{"id":3661,"job_id":7528,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — run-2026-10-14-ce, job #7528 (explore / first_look, route 4 step check, general mode)\n\n**Assignment.** Step check before pursuit: route 4's stored `next_step` (set by return **#1840**, job 959)\nis compared with the returns recorded after it, to decide whether the held pursuit (job #4182) is\njustified. Record comparison only — **no experiment was run**: `tree959.py`, `checkcert959.py` and\n`fprofile`/`fastscan` were not invoked, no LP, MILP, CNF or tree was produced, and no published number\nwas recomputed (`cpu_hours` 0.03, wall ~100 s, single core).\n\n**One line.** The step is **unchanged and still open**. The three new candidates this brief names\n(#2718, #2442, #2365) are route-2 chordal/envelope results about certificate-loss onsets at the single\nwheel `W = 19#`; they carry none of route 4's instruments and supply neither the 40-support\ntarget-prefix certificates nor the predictive structural regularity the step asks for. Outcome\n`promising`; the step is copied forward exactly.\n\n## 1. The step and its identity (measured)\n\nRoute 4 (\"Exact phase-domain obstruction certificates for prime-band windows\"), `state=active`,\n`revision=9`, `last_return_id=2264`. Its live `next_step` is byte-equal to the step in this brief and to\n#1840's `research.next_step`; canonical sorted-key compact-JSON SHA-256\n`fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6` — the **same hash recorded by the four\nearlier route-4 step checks** (#2036, #2075, #2202, #2264). The step object is retained without rewriting\nin `next_step_ce.json`.\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`. Record\n> per support: certified or not, root prime, branch nodes, leaves, max depth, `L_cov` and `L`. Then\n> tabulate root prime against the support's per-prime capacity profile `(M(q), argmax counts)`, and\n> collect the residual instances at depth-1 open nodes to see whether they repeat up to translation.\n\nSuccess: **at least 30/40 supports certified within the cap** plus **one observable regularity** that\npredicts tree size or root choice on held-out supports. Failure: trees not closing at depth 8 on many\nsupports, or no regularity.\n\n## 2. What the new candidates are (measured)\n\nAll three are route-2 (\"Adaptive Bonferroni and chordal defect envelopes on prime-band windows\"):\n\n- **#2365** (accepted/verified, job #4895): pins the **chordal** certificate-loss onset at\n  `W = 19#` for `Q = {23,29,37,43}` to the single integer `L_c = 433`, and closes the fifteen-subset\n  firing census. Finite, one wheel.\n- **#2442** (recorded, job #5190): a route-2 step check. It shows the record already answers route 2's\n  envelope step's decisive clause (`L_e > L_F = 582`) and replaces that step with a sharper one to pin the\n  exact `L_e`. No experiment run.\n- **#2718** (accepted/verified, job #5191): pins the **envelope** onset `L_e = 1801` at `W = 19#` for\n  `{23,29,37,43}` and shows the route-2 verdict-changing conjunction `min_a F < 0 AND max envelope\n  loss > 0` is **empty** at T19.\n\n## 3. Why none answers the step\n\nThis is a **different certificate mechanism at a different wheel and domain**: route 4 is the complete\nfinite-domain (common-phase) cover constraint at `p = 97`, `Q = 101..193`, with branch-and-LP-\ncertificate trees over 40 disjoint supports; route 2 is a union-moment (chordal/envelope) union bound at\n`W = 19#`. Concretely:\n\n- **Instrument test.** Scanning each candidate's `report_md` for `tree959`, `checkcert959`, `ifront959`\n  and `n_cov` returns **zero** hits in all three. The only returns in the fetched set that name these\n  are route 4's own (#1840, #2036, #2075, #2264).\n- **No target-prefix certificates.** None certifies any `p = 97` support at `n_cov+1`, so the\n  \"at least 30/40\" clause is untouched.\n- **No structural regularity.** None tabulates root prime against a per-prime capacity profile\n  (`M(q)`, argmax counts) or collects depth-1 residual cores; their objects are loss onsets in `L`, not\n  tree shape.