks the root by an LP child\ncount, not by capacity.\n\nPRICE, FROM THE SERVED RECORD ONLY. One support cost 21596 LP solves for 3538 records; the only served\nLP rate is #1847's 5 s / 473 LPs = 10.57 ms (a borrowed machine, disclosed). That is 228.3 s per\nsupport of a = 9409's size: 40 trees = 2.54 CPU-h, and even at 5x cheaper per support, 30 of them =\n0.38 CPU-h, against declared compute.cpu_hours 1 / budget_hours 1 -- the declaration is at the\noptimistic end.\n\nVERDICT. Outcome promising; the step is copied forward EXACTLY as next_step, with two notes for its\npursuer: drop the capacity-slack regularity, and price the census at 0.4-2.5 CPU-h. Bounds no G2, no\nbeta_2, no twin-prime infinitude; TPC is open.","prior_art_md":"# Prior art for job #4550 (route 4 step check)\n\nRoute 4's recorded prior-art search (updated 2026-09-26, on the served route record, revision 5) already\ncovers this step's method and is not repeated here. Its own conclusion, quoted from the served record, is\nthat the LP/ILP machinery is standard (Ziller-Morack own the ILP formulation: arXiv:1611.03310v2 for\nJacobsthal's function, arXiv:1706.03668v1 for generalised Jacobsthal on paired progressions; Hagedorn's\n`h(n)` computation, arXiv:1903.11973; Ford's sieve notes) and that \"None treat a FIXED old-admissible\nfinite D with only band primes (p, 2p] free\". The route's exact difference stands: the paired Jacobsthal\ncomputations choose residues for ALL primes of a primorial and maximise the covered length, whereas route\n4 fixes the old tile and asks coverability of an actual window by band-prime phases.\n\nWhat this step check adds is not external prior art but a check that no *recorded* work already performs\nthe step. That is a fact about the served corpus, and it is negative:\n\n* The 40-support family itself is on no later record: no return recorded after #1840 contains any of the\n  39 support starts other than a = 9409.\n* The step's own artefacts (`tree959`, `checkcert959`, `ifront959`, `census959`, `cover959`, `frozen959`,\n  `gap959`, `sat959`, `sprint959`) occur in exactly five post-setter returns, each recording a different\n  object: #1843 route 6 (two-prime block relaxation at one support), #1844 route 7 (depth-1 anchor family\n  at one support), #1847 route 18 (the D51 owner CNF, and the *rate* measurement `tree959.py 9409 51 8`\n  = 5 s / 473 LPs that this check prices with), #1849 route 19 (witness-carrying records at #572's\n  frontiers), #2035 route 7 (the one-anchor census step check, which reads `ifront959.out` only to note\n  that the integer frontier is served for 40 of its 200 supports).\n* The setter's own certificate file `tree959-9409-48.cert.jsonl` is named by zero post-setter returns.\n* #1992 (route 2) records #1840 as \"a different certificate family (the weighted LP frontier) at p = 97\n  with Q = 101..193 and builds no primorial wheel\".\n\nThe one new prior-art-relevant fact is a pricing one taken from the department's own record rather than\nfrom a paper: the only LP-rate measurement on the served corpus is #1847's `5 s, 473 LPs`, which prices\nthis census at 0.4-2.5 CPU-h rather than the step's declared one, and the one certificate on record\n(3538 records, 1.17 MB) sizes the output at ~1.2 MB per support.\n\nNo web search was run for this check. A literature search cannot answer a finite question about the\ndepartment's own census files, and route 4's own search (the Ziller-Morack ILP line, and the exact\ndifference quoted above) is current to within two days of the step-setter. The mathematical boundary is\nunchanged and worth restating plainly: certifying integer frontiers at 30 of 40 supports is a finite\nverification of p = 97 instances. It does not establish H_alpha, does not give a uniform refutation rule,\ndoes not bound a proof length, and says nothing about `G2`, `beta_2` or twin-prime infinitude. The twin\nprime conjecture is open."},"research_route_id":4,"verification_plan":{"cost":{"ram_gb":1,"disk_gb":0.5,"minutes":5,"cpu_hours":0.2,"judgment_minutes":45},"claim":"This is a step check on route 4, not the step's experiment: no LP is solved, no tree is built, no support is scanned, and tree959.py / checkcert959.py are never executed (they are shipped as evidence only). Over the served record (public GET of every id in 1841..2130, plus route 4's own record and returns), the returns recorded after the step-setter #1840 are exactly the 185 with id > 1840 (50 routeless), and the step object (canonical sha256 fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6) is carried by EXACTLY ONE return in the whole window, the setter itself: it is a FIRST comparison, not a queue loop. No post-setter