{"id":2225,"job_id":4855,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #4855 — route 80 first-look step check (new candidate #2213)\n\n**Verdict: `promising` — the step set by #1933 is still open; copied exactly as `next_step`.**\n\nNo experiment was run and no computation was reproduced (the assignment forbids both). This is a\ncomparison of the served record, reusing #2211's conclusions and comparing only the new candidate the\nbrief names.\n\n## What the step is\n\nRoute 80 is *No-wrap dominance: the corrected covering run never exceeds the non-wrapping run*.\nIt is `active`, **revision 9**, `last_return_id` **2211**, `origin_return_id` **1019**. Its served\n`next_step` has canonical (sorted-key, compact-separator) JSON sha256\n`8ddff1cc1a111f7cec4ebc7cf84cc3408b102ca9279d2ba98877ed72e4a7bd52`, which equals **#1933**'s\n`research.next_step` exactly (the setter: job #4318, type `explore`, outcome `result`, status\n`pending`, model `claude-opus-5-5`). The revision rose 8 -> 9 with **#2211** (a prior step check,\noutcome `promising`) but the step bytes are unchanged.\n\nThe step is *Port `certk.py`'s enumeration and exact transfer check (job 4318's return) to C, with\nslots from a sieve of the first and last few hundred slots (the left seam side from the palindrome);\nrun k = 5, 6, 7 at x = 17, 19, 23 with the block-prefix check; confirm every T failure with `wincov.c`;\nreport `l_max_k`, the T failures, K, and `k_exc(x)` or its lower bound per level.* The question is\n`k_exc(x)`, the least |Q| for which a two-sided seam run beats `nonwrap(Q)` with no killable block, at\nx = 17, 19, 23. #1933 measured it as 5, 5, 6 at x = 7, 11, 13; the step asks whether it keeps rising\ntoward Lemma G's `k_max(x)` (#1929). Success means k = 5 is certified (no T failure) at x = 17, 19, 23\nand `k_exc(x) >= 6` there; failure is a `wincov`-confirmed exceedance at k = 5 with no killable block.\n\n## Route 80's own returns (9)\n\n#1019 (direction, `proposed`), #1022 (explore, `promising`), #1543 (explore, `result`, accepted/verified,\n|Q| = 1 theorem), #1827 (explore, `result`, pending, T_5 refuted + 7..997 certified), #1913 (explore,\n`progress`, step restated), #1922 (explore, `promising`, step re-copied unchanged), #1929 (explore,\n`result`, pending, |Q| = 3 dominance and Lemma G), #1933 (explore, `result`, pending — the setter),\n#2211 (explore, `promising` — the prior step check, step re-copied unchanged).\n\n`last_return_id` is **2211**: no return after #1933 reports the x = 17, 19, 23 run; #2211 only\nre-confirmed the step is open. #1913 and #1922 both carried the earlier step (`3b8cef27…`); #1933\nrewrote it to the present x = 17, 19, 23 experiment and reported the small-|Q| exceedances\n(5, 5, 6 at x = 7, 11, 13). The x = 17, 19, 23 run has never been reported.\n\n## The comparison returns\n\n#2211 already compared the eight returns the brief names (#2187, #2080, #2027, #2020, #1994, #1970,\n#1937, #1936): none mentions `k_exc`, `certk`, `wincov`, `l_max`, `k_block`, `k_max`, `nonwrap`,\n`block-prefix` or `4318`; their only `seam` occurrences (#2080, #2027) are route 76's T_37/T_41\ncensus seams and their only `17,19,23` occurrences (#1994, #1970, #1936) are the killer set\n{17,19,23} at base P = 2310 on routes 170/171. This run reuses that conclusion and compares only the\n**new** candidate named by the brief:\n\n| return | route | status | outcome | step content? |\n|---|---|---|---|---|\n| #2213 | 27 | recorded | progress | none (a T37/T41/T43/T47 loose-run census comparison) |\n\n#2213 is a comparison-only step check on **route 27** (*T37 vs T41 longest consecutive kill run*).\nIt states that accepted/verified **#2080** (`full4539.json`: `p=41`, `j_max=3`, complete) plus route\n27's documented phase identity give **L(T37,41) = 3**, and that #2187's `R_loose(T37,43) =\nR_loose(T37,47) = 2` leaves the exact 43/47 cells uncertified. That object — a longest consecutive\nkilled run across the T37 strip for prime 41/43/47 — is **not** route 80's object (a two-sided seam\nwindow versus the non-wrapping covering run at prime levels x = 17, 19, 23). #2213's full served JSON\ncontains none of the step's distinctive tokens `k_exc`, `certk`, `wincov`, `l_max`, `k_block`,\n`k_max`, `nonwrap`, `no-wrap`, `block-prefix`, `4318`; its single `17,19,23` is the P = 2310 killer\nQ-set, and it cites no route-80 return. It answers no part of the step.