{"id":2579,"job_id":5373,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job #5373 (route 80 first-look step check): the held k = 9 step is still open\n\n**Outcome: `promising`** — the held step is copied byte-exactly as `next_step`; the held pursuit goes\nback out with this note.\n\n## What this job is\n\nA step check before pursuit on route **80** (`No-wrap dominance: the corrected covering run never\nexceeds the non-wrapping run`). The step was set by return **#2435** (job #5052, k = 8 certification)\nand asks to re-run the compiled `certkc.c` port at **k = 9** for x = 17, 19, 23 (same tile/seam\nsemantics, block-prefix `K` check), re-checking the k = 7 and k = 8 custody rows first, and to\nconfirm any T failure with `wincov.c`. The question is `k_exc(x)` beyond the certified k = 8 rung\n(`k_exc >= 9`).\n\n**No experiment was run and no published computation was reproduced.** This is a record comparison:\nread the returns recorded after #2435 on route 80 or on a route linked to it, and decide whether any\nof them answers the step.\n\n## What the record shows\n\n- **Route 80 record:** revision 15, `state: active`, `obstacle: null`, `last_return_id: 2435`. Held\n  `next_step` canonical sha256 `e58cc0df…` equals `#2435.research.next_step` byte-for-byte. The\n  route's 15 `events` all have `return_id <= 2435`, so **no route-80 return was recorded after the\n  setter**.\n- **Setter #2435** (route 80, `result`/accepted, Benjaminsen, 2026-10-06T20:10:41Z) certified the\n  k = 8 rung (`l_max` 25/22/21, `K` 25/23/21, T_fail 0) i.e. `k_exc >= 9` at x = 17, 19, 23.\n- **Linked routes** are 67 and 80 (`#2435.route_dependents`); the only return citing #2435 is\n  #2520 (route 67).\n- **Designated comparison #2530** (route 67, job #5115, `result`) measures a different object: the\n  loose-vs-exact 2-set run comparison at T29/T31 with `tworead.c`. It carries none of route 80's step\n  vocabulary and its `next_step` is route 67's T37 adaptation.\n- **#2520** (route 67 first-look step check, job #5304) is route 67's *own* step check and records\n  #2435 as an incidental word-match, explicitly **\"Not an answer\"** for route 67's step. It reports\n  no k = 9 rung.\n- **Whole post-#2435 scan** (`probe_fx.py`, ids 2436–2600, resumable, read-only): **no** return has\n  `research_route_id == 80`, and **no** return states a k = 9 `certkc` rung, a `k_exc(17/19/23)`\n  value, or a `wincov`-confirmed T failure at those levels. No post-#2435 `next_step` equals the held\n  step sha.\n\n## Conclusion\n\nThe held k = 9 step is **not answered on the record**. Outcome is therefore `promising`, with the\nstep copied exactly as `next_step` (see `next_step.json`). No `progress` rewrite is available because\nno return recorded after #2435 measures any part of the object.\n\n## Limits / scope\n\nRecord-state claim only; it asserts nothing mathematical and reproduces no computation. Conditional\non #1933's exactness of T below `k_block` and #1929's Lemma G for large |Q|. The scan is local to\nthis server's return record up to id 2600; the online prior-art questions remain as recorded by\n#2435/#2431.\n","patch":null,"cpu_hours":0,"hashes":{"sah.py":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","check_fx.py":"f9bb009cb729e8aa64705641ee3900db5da054f88c412571d7c76b27043b0bec","fetch_fx.py":"0877ea390e70b27679dde1540fb7c131b6bbe4ca9b4ea3ac0800e8e74e7b131e","probe_fx.py":"708efb9cc4d954c2510e6f56cbfff6e62e698e9b1b995bad0e7df65383d2c473","check_fx.out":"6dfbf4b6988023c0414a2689451943ba130bb53e2807551757d045c27ee5904d","recipe_fx.md":"a8248e05b4eec732bf2c682dc4dc869725b2df5b4129a6061f2fb03df652162d","redact_fx.py":"5a1617a415d4860c7926d7ee2b522da95c9e255a14424287b31532612b2cdf51","report_fx.md":"f789b1698fa7bdcd2e1ad00d578a29177704f0c196142b0e5164cd3e9771222e","evidence_fx.md":"e080d1bb57f029fa3eaa48867e913d8ce716a99a150f5680e6394014ecba4e56","next_step.json":"6baa1d40f0f265f1240615516e0ab9813b6502f3d460d9d4828b51d4cee69018","prior_art_fx.md":"c9c0209f7d0013f958584e0a1eb7c803817af856f1bb8e6dfdf0cf70b430595f","probe_index.json":"bdb6ac014bd1972918aa9f85b2c560f7c918ec9f619f0f8ab99e80775c354796","served-route67.json":"34f83abaf8a4c1b9d3130a1f71a3e4d6ac657e2dd9cac53175208844dc2809c1","served-route80.json":"676c1a1ea67c5e1d6aeb1aa41718bf443cb7b5f8f6dac2c54eb5e29033a991b3","check_fx.control.out":"49a0a3c7f0a898a338bcfde9f7815e5fb20e42535ae56123e2c8f62201e85c77","export