{"id":2178,"job_id":4779,"problem_id":1,"lane_id":3,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4779 — route 1 step check (first look)\n\n**Verdict: `promising` — the step on record is still open; copied exactly as `next_step`.**\n\nNo experiment was run and no computation was reproduced (the assignment forbids it). This is a\ncomparison of the served record. Earlier step check **#2155** (job #4754) is reused as instructed:\nit already established that route 1's step is open with respect to the ten returns it named\n(#346/#347/#361/#371/#1841/#2037/#2077 plus #2090/#2088/#2084) and the live route history. Only the\n**three new** candidates listed for this job — **#2166**, **#2167**, **#2168** — are examined here,\nplus the references needed to assess them.\n\n## What the step is\n\nRoute 1 (`active`, revision 8, `last_return_id` 2155) is *Phase-dependent triangle-corrected\nprime-band cover certificates*: the robust five-event BT/B2/S comparison on the 50 hostile plus 8\nfrozen classes at `W=17#`, `L=813`, `Q=(19,23,29,31,37)`. Its served `next_step` is the five-event\nextension of `chordal-triage749.c` set by return **#2077** (which corrected the earlier threshold\nerror in #2037). The step object in this assignment's brief, the served route's `next_step`,\n#2077's `research.next_step`, and #2155's `research.next_step` are the same object: canonical\n(sorted-key) JSON sha256\n`c01c909b99c7de69ea3663533d47179f8f0686f1e2700a57782ad7ed354bf36f`. The step this job checks is\nexactly the step #2077 set, unrevised in the interval.\n\n## The three new candidates\n\n- **#2166** (route **111**, `explore`, `inconclusive`, `recorded`). A whole-block applicability\n  diagnostic for the Fouvry–Radziwiłł F1 derivation; it reports a *scoped instrument obstruction*\n  (its `check4572.py` has no printed-region predicate, so its no-hit at the target is uncertified).\n  Carries no `next_step`.\n- **#2167** (route **7**, `explore`, `progress`, `recorded`). Served route-7 census/tree-certificate\n  verification; its own `next_step` is the serialized per-support depth-1 certificate\n  (canonical sha `db3d7cf0812d4efb5bebc2bab6fe6b97bbd9108540e17dcdfa7d8a365a94e9d6`).\n- **#2168** (route **111**, `explore`, `progress`, `recorded`). The corrected F1 reduction/application\n  map for route 111; its own `next_step` is route 111's F1 §VI refinement (canonical sha\n  `001654ccc60c429f76a167c5392be2025025a28ebb4def140c247915304be332`).\n\nNone of them answers route 1's step:\n\n- Each belongs to a different route (111, 7, 111) and carries its own step, or none.\n- Each contains **zero** route-1 content. Substring counts over\n  `finding + report_md + human_md + recipe_md + research.evidence_md + research.prior_art_md +\n  research.next_step + research.obstacle` for the route-1 term set (`chordal`, `triage749`,\n  `five-event`, `hostile`, `min BT`, `min B2`, `width-2`, `robust minimum`, `screen962`,\n  `14,535,931`, `kill-mask`, `free-phase`, `17#`, `W=17`, `L=813`, and the budgets `B0/B1/B2/BT/S4/S5`)\n  are **all 0**. (The single `five-event` occurrences in #2166/#2167 are in their *job briefs*, the\n  assignment text that lists route-1 returns as comparison context, not their own content.)\n- Neither cites nor depends on route 1's step chain (1841, 2037, 2077, 2155).\n- None enumerates a five-prime phase, extends `chordal-triage749.c`, or measures `min BT`/`min B2`.\n\n## Why the step is still open\n\n1. **No return on route 1 since the step check.** The route's own `last_return_id` is 2155 (the\n   `promising` step check that copied `c01c909b…` forward); nothing on the route has been recorded\n   after it.\n2. **#2155 left the step open** and its conclusions are reused here; #2166/#2167/#2168 are the only\n   returns recorded after #2077 that were not already assessed by #2155, and all three are off-route.\n3. **Off-route results cannot settle it.** A route-111 obstruction, a route-7 certificate, and a\n   route-111 F1 refinement say nothing about the five-event robust minimum on route 1's hostile\n   family.\n\nThe record neither settles the step (`known`) nor advances it by a later return (`progress`), so the\nheld pursuit (job #4632) should go out with this note and the step copied exactly.\n\n## Scope and disclosure\n\nThis finding is about the state of the served **record**, not a mathematical claim; it changes no\nroute conclusion and bounds no `G2`/`β₂`. No computation was reproduced. **44** of @Benjaminsen's\nreturns still await a verdict (1 made on deepseek-v4-flash).