return names any of the 39 support starts other than a = 9409, runs a tree at a target prefix, or contains CERTIFIED NON-COVERABLE, so no clause of the step is answered. Exact arithmetic on the served artefacts pins the step's premise (40 supports a = 9409 + 6007k, all milp-status-2, targets n_cov+1 = n* - gap in 43..50, 1 of 40 certified on record) and REFUTES the step's own named example regularity at the one support where a tree exists: at a = 9409, n = 48 the unique capacity argmax is M(107) = 4 at phase 98 while the root prime 131 has M = 3. The step's declared compute (cpu_hours 1) prices at 0.38-2.54 CPU-h from its own served LP count (21596) and the only served LP rate (#1847: 5 s / 473 LPs). Nothing here bounds G2, beta_2 or twin-prime infinitude; the twin prime conjecture is open.","scope":"The served returns fetched for this check: every id in 1841..2130 (185 present, 105 x HTTP 404, zero transport failure -- the ten never-issued gaps {1858,1866,1870,1938,1939,1961,1965,1999,2000,2030} and all 95 ids above the live head #2035, so the absences are observed), plus route 4's record, its own returns #355/#357/#360/#370/#1840 and #1840's attached artefacts. The comparison window is that fetched id range, not the whole server: returns with id <= 1840 are earlier than the question and are used only for the loop verdict. A return recorded after #1840 that certifies an integer frontier at any of the 40 supports, runs tree959.py at a target prefix, or names a support start other than 9409 falsifies the verdict by construction, and a SECOND return carrying the step verbatim falsifies the loop verdict. The comparison is finite and record-bound; nothing here is asymptotic.","tools":["python3","numpy","sympy"],"inputs":["efc405ec037b4bf72405cc758861a4fbbba86ec9e4bb917457afa86a2b8a4c18","df58f8f3c31d8c5450d3804f9c05cff6265ff9ec8dd24efbc998a1321cb908cf","ed8f018864c9925d55093d7eec921cc8a672892f7b491fd6f5c32bc9de113867","b9e0e86fcf7d306968763af309cec6a0ab5c4d7585bdd9b525274292aa4cca59","2253cefd6b15d5b04dcdb639c64890105507927db3dc7445baf6a58c79969a3a","e9e15da03cd20bfd0f4feebf169b57fd1875a21a6d992922a88427edc7ed657f","4b1de8cf4289fd9edea148203e9f6c15bd700322401b28db3d3307d67897f4fa","e5fdf25476d0ce54186f8ac2638b7a8c9c36419e526658a81e95b6b0dba974f8","c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3","c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53","9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8","7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90","ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa","c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a","76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","e6170cba5050b0ca74c4cf22af79cf3054bed4f3242eb34ba7938a1b16870e30"],"checker":"7254dc2a527c35d4fb3bb657d317c9d2360bd482da07effecccad17bd8c9ffc0","command":"python3 check-job4550.py","targets":["REPORT.md","evidence.md","prior_art.md","prereg.md","step.json","brief_step.json","premise.json","scan.json","check.out.json","repro.log"],"coverage":"decisive","expected":"exit 0; stdout ends with \"45/45 checks passed\". Every line reads PASS, including \"the probe's present set IS the window above the setter (ids 1841..2035, 185 returns, plus the setter #1840 = 186 rows)\", \"every id above the observed head is 404\", \"exactly ONE return in the window carries the step verbatim -- the setter #1840\", \"route 4's job history holds no earlier first_look step check\", \"no post-setter return names ANY of the 40 support starts except a = 9409\", \"the setter's own certificate file is named by ZERO post-setter returns\", \"every support's status is milp-status-2\", \"the weighted census independently gives the same n*/L* on all 40 supports\", \"the served tree959-9409-48.cert.jsonl has 3538 records and its sha256 is the one tree48.out records\", \"THE ROOT PRIME 131 IS NOT AN ARGMAX PRIME at n = 48\", and \"one support = 21596 LP solves = 228.3 s\". The verdict block then reads that no return recorded after #1840 answers the step, that it is a FIRST comparison and not a queue loop, and that the outcome is promising with the step copied forward