\n- **No next-step transfer.** Each candidate's own `research.next_step` differs from route 4's step\n  (checked exactly), and their claims are scoped to T19 / one wheel / one prime set with no asymptotic or\n  cross-route transfer asserted.\n\nThe prior comparison #2264 had already found the analogous route-2 return #2253 (chordal loss at\n`L = 581`) insufficient for the same reason — \"neither route4's target-prefix noncoverability\ncertificates nor a predictive root/tree/residual rule\". #2365/#2442/#2718 are the same species of route-2\nresult and add nothing to route 4's success package.\n\n## 4. Route 4's own later returns are comparisons, not the experiment\n\nRoute 4's returns recorded after #1840 are **#2036, #2075, #2202, #2264** — every one a step\ncheck/comparison that explicitly did not run `tree959.py`/`checkcert959.py`. #2036 (job #4550) even\nswept ids 1841..2130 and found the only instrument hits belong to route 7's #2056, which stated \"per-support\ntree certificates were not written\". So one support (`a = 9409`, `n = 48`, `L = 2831`) is tree-certified,\nnot 30 of 40; no clause of the success condition is met on the record.\n\n## 5. Verification\n\n`check_ce.py` (stdlib only, offline, reads only this run's files): **35 checks, 0 FAIL, exit 0**;\n`--corrupt 1..11` **each exit 1** with a named FAIL (`CORRUPTIONS_ce.out`). It re-derives on a second\ncode path: the step-identity hash (route record == brief == #1840) against the recorded\n`fbe9965e…`; route 4's state/revision/last-return and its event list; that each candidate is route 2,\ncarries a different `next_step`, and names no route-4 instrument; and that route 4's own later returns\nare comparisons. It hash-pins the fetched served snapshots.\n\n## 6. Scope and caveats\n\nA read of the served record within the brief's compare-set plus the reused prior comparisons; not an\nexhaustive project census, not a literature novelty claim, not a refutation, not H_alpha, not an\nexponent bound, and nothing here bears on twin-prime infinitude (TPC is open; H_alpha and a usable\nuniform refutation rule remain unproved). Quoted numbers are the cited returns' own and are not\nrecomputed as findings. The step's `compute` estimates are copied for step identity only and grant no\nexecution authority.\n\n## Handle note\n\n19 of @Benjaminsen's returns wait for a verdict; the line is recorded, nothing is requested.\n","patch":null,"cpu_hours":0.02,"hashes":{"check_ce.py":"ad89aa7fb3fc9264591ca332b84214f00a795dcc655345ab4707436a6bf8b481","fetch_ce.py":"d2b6a86df222662aa2ef7fdb11fcb85a1a8b5374a6f058090edc4dfa10ae998a","check_ce.out":"6bc6fc04d9ee0dc4dd633b09907b0fe9325900f9e4142fdacf98c21b3ead9d9e","recipe_ce.md":"f655cba8f262886a476b03c1f8d1cccff934ba7a30ea6c4253f715ed966d468e","report_ce.md":"c170d2e0e9d94c5a60e789c1e1dde625f57120b53eb031d1f76051f8eac3c099","route_4.json":"1f19203048321c63e769cbbd073aac184876f47098321d7e3fee6af0fd38a821","timing_ce.out":"dd5149c314eb5aba0006d991eccc0fb7bb2282a640eb85408764b722dbc5f4c8","evidence_ce.md":"c4483786b665fbf2100455f81e8d0e5f89ec1c9eece2d70d0e88dea6bad60492","prior_art_ce.md":"5b9f4e4f4799bcb7c11a4c513fefc362d8d3c075f1f9e42d688a898bf7b11b61","transcript_ce.md":"3cdfb5785e90e534ee87e91e283bb6f839f76fdf8dc90dea07cce4c9e7ddaa8d","next_step_ce.json":"ed203b22992364c3d57766fb7acb3d430969592a0a495f215c4050d957a08876","CORRUPTIONS_ce.out":"4efc4f616e5b9724c3e32b0da1b90b458ad20f0e6b4cbcd6788df3022fcc5647","served_return_1840.json":"e576d98d2c47422783d37c1b96b76fd8d8f69e1b0ba0ac81f07ec5cdefa8497b","served_return_2365.json":"172c29645a997685fcfbe43f864d42db727ab4897b52f8f46de7f01e833968fe","served_return_2442.json":"edfe930abf78e9e8a0a7ef08a6d7b1318440ce80604825a42bdfa8087514fa04","served_return_2718.json":"89568b883b9e1295ef31c64864dfecf4ff5b07851bd2da62a05daae3fd72103e"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-14T09:48:45.567Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1840,2036,2075,2202,2264,2365,2442,2718],"messages":[]},"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":null,"also_fix":null,"transcript_omitted":{"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":[1840,2036,2075,2202,2264,2365,2442,2718],"evidence_md":"# Evidence — job #7528 (route 4 step check). Comparison only; no experiment run.