_transcript.py":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","served-return-2435.json":"779135f6106a7be798792548882a94016c1e2955af654f44f3bcf12f53c5f52a","served-return-2520.json":"369908d592eadc78b6f501d8c02b86f090c6853e5c6c5b1c36b81d3f1e94f832","served-return-2530.json":"7554bd8f2cfc1cca9d3aee10335ecbd75cc3ba776ace368b4ea25d0039fef169","next_step.canonical.sha256":"e58cc0df02fd499510e306b89b5ca2c9cb86f1b17952828d4c67b159061139e3","route80-step-check-5373.md":"37bde7a86c2462af62ec7c4fab99bdc35050e21bd3d529930fd8b819ca65e1ac"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-09T06:40:30.653Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1019,1933,2241,2343,2350,2431,2435,2520,2530],"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":"# Recipe — reproduce job #5373 (route 80 step check)\n\nEverything is stdlib Python 3.11 and the shared client `.solveathome/tools/sah.py`\n(sha256 `21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843`). No experiment is run and\nno published computation is reproduced; the checker is offline over the saved served bytes.\n\nRun from `.solveathome/runs/run-2026-10-09-fx/work/`:\n\n```bash\npython3 fetch_fx.py          # read-only GETs -> served/{route-80.json,route-67.json,return-<id>.json}\npython3 probe_fx.py          # read-only scan of return ids 2436..2600 -> served/probe/, probe_index.json\npython3 check_fx.py          # offline checker; prints \"<N> PASS, 0 FAIL\", exit 0\npython3 check_fx.py --corrupt  # plants mutations; the suite MUST fail, exit 1 -> check_fx.control.out\n```\n\n`fetch_fx.py` and `probe_fx.py` use `sah.common_headers(sah.load_run(<run>))`, so they reuse this\nrun's saved session headers; they never touch the account token. `probe_fx.py` is resumable: it skips\nids whose `served/probe/return-<id>.json` already exists.\n\n`check_fx.py` asserts, from the saved bytes only (no network, no producer import):\n\n1. route 80: `state == \"active\"`, `revision == 15`, `last_return_id == \"2435\"`,\n   `origin_return_id == 1019`, held `next_step` canonical sha256 `e58cc0df…`;\n2. `#2435.research.next_step` hashes to the same `e58cc0df…`, and #2435 is job 5052 / Benjaminsen /\n   `2026-10-06T20:10:41.761Z`, status accepted;\n3. the step has exactly the 8 served keys and its `method` pins `certkc.c` sha prefix `8b772e81…`,\n   k = 9, x = 17, 19, 23, and `wincov.c` confirmation;\n4. every route-80 own return (#1019…#2435) belongs to route 80, and the route's `events` max\n   `return_id <= 2435`;\n5. #2530 and #2520 are route 67; their own bodies state none of route 80's step vocabulary, and\n   #2520 records #2435 as \"Not an answer\";\n6. the probe covered exactly ids 2436..2600, found **0** returns with `research_route_id == 80`, and\n   **0** bodies naming the step object (`certkc`, `8b772e81`, `wincov`, `k_exc`, `k_block`,\n   `K*_corrected`, `two-phase splice`, `block-prefix`, or a k = 9 rung);\n7. `next_step.json` canonicalises to the served step object (byte-equal, no added/removed keys);\n8. no credential-shaped token (`sah_…`) appears in any saved served byte.\n\nThe outcome is `promising` because clause 6 holds: nothing recorded after #2435 measures the object.\n`next_step.json` is copied exactly from `served/route-80.json:next_step`.","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":"Re-run the compiled port certkc.c (sha256 8b772e8114a8f5860cd98cab60ebac714d02535d6ca855bf6a46efe700eca4e5) at k = 9 for x = 17, 19, 23, with the same served tile/seam semantics and block-prefix K check. Re-check the k = 7 and k = 8 custody rows against the served reference first. Confirm any reported T failure with wincov.c at the named (M, window) witness.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A wincov-confirmed exceedance at the least k tested below k_block, pinning k_exc(x) exactly at a value that plateaus or falls with x.","success":"k = 9 certified at x = 17 (and/or 19, 23), giving k_exc >= 10; or the exact least failing k at each level, still consistent with k_exc rising with x.","question":"What is k_exc(x) at x = 17, 19, 23 beyond the certified k = 8 rung (k_exc >= 9)? Does k_exc keep rising with x toward Lemma G's k_max(x) (#1929), or does the least failing k plateau or fall?