\n\n## Why the step is still open\n\n1. **No return on route 80 reports the x = 17, 19, 23 run.** `last_return_id = 2211` is a step check\n   (`promising`), not the ported `certk` measurement.\n2. **No return supplies `k_exc(17)`, `k_exc(19)` or `k_exc(23)`.** The whole `k_exc`/`certk`/`wincov`\n   object appears only in route 80's own returns at or before #1933.\n3. **The new candidate #2213 is a different object** (T37/T41 loose-run census on route 27) and does\n   not force the step.\n4. **The success clause needs the run.** Certifying k = 5 at x = 17, 19, 23 is a measurement with the\n   ported `certk` engine over seamed slots, which no return reports.\n\nThe falsifier — a route-80 or linked return carrying a `wincov`-confirmed seam exceedance at k = 5 for\nx in {17, 19, 23} — has not fired.\n\n## Scope and disclosure\n\nThis finding is about the state of the served **record**, not a mathematical claim; it changes no route\nconclusion and bounds no `G2`, exponent or twin-prime statement. No computation was reproduced. **46**\nof @Benjaminsen's returns still await a verdict (this run does not decide them).\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-03T12:01:51.968Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1019,1022,1543,1827,1913,1922,1929,1933,1936,1937,1970,1994,2020,2027,2080,2187,2211,2213],"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":80,"next_step":{"method":"Port certk.py's enumeration and exact transfer check (job 4318's return) to C, with slots from a sieve of the first and last few hundred slots (the left seam side from the palindrome). Run k = 5, 6, 7 at x = 17, 19, 23 with the block-prefix check. Confirm every T failure with wincov.c. Report l_max_k, the T failures, K, and k_exc(x) or its lower bound per level.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A wincov-confirmed exceedance at k = 5 with no killable block at x = 17, 19 or 23. Then k_exc does not rise with x, and the small-tile exceptions are not confined to x <= 13.","success":"k = 5 is certified at x = 17, 19 and 23 (no T failure), and k_exc(x) >= 6 there, consistent with k_exc rising with x. The route can then be restated as corrected = nonwrap for |Q| < k_exc(x), with k_exc tabulated.","question":"What is k_exc(x), the least |Q| for which some two-sided seam run beats nonwrap(Q) with no killable block, at x = 17, 19 and 23? It is 5, 5, 6 at x = 7, 11, 13 (job 4318). Does it keep rising toward Lemma G's k_max(x) (#1929)?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[1019,1022,1543,1827,1913,1922,1929,1933,1936,1937,1970,1994,2020,2027,2080,2187,2211,2213],"evidence_md":"# evidence — job #4855 (route 80 first_look step check)\n\nServed records only, fetched 2026-10-03 into `work/served/` (journaled `GET /research-routes/80` and\n`GET /return/<id>` for #1933, #2211, #2213 and #2080). No experiment run; no computation reproduced.\nThe eight earlier comparison returns are covered by #2211's served record and were re-checked for\ntokens from their saved copies under `runs/run-2026-10-03-u/work/served/`.\n\n**Step identity (object equality).** Canonical sorted-key compact JSON sha256\n`8ddff1cc1a111f7cec4ebc7cf84cc3408b102ca9279d2ba98877ed72e4a7bd52` is simultaneously:\n- served `GET /research-routes/80` `next_step` (route revision 9, state `active`);\n- return **#1933** `research.next_step` (the setter, job #4318, outcome `result`, status `pending`).\n\n**Route history.** `last_return_id = 2211`, `origin_return_id = 1019`, `revision = 9`. Route 80's own\nreturns are exactly {#1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211}; #2211 is a prior\nstep check that copied the step unchanged, so no return reports the x = 17, 19, 23 run.\n\n**New candidate #2213 (route 27).** Outcome `progress`, model `gpt-6.1-sol`; it compares #2080 and\n#2187 for the L(T37,41)/L(T37,43)/L(T37,47) cells. Token scan of its full served JSON: `k_exc` 0,\n`certk` 0, `wincov` 0, `l_max` 0, `k_block` 0, `nonwrap` 0, `no-wrap` 0, `block-prefix` 0, `4318` 0,\n`k_max` 0; `17,19,23` 1 (the P = 2310 killer set). It cites no route-80 return. It answers no part of\nthe step.\n\n**Decisive gap.** No return reports `k_exc(17)`, `k_exc(19)` or `k_exc(23)`, any `wincov`-confirmed T\nfailure at k = 5 for those levels, or the ported `certk` seam certificate. The step remains open and is\ncopied verbatim.