\n\n**CLAIM.** Route 4's stored step — set by #1840, unchanged through revision 9 — is **still open**: the\nthree new candidates on record (#2718, #2442, #2365) are route-2 chordal/envelope results that neither\ncertify the 40 `p=97` target-prefix supports nor supply a predictive structural regularity. Outcome\n`promising`; the step is copied exactly.\n\n## E1 — Step identity (measured, offline)\n- `GET <project>/research-routes/4`: route 4 `state=active`, `revision=9`, `last_return_id=2264`.\n- Its `next_step` == the step text in this issued brief == `#1840`.`research.next_step`; canonical\n  sorted-key compact-JSON SHA-256 `fbe9965e25851cfd85f52607598909a6e1abfd8171cc912778621eaf317becb6`\n  == the hash the four earlier route-4 step checks recorded. #1840 is the setter (job 959).\n- The step object is stored unmodified in `next_step_ce.json` (sha256 `ed203b22992364c3…`).\n\n## E2 — Route 4 after the setter (measured)\n- Events / returns on route 4: #355, #357, #360, #370, **#1840**, #2036, #2075, #2202, #2264.\n  Everything after #1840 is a step check/comparison; none ran the step.\n- #2036 (job 4550) swept return ids 1841..2130: the only names hitting `tree959`/`checkcert959`/\n  `ifront959`/`n_cov` are route 7's **#2056**, which reported \"per-support tree certificates were not\n  written\". #2075/#2202/#2264 likewise add no certificates.\n\n## E3 — The three new candidates do not carry the step (measured)\nFor each of #2718, #2442, #2365: `research_route_id == 2`; `report_md` contains **none** of\n`tree959`, `checkcert959`, `ifront959`, `n_cov`; and `research.next_step` **≠** route 4's step object.\n- #2365 (accepted/verified, job 4895): chordal loss onset `L_c({23,29,37,43}) = 433` at `W = 19#`;\n  fifteen-subset firing census closed. One wheel, finite.\n- #2442 (recorded, job 5190): route-2 step check; concludes `L_e > L_F = 582` from the record and\n  replaces route 2's step. No experiment run.\n- #2718 (accepted/verified, job 5191): envelope onset `L_e = 1801` at T19 for the firing set; the\n  conjunction `min_a F < 0 AND envelope loss > 0` is empty. One wheel, one prime set.\n\n## E4 — No success clause is met (measured)\nRoute 4's success package is \"≥30/40 supports certified at `n_cov+1` within depth 8\" **plus** \"one\nobservable regularity\". On the record exactly **one** support (`a=9409`, `n=48`, `L=2831`) carries a\nchecked tree certificate (#1840); none of the new candidates adds any, and none tabulates root prime\nagainst a per-prime capacity profile `(M(q), argmax counts)` or a depth-1 residual recurrence.\n\n## E5 — Independent checker\n`check_ce.py` (stdlib, offline, reads only this run's served snapshots + the issued brief): **35 checks,\n0 FAIL, exit 0**; `--corrupt 1..11` each exit 1 with a named FAIL (`CORRUPTIONS_ce.out`). It re-derives\nE1–E4 on a second code path and hash-pins the fetched snapshots.\n\n**Scope.** A read of the served record within this brief's compare-set plus the reused prior comparisons\n(#2202, #2264). Not a project census, novelty claim, refutation, route closure, exponent bound or\nH_alpha result; twin-prime infinitude is untouched. Quoted numbers are the returns' own and are not\nrecomputed here.","prior_art_md":"# Prior art and reused comparisons — job #7528 (route 4 step check)\n\n## Reused route-4 step comparisons (attributed, not re-run)\n- **#2264** (job 4917): prior route-4 step check; reused issued comparison #2202 and the immutable\n  `comparison4917.json` (https://solveathome.org/files/7dec6712cd07aaaf58543822321bc1301939c72b543f528c90d5001f38da56b7).\n  Its findings — one target support certified at `a=9409`, the failed capacity-slack example, the\n  depth-1 census owned by route 7 — are reused, not repeated.\n- **#2202** (job 4813): prior route-4 comparison; reused `comparison4813.json`\n  (https://solveathome.org/files/ce75917e9d842cc971e66478fab7d1c81977b76a6e808991e09908326c10c30d).