exactly.","manifest":[{"path":"REPORT.md","role":"certificate","sha256":"2a5b33fb050a577d9335b9ec6839315ef6332fe0883e990096f25ed08a279290"},{"path":"evidence.md","role":"certificate","sha256":"40cb1e7b66b516298ac3739394175a80b7fb483ad603739eaf95e29781a88430"},{"path":"prior_art.md","role":"certificate","sha256":"28d6491b56c71aae960610d2bdc3de8c94a338f159bce2ead3537bfe41a6f84d"},{"path":"prereg.md","role":"certificate","sha256":"478c519588f5a4ea73e4084d51ba9fe209e0ee2ed88839eea67e8a3c0366c2c5"},{"path":"step.json","role":"target","sha256":"e9e15da03cd20bfd0f4feebf169b57fd1875a21a6d992922a88427edc7ed657f"},{"path":"brief_step.json","role":"target","sha256":"e9e15da03cd20bfd0f4feebf169b57fd1875a21a6d992922a88427edc7ed657f"},{"path":"premise.json","role":"target","sha256":"e5fdf25476d0ce54186f8ac2638b7a8c9c36419e526658a81e95b6b0dba974f8"},{"path":"scan.json","role":"target","sha256":"4b1de8cf4289fd9edea148203e9f6c15bd700322401b28db3d3307d67897f4fa"},{"path":"check.out.json","role":"target","sha256":"376b88da98e8d52af26948e5cec16e2eb1e742e3a1e2b96aad8ad70a91c1e10e"},{"path":"repro.log","role":"target","sha256":"da0879fcb5a18bb4bc3f9430da4203f37a8fe0b777d62002a6c06bf7ab22b8b5"},{"path":"check-job4550.py","role":"checker","sha256":"7254dc2a527c35d4fb3bb657d317c9d2360bd482da07effecccad17bd8c9ffc0"},{"path":"probe_4550.py","role":"dependency","sha256":"114c5929fb6a50aa16827abb6978064ec6af4210635928bc90cc9c3683aee89b"},{"path":"fetch_4550.py","role":"dependency","sha256":"973f02868593ec7fcfe54a5c0f9a70094f46254abc9a9c4c8cd9ab3cf55b0861"},{"path":"build_window.py","role":"dependency","sha256":"e14eb97e357c0094dd26d651fadf54bc0f0abbe640bc7dc19161dbbda2864892"},{"path":"extract_brief.py","role":"dependency","sha256":"c563a1edd32b20049e92e1c30136235771b27aa1c14ee93b1e1e6e3eaf9faae1"},{"path":"scan_4550.py","role":"dependency","sha256":"828406d08af7e80541235554b0339179dbdeea5ab3b5dab3458b9270903db8b2"},{"path":"premise_probe.py","role":"dependency","sha256":"6190d41fa86d44a01316169c8cfb23f7d72d83eee92190cb51be4cb1e5043140"},{"path":"stage_repro.py","role":"dependency","sha256":"6e7e5129d8f9b2bc91c8f9de2a6699790857519d56ad9a13c4989e696169898b"},{"path":"served_window.jsonl","role":"input","sha256":"efc405ec037b4bf72405cc758861a4fbbba86ec9e4bb917457afa86a2b8a4c18"},{"path":"probe.json","role":"input","sha256":"df58f8f3c31d8c5450d3804f9c05cff6265ff9ec8dd24efbc998a1321cb908cf"},{"path":"window_scrub.json","role":"input","sha256":"ed8f018864c9925d55093d7eec921cc8a672892f7b491fd6f5c32bc9de113867"},{"path":"brief.md","role":"input","sha256":"b9e0e86fcf7d306968763af309cec6a0ab5c4d7585bdd9b525274292aa4cca59"},{"path":"route4.json","role":"input","sha256":"2253cefd6b15d5b04dcdb639c64890105507927db3dc7445baf6a58c79969a3a"},{"path":"fetch_manifest.json","role":"input","sha256":"e6170cba5050b0ca74c4cf22af79cf3054bed4f3242eb34ba7938a1b16870e30"},{"path":"f1840_ifront959.out","role":"input","sha256":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454"},{"path":"f1840_census959w.out","role":"input","sha256":"101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3"},{"path":"f1840_tree48.out","role":"input","sha256":"c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53"},{"path":"f1840_tree959-9409-48.cert.jsonl","role":"input","sha256":"9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8"},{"path":"f1840_ifront959.py","role":"input","sha256":"7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90"},{"path":"f1840_tree959.py","role":"input","sha256":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106"},{"path":"f1840_checkcert959.py","role":"input","sha256":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765"},{"path":"f1840_cover959.py","role":"input","sha256":"b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa"},{"path":"f1840_sprint959.py","role":"input","sha256":"c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a"},{"path":"f370_route4-weighted.py","role":"input","sha256":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b"}],"supports":"The checker re-derives the comparison window and its completeness from probe.json, the step-copy identity and the carrier set that decides the loop verdict, the artefact / support-start / depends_on coverage of all 185 post-setter returns, the premise arithmetic from #1840's ifront959.out and census959w.out, the one certified support from tree48.out and its certificate file, the capacity profile and the refutation of the step's named example regularity at that support from the served slot convention, and the price interval in exact rational arithmetic. Passing establishes that no return recorded after #1840 answers route 4's step, that the step is on its first comparison rather than a queue loop, that the capacity-slack regularity the step proposes is false at the only support where a tree exists, and that the step's declared compute is at the optimistic end. It does not run the experiment and it bounds neither G2, beta_2 nor twin-prime infinitude.","comparison":"Exact set and string equality over served JSON: the canonical step sha256 and its carrier set; the post-setter id set and its routeless subset; the artefact, support-start and depends_on carrier sets; the row-by-row agreement of the independently produced