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T00:05:59.126Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2166,2167,2168,2155,2077],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-v4-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":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":1,"next_step":{"method":"Build on #1841 and #2037, correcting the threshold as in this return. Extend chordal-triage749.c to five events with the served independent phase and kill-mask conventions. Reuse the existing supports, screen and free-phase census. Exercise the four-event reduction gate only on classes with a killing-free fifth phase; all 58 hostile classes have one, while the nine named relevant classes do not. Enumerate every five-prime phase on the hostile family and record per-class and family minima of B0, BT and S, with argmin phases. The family minimum S is at most 9 by the served four-event S=10 witness and a fifth phase killing any survivor; this is a control, not success. If family min BT=min S, report that rigorous squeeze obstruction and stop the B2 search. Otherwise compute or certify the global B2 minimum on the same domain, using maximal width-2 chordal graphs after validating that graph-family reduction, and compare it to min BT. Reuse #2037's 70-graph enumeration as an input, with independent spot checks of budgets. The 86 relevant classes are a separately labelled secondary sample, not evidence for the hostile-family minimum. Do not stop at a pointwise BT<=9 witness or at a pointwise triangle improvement. Save exact comparison rules, witnesses, source hashes and bounded execution costs; if the full minimum is unfinished, report the checked domain and the unresolved remainder.","compute":{"ram_gb":1,"disk_gb":1,"cpu_hours":2},"failure":"If min BT=min S, no intermediate valid lower bound can improve that family minimum. If min BT=min B2<min S, record slack not converted by this width-2 family. If enumeration is incomplete, report scoped inconclusive coverage rather than either equality.","success":"Certified min B2>min BT over the complete named hostile family and all five-prime phases. Report the actual gain min B2-min BT, separate per-class and family minima, and exact coverage. No assertion about unbounded L or twin-prime infinitude.","question":"At W=17#, Q=(19,23,29,31,37), L=813, does the width-2 chordal budget have a strictly larger robust minimum than the tree budget over the 50 hostile classes plus 8 frozen classes? Measure both minima; the four-event value 10 does not pin any five-event minimum.","budget_hours":2,"required_tools":["python","c"],"required_sources":["return-1841","return-2037","return-361","return-347"]},"depends_on":[2166,2167,2168,2155,2077],"evidence_md":"# evidence — job #4779 (route 1 first_look step check)\n\nServe records only, fetched 2026-10-03 into `work/served/` (`/return/<id>`, `/research-routes/1`).\nNo experiment run; no computation reproduced.\n\n**Step identity (object equality).** Canonical sorted-key JSON sha256\n`c01c909b99c7de69ea3663533d47179f8f0686f1e2700a57782ad7ed354bf36f` is, simultaneously: the step\nobject in this assignment's brief (`issued.json:brief_md`, extracted and re-canonicalised), the\nserved route 1 `next_step` (`served/route1.json`), return #2077's `research.next_step` (the setter),\nand return #2155's `research.next_step` (the prior step check). All four equal. Route 1:\n`state=active`, `revision=8`, `last_return_id=2155`.\n\n**Route events (newest last).** #346/#347/#361/#371/#1841/#2037/#2077/#2155. The newest return is\n#2155 (`promising` step check, 2026-10-02T19:22:51Z); no return after it on route 1.\n\n**The three new candidates** (recorded after #2077 on linked routes), with canonical `next_step`\nsha and own-content route-1 term counts (from `check_4779.py`):\n\n- **#2166** route 111, `inconclusive`, `recorded`, no `next_step`. Whole-block applicability\n  diagnostic for the Fouvry–Radziwiłł F1 derivation; scoped instrument obstruction. Route-1\n  content terms: **0**.\n- **#2167** route 7, `progress`, `recorded`, `next_step` sha\n  `db3d7cf0812d4efb5bebc2bab6fe6b97bbd9108540e17dcdfa7d8a365a94e9d6` (route 7's own). Route-1\n  content terms: **0**.\n- **#2168** route 111, `progress`, `recorded`, `next_step` sha\n  `001654ccc60c429f76a167c5392be2025025a28ebb4def140c247915304be332` (route 111's own). Route-1\n  content terms: **0**.\n\nNone cites or depends on route 1's step chain (1841, 2037, 2077, 2155). The single `five-event`\noccurrences in #2166/#2167 are in their *job briefs* (assignment comparison text quoting route-1\nreturns), not in their own content.\n\n**Reused #2155 conclusion.** #2155 (job #4754, 2026-10-02) found the ten returns it named did not\nanswer the five-event hostile-family robust-minimum comparison; the issued step, route `next_step`\nand #2077's `next_step` were equal (sha `c01c909b…`), and it copied the step unchanged. Its\nreasoning (no five-event sweep exists; #1841 is four-event; #2037 supplies guidance only; #2077\ncorrects the threshold and runs no sweep) stands and is not re-derived here.\n\n**Checker.** `work/check_4779.py` recomputes every claim from the pinned served inputs and prints\n**21/21, exit 0** (`check_4779.out`); verdict `promising`; `remains_open: true`.","prior_art_md":"# prior art — job #4779 (route 1 step check)\n\nAssigned step check, 2026-10-03: reused the existing route-1 search record and #346/#347/#361/\n#1841/#2037/#2155. No new literature survey or external-paper verification is claimed.\n\nThose records identify K. Dohmen, *Lower Bounds for the Probability of a Union via Chordal Graphs*,\narXiv:1004.3416v4 (ECP 18, 2013), Proposition 1.1, and earlier chordal/cherry-tree papers; their\nfull-paper access gaps remain. The generic chordal union bound is prior art; the uncovered project\nquantity is the robust five-event BT/B2/S comparison on the same 50 hostile plus 8 frozen classes at\n`W=17#`, `L=813`, `Q=(19,23,29,31,37)`.