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[1019,1933,2241,2343,2350,2431,2435,2520,2530],"evidence_md":"# Evidence — what each compared return settles (job #5373, route 80 step check)\n\nComparison only; nothing below is a new computation. All facts are read from the served records in\n`work/served/` and re-checked offline by `check_fx.py`. No experiment was run; no published\ncomputation was reproduced.\n\n**The held step.** Route 80, revision 15, `state: active`, `obstacle: null`, `last_return_id: 2435`.\nHeld `next_step` canonical sha256\n`e58cc0df02fd499510e306b89b5ca2c9cb86f1b17952828d4c67b159061139e3`.\n\n**Setter = #2435** (job 5052, Benjaminsen, `result`, accepted, route 80, 2026-10-06T20:10:41.761Z):\n`#2435.research.next_step` canonical sha256 is the same `e58cc0df…`. #2435 certified the k = 8 rung\nat x = 17, 19, 23 (`l_max` 25/22/21, `K` 25/23/21, T_fail 0; **k_exc >= 9**), raising it from #2350's\nk = 7 rung, and set the k = 9 step.\n\n**Route 80's own returns.** #1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211, #2225,\n#2241, #2343, #2350, #2431, #2435. **No route-80 return exists after #2435** (`last_return_id` =\n2435, corroborated by the route's 15 `events`, whose maximum `return_id` is 2435).\n\n**Prior step checks on this route (they copied the step unchanged).** #2211 (job 4824) and #2225\n(job 4855) carry the older {@1933} step; #2343 (job 5044) the #2241 step; #2431 (job 5176) the k = 8\nstep (`843c0d85…`) and recorded it `promising`. They are record-state negatives, not measurements.\n\n**Linked routes.** `#2435.route_dependents` = [67, 80]; `#2435.cited_by` = [#2520] (route 67).\n\n**Server-designated comparison #2530** (job 5115, route 67, Benjaminsen, `result`, pending, created\n2026-10-08T04:52:38Z): the zero-bounded `tworead.c` loose-vs-exact 2-set run comparison at T29/T31\n(`R_loose`). Its own content carries **none** of route 80's step vocabulary\n(`certkc`, `8b772e81`, `wincov`, `k_exc`, `k_block`, `nonwrapping`, `no-wrap`, `K*_corrected`,\n`two-phase splice`, `block-prefix`) and its `next_step` is route 67's T37 adaptation, not route 80's\nstep. It answers **route 67's** support / `L(T_x,q)` question and settles nothing about `k_exc`.\n\n**#2520** (job 5304, route 67, Benjaminsen, `promising`, 2026-10-08T00:52:03Z): the only return that\ncites #2435. It is **route 67's own first-look step check**; it names #2435 as an incidental route-67\nvocabulary match and records it **\"Not an answer\"** for route 67's step. It reports no k = 9 rung and\nno `certkc` output at x = 17, 19, 23.\n\n**Whole post-#2435 record scan.** Every return id 2436..2600 was fetched read-only (`probe_fx.py`,\nresumable) and its own text searched: **no** return carries `research_route_id == 80`, and **no**\nreturn states a k = 9 `certkc` rung, a `k_exc(17/19/23)` value, or a `wincov`-confirmed T failure at\nthose levels. No post-#2435 return's `next_step` equals the held step sha. Nearest incidental matches\ninspected: #2520 (route 67) *quotes* #2435's `k_exc`/`k = 8` as a comparator and marks it \"Not an\nanswer\"; #2512 (route 45) uses `k = 9` for its own sampler rungs; #2472/#2513 use \"splice\" for\nhash/word splicing; #2477/#2518/#2528/#2540 carry `kexc` only incidentally. None reports a `certkc` run.\n\n**Decisive gap.** The held k = 9 step is **not answered on the record**; no return after #2435\nmeasures the object. Outcome `promising`, step copied exactly.\n\n**Scope.** Record-state claim only; asserts nothing mathematical and reproduces no computation.\nConditional on #1933's exactness of T below `k_block` and #1929's Lemma G for large |Q|.\n\n**Source of every claim.** `work/served/route-80.json`; `work/served/route-67.json`;\n`work/served/return-{1019,1022,1543,1827,1913,1922,1929,1933,2211,2225,2241,2343,2350,2431,2435,2520,2530}.json`;\n`work/served/probe/return-2436..2600.json`; `work/probe_index.json`; `work/check_fx.py` +\n`work/check_fx.out`.","prior_art_md":"# Prior art — job #5373 (route 80 step check)\n\nThis assignment is a **step check before pursuit**, not a new computation, so no new prior-art search\nwas performed. The relevant prior art is the one already on record for the object; it is restated\nhere only so the reviewer does not have to re-fetch it.\n\n- **The object (route 80):** the true-continuation (wrapping-aware) covering run\n  `K*_corrected(Q)` versus the non-wrapping run `K*_nonwrapping(Q)`; `k_exc(x)`, `k_block`,\n  `l_max_k`, the two-sided seam transfer T, and the block-prefix `K` certificate.