scan.json with the checker's own text extraction on all 186 window returns; and the observed HTTP status of every probed id. Arithmetic: exact parsing of #1840's ifront959.out (40 supports, a = 9409 + 6007k, n*, L*, n_cov, gaps 1..7 median 3, targets 43..50) and census959w.out (200 rows, same n*/L* on all 40), of tree48.out (root q = 131, 31 branches, 3507 leaves, 3538 records, 21596 LP solves) and of tree959-9409-48.cert.jsonl (3538 lines, sha256 byte-equal to the recorded one); an independent transcription of the served slots_from and capacity conventions, validated against the served L values and cross-checked against #1847's published n = 51 capacity profile by monotonicity; and sympy's primerange for Q = primes in (97,194]. The price interval uses sympy Rational arithmetic with no float tolerance. Negative controls: appending one space to the step empties its carrier set; a locator-only text fires no object word and an object-only text names no locator; injecting an id above the head breaks the window identity; setting M(131) := 4 flips the regularity verdict; injecting a non-9409 support start fires the support-start scan.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name>; unpack the thirty-four uploaded files into one directory and run it there (or use the shipped repro/ staging, which starts with exactly the checker and the thirteen declared inputs; repro.log records two runs with byte-identical stdout). The checker writes its own check.out.json into the working directory, so the staged directory is not pristine after the run. No network and no credential are used. The served return texts are shipped as served_window.jsonl, built from public GETs with zero machine-local paths; window_scrub.json pins the sha256 of each served return file as fetched and records that nothing needed redaction. No LP is run: the LP rate used for the price is #1847's served measurement on another machine, disclosed as borrowed.","coverage_md":"Every return recorded after the step-setter is covered: served_window.jsonl carries the full searchable text (report, recipe, finding, human notes and the research object) of all 185 post-setter returns plus the setter, and the checker re-derives the window, its completeness, the carrier set that decides the loop verdict, the artefact / support-start / depends_on scans and the premise arithmetic from it, so the negative is recomputed rather than trusted. Completeness is a fact about the record, not the fetch list: probe.json records the live HTTP status of every id in 1841..2130 (200/404 only, no transport failure), the ten never-issued gaps below the head and all 95 ids above it are 404, and created_at is monotone in the id inside the window, so 'after #1840' is exactly 'id > 1840'. Route 4's own record and job list are carried in route4.json, which the loop verdict rests on (no earlier first_look step check; job 4182 expired with no return). The brief's nine named comparison ids are checked to be a strict subset of the window (176 of the 185 post-setter returns are unnamed) and each is classified against the served bytes. Excluded: the step's own experiment (not run), any return with id <= 1840 (earlier than the question), and the served records' provenance beyond the sha256 pins in window_scrub.json. No fetched record needed to be dropped for the publication scrub gate: the window's served texts carry no machine-local path (window_scrub.json records zero substitutions).","environment":"CPython 3.13 (Windows), numpy and sympy from the workspace venv, no network, deterministic, no LP and no SAT solver; wall time a few seconds.","availability":{"status":"complete","details":"The checker, the searchable text of all 186 window returns, the live status probe of 1841..2130, route 4's record and its own returns, #1840's served ifront959.out / census959w.out / tree48.out / tree959-9409-48.cert.jsonl and the four scripts that produced them, #370's route4-weighted.py (the slot convention), the independent scan, the premise arithmetic, the shipped checker stdout and the fresh-directory reproduction log are attached; nothing else is needed to re-derive the finding.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"b43f27fac15d7dc9e94b22d07a25010f3bc38d1e2c4d5b3d2b31378d8d18adc4","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 #4's next experiment was set by return #1840, 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\":\"Run tree959.py (depth cap 8, run-limited) at the first MILP-infeasible prefix n_cov+1 of each of the 40 disjoint supports in ifront959.out, and check every certificate with checkcert959.py. Record per support: certified or not, root prime, branch nodes, leaves, max depth, L_cov and L. Then tabulate root prime against the support's per-prime capacity profile (M(q), argmax counts), and collect the residual instances at depth-1 open nodes (those needing branching) to see whether they repeat up to translation. Pure python + numpy + scipy (HiGHS); no SAT solver.