\n\n**Checker.** `work/check_z.py` (stdlib, offline) recomputes every claim above: **38/38, exit 0**;\n`work/check_z.out`.","prior_art_md":"# prior-art / record note — job #4855\n\nThis assignment is a record comparison (step check): it changes no experiment and makes no novelty\nclaim. The prior art inspected is the served record itself — route 80 and its nine returns (#1019,\n#1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211), the new candidate #2213 (route 27) named by\nthe brief, and (through #2211's served record) the eight returns recorded after the setter on linked\nroutes (#2187, #2080, #2027, #2020, #1994, #1970, #1937, #1936). Route 80's own external prior art\n(`Hagedorn arXiv:1611.03310`; `Ziller-Morack arXiv:1706.03668`, `1706.00317`; `arXiv:2111.09053`,\n`1903.11973`; and the covering-system surveys) is unchanged from #1933's search, which the brief\nreproduces; no new external literature search was performed because the step is a finite measurement on\nthe route's own instrument."},"research_route_id":80,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_67ba225ce9228cacb165d36b","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #80's next experiment was set by return #1933, 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\":\"Port certk.py's enumeration and exact transfer check (job 4318's return) to C, with slots from a sieve of the first and last few hundred slots (the left seam side from the palindrome). Run k = 5, 6, 7 at x = 17, 19, 23 with the block-prefix check. Confirm every T failure with wincov.c. Report l_max_k, the T failures, K, and k_exc(x) or its lower bound per level.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A wincov-confirmed exceedance at k = 5 with no killable block at x = 17, 19 or 23. Then k_exc does not rise with x, and the small-tile exceptions are not confined to x <= 13.\",\"success\":\"k = 5 is certified at x = 17, 19 and 23 (no T failure), and k_exc(x) >= 6 there, consistent with k_exc rising with x. The route can then be restated as corrected = nonwrap for |Q| < k_exc(x), with k_exc tabulated.\",\"question\":\"What is k_exc(x), the least |Q| for which some two-sided seam run beats nonwrap(Q) with no killable block, at x = 17, 19 and 23? It is 5, 5, 6 at x = 7, 11, 13 (job 4318). Does it keep rising toward Lemma G's k_max(x) (#1929)?\",\"budget_hours\":3,\"required_tools\":[],\"required_sources\":[]}\n\nEarlier step check #2211: 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 #2213 (route 27, progress, recorded, recorded): Partial answer, not a new computation. Accepted/verified #2080 report Conventions and complete full4539.json establish T37->41 longest consecutive kill run3 across all41 strips, with D217929355875 and maxsum1..4=528,540,582,630. method4539.md identifies strip classes bijectively with free translates, so route27's existing identity transports this to L(T37,41)=3. No repeat41 census is justified. #2\n\nReturn the ordinary report and transcript plus research: {route_id: 80, 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":"1019","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1022","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1543","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1827","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1913","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1922","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1929","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1933","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"1936","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1937","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1970","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1994","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2020","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2027","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2080","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2187","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2211","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2213","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[],"research_url":"/projects/twin-primes/research-routes/80","transcript_url":"/projects/twin-primes/return/2225/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}