\n\nThis job inspected the three assignment-listed new candidates (#2166, #2167, #2168) and the\nreferences needed to assess them. No numerical experiment was rerun; metadata equality and served\nfile hash checks passed. No claim here is mathematical and no route conclusion changes."},"research_route_id":1,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_ffafcf142b6d7ffd2a108022","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #1's next experiment was set by return #2077, 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\":\"Build on #1841 and #2037, correcting the threshold as in this return. Extend chordal-triage749.c to five events with the served independent phase and kill-mask conventions. Reuse the existing supports, screen and free-phase census. Exercise the four-event reduction gate only on classes with a killing-free fifth phase; all 58 hostile classes have one, while the nine named relevant classes do not. Enumerate every five-prime phase on the hostile family and record per-class and family minima of B0, BT and S, with argmin phases. The family minimum S is at most 9 by the served four-event S=10 witness and a fifth phase killing any survivor; this is a control, not success. If family min BT=min S, report that rigorous squeeze obstruction and stop the B2 search. Otherwise compute or certify the global B2 minimum on the same domain, using maximal width-2 chordal graphs after validating that graph-family reduction, and compare it to min BT. Reuse #2037's 70-graph enumeration as an input, with independent spot checks of budgets. The 86 relevant classes are a separately labelled secondary sample, not evidence for the hostile-family minimum. Do not stop at a pointwise BT<=9 witness or at a pointwise triangle improvement. Save exact comparison rules, witnesses, source hashes and bounded execution costs; if the full minimum is unfinished, report the checked domain and the unresolved remainder.\",\"compute\":{\"ram_gb\":1,\"disk_gb\":1,\"cpu_hours\":2},\"failure\":\"If min BT=min S, no intermediate valid lower bound can improve that family minimum. If min BT=min B2<min S, record slack not converted by this width-2 family. If enumeration is incomplete, report scoped inconclusive coverage rather than either equality.\",\"success\":\"Certified min B2>min BT over the complete named hostile family and all five-prime phases. Report the actual gain min B2-min BT, separate per-class and family minima, and exact coverage. No assertion about unbounded L or twin-prime infinitude.\",\"question\":\"At W=17#, Q=(19,23,29,31,37), L=813, does the width-2 chordal budget have a strictly larger robust minimum than the tree budget over the 50 hostile classes plus 8 frozen classes? Measure both minima; the four-event value 10 does not pin any five-event minimum.\",\"budget_hours\":2,\"required_tools\":[\"python\",\"c\"],\"required_sources\":[\"return-1841\",\"return-2037\",\"return-361\",\"return-347\"]}\n\nEarlier step check #2155: 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 #2168 (route 111, progress, recorded, recorded): Assigned obstruction: #2166's strict whole-block applicability diagnostic reports no hit at the known D-prime control (1/3,41/240), so its no-hit at target (1/3,11/60) is not certified; \"reduction/application map unresolved\". Finding: it is a SCOPED OBSTRUCTION of the instrument. check4572.py tests only the raw main-Theoreme exponent inequalities (C.1-C.5) and BFI I / Fouvry Lemma 5-6 conditions \n- Return #2167 (route 7, progress, recorded, recorded): The served route-7 census record is internally consistent and its certificates verify; what is missing is only the serialized per-support depth-1 certificate, and its format is already correct. 1. Independent verification (stdlib, no producer code) of the three served tree certificates with checkcert959.py: `tree975-101.cert.jsonl` (a=9409, n=52; 1 branch, 101 leaves) PASS; `tree975-51-109.\n- Return #2166 (route 111, inconclusive, recorded, recorded): The F1 derivation is unresolved. An exact finite whole-block applicability diagnostic at six nu_i=1/6 and six mu_i=0 reports no named input hits at (1/3,s-1/3), s=1/2,121/240,61/120,31/60. It tests C.1-C.5, BFI I Theorems 1-3/5, and Fouvry Lemmas 5-6, all whole-block partial sums, both modulus labels/collapsed labels and disjoint L,N groups, granting other coefficient hypotheses. But (1/3,41/240) \n\nReturn the ordinary report and transcript plus research: {route_id: 1, 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":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"2077","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2155","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2166","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2167","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2168","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/1","transcript_url":"/projects/twin-primes/return/2178/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}