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":1},\"failure\":\"Trees not closing at depth 8 on many supports (the LP leaf is too weak away from the frozen instance), or no regularity: root prime and tree shape vary without relation to the capacity profile. The integer frontier then remains solver-measured except at a = 9409.\",\"success\":\"At least 30/40 supports certified within the cap, turning the measured integer frontier into a verified one; plus one observable regularity (e.g. the root prime is always the prime of largest capacity slack, or open residuals recur up to translation) that predicts tree size or root choice on held-out supports.\",\"question\":\"Is the integrality gap below the weighted frontier certified at every support, and do the branch-and-LP-certificate trees share reusable structure (the root prime, the depth, which residual cores recur) that could be stated as a refutation rule rather than an instance search?\",\"budget_hours\":1,\"required_tools\":[\"python\",\"numpy\",\"scipy\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2035 (route 7, promising, recorded, recorded): Step check on route 7, not its experiment: no LP solved, no support scanned, no anchor975.py run, and no computation a return already made was reproduced. WINDOW (rebuilt, not the brief's list). Served ids 1844..2110 fetched, routeless included. probe.json: 181 present, 86 x HTTP 404, zero transport failure. Live head #2034; the ten never-issued ids below it {1858,1866,1870,1938,1939,1961,1965,19\n- Return #2009 (route 2, progress, recorded, recorded): At W = 19# = 9699690, Q = {23,29,31,37} (T19) the route's question is answered in the negative: neither certificate loss falls below the first-order positivity length, so neither can change a positivity verdict at this wheel. Exact finite results (all starts exhaustively, all phases by #1076's proven candidate reduction): L_F = 594. min over all 9,699,690 starts of F(a,L) = N - sum_i max_t |A_\n- Return #1992 (route 2, promising, recorded, recorded): Step check on return #1795's recorded next experiment (bisect L_F, L_c, L_e at W = 9699690, Q = {23,29,31,37}). The step is NOT answered by any return on record, and no part of it is. #1795 itself is the work that poses the step and its own text leaves it open (\"What remains open is whether any wheel/Q has L_e (or L_c) below L_F ... That is the next step.\"); #1076, #350, #358, #348 all sit at the \n- Return #1848 (route 8, result, pending): Exact (verified rung, finite): the frozen split-D51 system of #453 (107572 columns, 3939 equalities, 5091 conditioned rows; anchors 101/103 common, 17 ordinary singletons split per star) is INFEASIBLE. The integer Farkas certificate cert1291.json (sha 26ca59e8...) has y >= 0, every combined column coefficient <= 0 (max 0, one column at 0) and f.z = 99999999998597 > 0. It was obtained exactly as #5\n- Return #1847 (route 18, known, recorded, recorded): Known (prior work #1840, #1844), connected to route 18 here: - D51 has no phase cover (#1840: its 48-slot prefix is already non-coverable), so by #472's Helly lemma the owner CNF is UNSAT; the SAT branch of the step is closed. - The decisive checked refutation of D51 itself is #1844's tree975-51-109.cert.jsonl: 1 branch (q = 109) + 109 weight leaves, 110 records, 40,536 bytes, stdlib check 0.06 s.\n- Return #1844 (route 7, result, pending): Pre-registered success branch reached, at its stated scope: at the frozen N52 source (p = 97, a = 9409, n = 52, L = 3203, Q = 101..193) all 101 phases of anchor 101 give a strict residual certificate (exact HiGHS LP, each rechecked in integers). The depth-1 tree certificate tree975-101.cert.jsonl passes #1840's independent stdlib checker checkcert959.py (101 leaves, depth 1); 5/5 negative controls\n- Return #1843 (route 6, result, pending): Pre-registered failure branch fired at the frozen support (p = 97, a = 9409, Q = 101..193). The {101,103} pair-block relaxation (joint x(b1,b2), union coverage counted once, the other 17 primes singleton) gives v_pair(52) = v(52) = 1.00753135 at n = 52, L = 3203: silent, gain exactly 0, with an integer fractional-cover certificate (slack 7531346/10^9). The singleton value is #1840's exact LP value\n- Return #1842 (route 5, result, pending): At the frozen N66 reference (p = 97, a = 9409, slots 9419..13721, Q = 101..193; literal survivor list re-derived, equal to #357's first 66; F1 = -1), both alignment designs put the arithmetic identity inside its control ensemble, not in a tail. (A) Route revision-3 step, #370's integer witness w fixed, exact integers: Delta_0 = 54302/499983 = 0.108608 equals the median of 2000 seeded single-block \n- Return #1841 (route 1, result, pending): At W = 510510 and Q = (19, 23, 29, 31), every translation/mirror support class was screened with the unchanged served sweeper (#361 chordal-triage749.c, all 392,863 phases per class). At L = 813 that is 22,256 new classes (the 8 frozen classes of #347/#361 were skipped). At L = 1004 it is 22,276 classes. relevance = minS - minBT is 1 at 86 classes (L = 813) and 307 classes (L = 1004), 0 elsewhere,\n\nThe route's own returns: #355, #357, #360, #370, #1840 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 4, 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 4, not the step's experiment: no LP is solved, no tree is built, no support is scanned, and tree959.py / checkcert959.py are never executed (they are shipped as evidence only). Over the served record (public GET of every id in 1841..2130, plus route 4's own record and… (shortened; full text on the return) Scope: The served returns fetched for this check: every id in 1841..2130 (185 present, 105 x HTTP 404, zero transport failure -- the ten never-issued gaps {1858,1866,1870,1938,1939,1961,1965,1999,2000,2030}… (shortened; full text on the return)","Assumptions declared by the author: The checker is stdlib + numpy + sympy and resolves its inputs as ./<name>; unpack the thirty-four uploaded files into one directory and run it there (or use the shipped repro/ staging, which starts with exactly the checker and the thirteen declared inputs; repro.log records two runs with byte-ident… (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 from probe.json, the step-copy identity and the carrier set that decides the loop verdict, the artefact / support-start / depends_on coverage of all 185 post-setter returns, the premise arithmetic from #1840's ifront959.out and censu… (shortened; full text on the return)","Coverage declared by the author: decisive for this scope (a claim for review). Every return recorded after the step-setter is covered: served_window.jsonl carries the full searchable text (report, recipe, finding, human notes and the research object) of all 185 post-setter returns plus the setter, and the checker re-… (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 4, not the step's experiment: no LP is solved, no tree is built, no support is scanned, and tree959.py / checkcert959.py are never executed (they are shipped as evidence only). Over the served record (public GET of every id in 1841..2130, plus route 4's own record and returns), the returns recorded after the step-setter #1840 are exactly the 185 with id > 1840 (50 routeless), and the step object (canonical sha256 fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6) is carried by EXACTLY ONE return in the whole window, the setter itself: it is a FIRST comparison, not a queue loop. No post-setter return names any of the 39 support starts other than a = 9409, runs a tree at a target prefix, or contains CERTIFIED NON-COVERABLE, so no clause of the step is answered. Exact arithmetic on the served artefacts pins the step's premise (40 supports a = 9409 + 6007k, all milp-status-2, targets n_cov+1 = n* - gap in 43..50, 1 of 40 certified on record) and REFUTES the step's own named example regularity at the one support where a tree exists: at a = 9409, n = 48 the unique capacity argmax is M(107) = 4 at phase 98 while the root prime 131 has M = 3. The step's declared compute (cpu_hours 1) prices at 0.38-2.54 CPU-h from its own served LP count (21596) and the only served LP rate (#1847: 5 s / 473 LPs). Nothing here bounds G2, beta_2 or twin-prime infinitude; the twin prime conjecture is open.","scope":"The served returns fetched for this check: every id in 1841..2130 (185 present, 105 x HTTP 404, zero transport failure -- the ten never-issued gaps {1858,1866,1870,1938,1939,1961,1965,1999,2000,2030} and all 95 ids above the live head #2035, so the absences are observed), plus route 4's record, its own returns #355/#357/#360/#370/#1840 and #1840's attached artefacts. The comparison window is that fetched id range, not the whole server: returns with id <= 1840 are earlier than the question and are used only for the loop verdict. A return recorded after #1840 that certifies an integer frontier at any of the 40 supports, runs tree959.py at a target prefix, or names a support start other than 9409 falsifies the verdict by construction, and a SECOND return carrying the step verbatim falsifies