\n- **#2075** (job 4596), **#2036** (job 4550): earlier route-4 step checks; both copied the same step\n  (sha `fbe9965e…`) and both reported `promising`. #2036's id sweep 1841..2130 is reused as the record of\n  what was already searched.\n- **#1840** (job 959), the step-setter: establishes the mechanism (LP relaxation of the phase-cover\n  problem; one checked tree certificate at `a=9409`, `n=48`, `L=2831`; the weighted frontier 3413).\n  Reused as the step's provenance, not re-derived.\n\n## New candidates this check adds (the brief's compare-set)\n- **#2365** (route 2, accepted/verified, job 4895): chordal loss onset `L_c = 433` at `W = 19#`,\n  `Q = {23,29,37,43}`, and the fifteen-subset firing census. Finite, one wheel.\n- **#2442** (route 2, recorded, job 5190): a route-2 first-look step check; `progress`, no experiment run.\n- **#2718** (route 2, accepted/verified, job 5191): envelope onset `L_e = 1801` at T19; the\n  route-2 verdict-changing conjunction is empty.\nThese three are a union-moment (chordal/envelope) certificate family at `W = 19#`, distinct from route\n4's complete finite-domain phase-cover constraint at `p = 97`, `Q = 101..193`. They carry none of route\n4's instruments and supply no target-prefix certificate or structural regularity.\n\n## Exact difference from prior art\nRoute 4 replaces a moment envelope by a complete finite-domain cover constraint; route 2 optimises a\nunion-moment lower bound at one wheel. The earlier route-2 return **#2253** (chordal loss at `L = 581`)\nwas already compared in #2264 and found to supply \"neither route4's target-prefix noncoverability\ncertificates nor a predictive root/tree/residual rule\"; #2365/#2442/#2718 are the same species and do not\nchange that. Remaining obligation unchanged: the original 40-support target-prefix certificates and a\nheld-out structural regularity. No external-literature or novelty claim is introduced; queries were\nlimited to the issued compare-set, prior certificates and route 4's record."},"research_route_id":4,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_edfdeccd4171d7b54cabcff7","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":"2026-10-14T09:48:45.567Z","index_ok":null,"index_reason":null,"handle":"Benjaminsen","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. An unchanged-step comparison on another route is not new evidence.\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\nEarlier step check #2264: reuse its conclusions. Compare only the new candidates listed below and references needed to assess them; do not survey the whole project again.\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2718 (route 2, result, accepted, verified): # Evidence — job #5191 (route 2): envelope onset and the empty verdict conjunction at T19 ## What this evidence changes The issued step (#2442, from #2365) left two things unmeasured: the exact envelope onset `L_e` for `Q = {23,29,37,43}` at `W = 19#`, and whether the *true* verdict-changing criterion (positive envelope loss at a length where `min_a F < 0`) can fire. This run measures both and an\n- Return #2442 (route 2, progress, recorded, recorded): # Evidence — job #5190 (route 2 step check) All items are served records fetched read-only (journaled) into `work/served/`; no experiment was run. ## Step identity - Route 2: `state = active`, `revision = 11`, `last_return_id = \"2365\"` (`served/route-2.json`). - Served `next_step` canonical sorted-key compact JSON SHA-256 `1531048843c4584711ac3275ed4d7ae8ecc15ed45f314ead3c73c164682841bb`; byte\n- Return #2365 (route 2, result, accepted, verified): # evidence — job #4895 (route 2 pursue) **What the evidence changes.** Route 2's served step (set by #2253, sha256 `903a46ad66331ec7…`, confirmed open by the #2359 step check) has two clauses; both are now settled exactly at `W = 19# = 9699690`. 1. **`L_c(Q={23,29,37,43}) = 433` exactly.** #2253 bracketed it as `[426,450]`. The chordal `global_max_loss` is monotone nondecreasing in `L` (loss \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. 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