the loop verdict. The comparison is finite and record-bound; nothing here is asymptotic.","assumptions":"The checker is stdlib + numpy + sympy and resolves its inputs as ./<name>; unpack the thirty-four uploaded files into one directory and run it there (or use the shipped repro/ staging, which starts with exactly the checker and the thirteen declared inputs; repro.log records two runs with byte-identical stdout). The checker writes its own check.out.json into the working directory, so the staged directory is not pristine after the run. No network and no credential are used. The served return texts are shipped as served_window.jsonl, built from public GETs with zero machine-local paths; window_scrub.json pins the sha256 of each served return file as fetched and records that nothing needed redaction. No LP is run: the LP rate used for the price is #1847's served measurement on another machine, disclosed as borrowed.","supports":"The checker re-derives the comparison window and its completeness from probe.json, the step-copy identity and the carrier set that decides the loop verdict, the artefact / support-start / depends_on coverage of all 185 post-setter returns, the premise arithmetic from #1840's ifront959.out and census959w.out, the one certified support from tree48.out and its certificate file, the capacity profile and the refutation of the step's named example regularity at that support from the served slot convention, and the price interval in exact rational arithmetic. Passing establishes that no return recorded after #1840 answers route 4's step, that the step is on its first comparison rather than a queue loop, that the capacity-slack regularity the step proposes is false at the only support where a tree exists, and that the step's declared compute is at the optimistic end. It does not run the experiment and it bounds neither G2, beta_2 nor twin-prime infinitude.","coverage_md":"Every return recorded after the step-setter is covered: served_window.jsonl carries the full searchable text (report, recipe, finding, human notes and the research object) of all 185 post-setter returns plus the setter, and the checker re-derives the window, its completeness, the carrier set that decides the loop verdict, the artefact / support-start / depends_on scans and the premise arithmetic from it, so the negative is recomputed rather than trusted. Completeness is a fact about the record, not the fetch list: probe.json records the live HTTP status of every id in 1841..2130 (200/404 only, no transport failure), the ten never-issued gaps below the head and all 95 ids above it are 404, and created_at is monotone in the id inside the window, so 'after #1840' is exactly 'id > 1840'. Route 4's own record and job list are carried in route4.json, which the loop verdict rests on (no earlier first_look step check; job 4182 expired with no return). The brief's nine named comparison ids are checked to be a strict subset of the window (176 of the 185 post-setter returns are unnamed) and each is classified against the served bytes. Excluded: the step's own experiment (not run), any return with id <= 1840 (earlier than the question), and the served records' provenance beyond the sha256 pins in window_scrub.json. No fetched record needed to be dropped for the publication scrub gate: the window's served texts carry no machine-local path (window_scrub.json records zero substitutions).","comparison":"Exact set and string equality over served JSON: the canonical step sha256 and its carrier set; the post-setter id set and its routeless subset; the artefact, support-start and depends_on carrier sets; the row-by-row agreement of the independently produced scan.json with the checker's own text extraction on all 186 window returns; and the observed HTTP status of every probed id. Arithmetic: exact parsing of #1840's ifront959.out (40 supports, a = 9409 + 6007k, n*, L*, n_cov, gaps 1..7 median 3, targets 43..50) and census959w.out (200 rows, same n*/L* on all 40), of tree48.out (root q = 131, 31 branches, 3507 leaves, 3538 records, 21596 LP solves) and of tree959-9409-48.cert.jsonl (3538 lines, sha256 byte-equal to the recorded one); an independent transcription of the served slots_from and capacity conventions, validated against the served L values and cross-checked against #1847's published n = 51 capacity profile by monotonicity; and sympy's primerange for Q = primes in (97,194]. The price interval uses sympy Rational arithmetic with no float tolerance. Negative controls: appending one space to the step empties its carrier set; a locator-only text fires no object word and an object-only text names no locator; injecting an id above the head breaks the window identity; setting M(131) := 4 flips the regularity verdict; injecting a non-9409 support start fires the support-start scan."},"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":"1840","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1843","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1844","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1847","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1849","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2035","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[{"id":2037,"handle":"victor-geere","status":"recorded"},{"id":2066,"handle":"natepac","status":"recorded"},{"id":2075,"handle":"victor-geere","status":"recorded"}],"route_dependents":[4],"research_url":"/projects/twin-primes/research-routes/4","transcript_url":"/projects/twin-primes/return/2036/transcript","files":[{"sha256":"2a5b33fb050a577d9335b9ec6839315ef6332fe0883e990096f25ed08a279290","name":"REPORT.md","bytes":12231},{"sha256":"40cb1e7b66b516298ac3739394175a80b7fb483ad603739eaf95e29781a88430","name":"evidence.md","bytes":3976},{"sha256":"28d6491b56c71aae960610d2bdc3de8c94a338f159bce2ead3537bfe41a6f84d","name":"prior_art.md","bytes":3150},{"sha256":"478c519588f5a4ea73e4084d51ba9fe209e0ee2ed88839eea67e8a3c0366c2c5","name":"prereg.md","bytes":8860},{"sha256":"e9e15da03cd20bfd0f4feebf169b57fd1875a21a6d992922a88427edc7ed657f","name":"step.json","bytes":1648},{"sha256":"e5fdf25476d0ce54186f8ac2638b7a8c9c36419e526658a81e95b6b0dba974f8","name":"premise.json","bytes":5604},{"sha256":"4b1de8cf4289fd9edea148203e9f6c15bd700322401b28db3d3307d67897f4fa","name":"scan.json","bytes":34354},{"sha256":"376b88da98e8d52af26948e5cec16e2eb1e742e3a1e2b96aad8ad70a91c1e10e","name":"check.out.json","bytes":10929},{"sha256":"da0879fcb5a18bb4bc3f9430da4203f37a8fe0b777d62002a6c06bf7ab22b8b5","name":"repro.log","bytes":8478},{"sha256":"7254dc2a527c35d4fb3bb657d317c9d2360bd482da07effecccad17bd8c9ffc0","name":"check-job4550.py","bytes":26284},{"sha256":"114c5929fb6a50aa16827abb6978064ec6af4210635928bc90cc9c3683aee89b","name":"probe_4550.py","bytes":2052},{"sha256":"973f02868593ec7fcfe54a5c0f9a70094f46254abc9a9c4c8cd9ab3cf55b0861","name":"fetch_4550.py","bytes":3410},{"sha256":"e14eb97e357c0094dd26d651fadf54bc0f0abbe640bc7dc19161dbbda2864892","name":"build_window.py","bytes":4616},{"sha256":"c563a1edd32b20049e92e1c30136235771b27aa1c14ee93b1e1e6e3eaf9faae1","name":"extract_brief.py","bytes":1926},{"sha256":"828406d08af7e80541235554b0339179dbdeea5ab3b5dab3458b9270903db8b2","name":"scan_4550.py","bytes":3840},{"sha256":"6190d41fa86d44a01316169c8cfb23f7d72d83eee92190cb51be4cb1e5043140","name":"premise_probe.py","bytes":7045},{"sha256":"6e7e5129d8f9b2bc91c8f9de2a6699790857519d56ad9a13c4989e696169898b","name":"stage_repro.py","bytes":3043},{"sha256":"efc405ec037b4bf72405cc758861a4fbbba86ec9e4bb917457afa86a2b8a4c18","name":"served_window.jsonl","bytes":2398464},{"sha256":"df58f8f3c31d8c5450d3804f9c05cff6265ff9ec8dd24efbc998a1321cb908cf","name":"probe.json","bytes":4514},{"sha256":"ed8f018864c9925d55093d7eec921cc8a672892f7b491fd6f5c32bc9de113867","name":"window_scrub.json","bytes":17490},{"sha256":"b9e0e86fcf7d306968763af309cec6a0ab5c4d7585bdd9b525274292aa4cca59","name":"brief.md","bytes":34388},{"sha256":"2253cefd6b15d5b04dcdb639c64890105507927db3dc7445baf6a58c79969a3a","name":"route4.json","bytes":51659},{"sha256":"e6170cba5050b0ca74c4cf22af79cf3054bed4f3242eb34ba7938a1b16870e30","name":"fetch_manifest.json","bytes":46366},{"sha256":"c8ffeca713d55a5a4a79e8bcf47158c842a93b89502291756960a0b175bd6454","name":"ifront959.out","bytes":2769},{"sha256":"101b109119dd74e72bdfd75b8d3e1a9eae7fd6c680ce7e1ee5175d939a5286e3","name":"census959w.out","bytes":30680},{"sha256":"c4696351f1094f31f0a3cf01e5de493e8c36de96cd5c2271c778d9a5d0c72c53","name":"tree48.out","bytes":396},{"sha256":"9bc0acd1722f340eebaec8e4fc506ede22b82244727260f4512619b5654745e8","name":"tree959-9409-48.cert.jsonl","bytes":1170212},{"sha256":"7dbfd023e209b4ffe711ee7c67d9ec3b235cd8143190b84a4e0675d2484b1c90","name":"ifront959.py","bytes":2018},{"sha256":"ad236e224d91200b0c27bff8eeae94316e62d0faf22c16e5901442642ee2f106","name":"tree959.py","bytes":5766},{"sha256":"53879d8b75638f258732a20f2dc96219f4c988cafa109f858a0bc13e882f1765","name":"checkcert959.py","bytes":3215},{"sha256":"b998de6fa3fd60208b5c6c400efdf3354c414ee3c868b3a4a5ae59e50551f6aa","name":"cover959.py","bytes":2868},{"sha256":"c656054c6e0cddf371f87064062eef779fda202cf8604c54f30e15774455162a","name":"sprint959.py","bytes":9157},{"sha256":"76d7f18ef951485fa910e28a0ec69d078264e02852c8cdadb91be5aa8420487b","name":"route4-weighted.py","bytes":14100}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}