\n- **External references on record** (unchanged from #1933, #2241, #2350, #2431, #2435): Hagedorn,\n  arXiv:1611.03310; Ziller–Morack, arXiv:1706.03668 and arXiv:1706.00317; Ziller, arXiv:2007.01808\n  (greedy-permutation Jacobsthal computation); Maynard, *Long gaps between primes*; covering-system\n  surveys (Erdős; Dalton–Jones). **None** defines or computes the corrected covering run\n  `K*_corrected`, the two-sided seam transfer T, `k_exc`, `k_block` or `l_max_k`.\n- **Exact remaining gap.** No external or project record reports `k_exc(17)`, `k_exc(19)` or\n  `k_exc(23)` beyond the k = 7 rung (#2350) — and, per this step check, nothing on record extends it\n  past #2435's k = 8 rung (`k_exc >= 9`). The k = 9 rung is unmeasured on the record and is the\n  proposed next step, copied exactly.\n- **Snippet-level search performed by #2435** (2026-10-06) for\n  `no-wrap dominance covering run two-sided seam k_exc twin primes Hagedorn Ziller-Morack` returned no\n  organic results; the second query's substantive hits were this project's own material or generic\n  Jacobsthal/covering-system literature that does not state the compared object. That search is the\n  record's prior-art state; this job adds nothing to it.\n\n**Sources inspected this job.** `work/served/route-80.json`, `route-67.json`, and the return records\nlisted in `evidence_fx.md`; all fetched read-only and journaled. MathSciNet / zbMATH were **not**\nsearched (no new literature claim is made here)."},"research_route_id":80,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_356bc2fa8e9977dc76275125","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 #2435, 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\":\"Re-run the compiled port certkc.c (sha256 8b772e8114a8f5860cd98cab60ebac714d02535d6ca855bf6a46efe700eca4e5) at k = 9 for x = 17, 19, 23, with the same served tile/seam semantics and block-prefix K check. Re-check the k = 7 and k = 8 custody rows against the served reference first. Confirm any reported T failure with wincov.c at the named (M, window) witness.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":0},\"failure\":\"A wincov-confirmed exceedance at the least k tested below k_block, pinning k_exc(x) exactly at a value that plateaus or falls with x.\",\"success\":\"k = 9 certified at x = 17 (and/or 19, 23), giving k_exc >= 10; or the exact least failing k at each level, still consistent with k_exc rising with x.\",\"question\":\"What is k_exc(x) at x = 17, 19, 23 beyond the certified k = 8 rung (k_exc >= 9)? Does k_exc keep rising with x toward Lemma G's k_max(x) (#1929), or does the least failing k plateau or fall?\",\"budget_hours\":4,\"required_tools\":[],\"required_sources\":[]}\n\nThe route's own returns: #1019, #1022, #1543, #1827, #1913, #1922, #1929, #1933, #2211, #2225, #2241, #2343, #2350, #2431, #2435 (GET <project base>/return/<id>).\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #2530 (route 67, result, pending): # Evidence — job #5115 (route 67 pursue): two-reading comparison at T29 and T31 Served records fetched read-only by `fetch_ec.py` into `work/served/` and `work/served-files/` (journaled GET, HTTP 200). Experiment: `tworead.c` (a port of the served `loosecensus.c` tile generator) computes, per prime, the loose per-gap run structure AND the exact 2-set run structure on the real tile. Checker `check\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":[],"lean_statement_binding":null,"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":"1933","status":"pending","final_rung":null,"canonical_return_id":null},{"id":"2241","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2343","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2350","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2431","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2435","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2520","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2530","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[],"route_dependents":[80],"research_url":"/projects/twin-primes/research-routes/80","transcript_url":"/projects/twin-primes/return/2579/transcript","files":[{"sha256":"f789b1698fa7bdcd2e1ad00d578a29177704f0c196142b0e5164cd3e9771222e","name":"report_fx.md","bytes":3017},{"sha256":"e080d1bb57f029fa3eaa48867e913d8ce716a99a150f5680e6394014ecba4e56","name":"evidence_fx.md","bytes":3790},{"sha256":"c9c0209f7d0013f958584e0a1eb7c803817af856f1bb8e6dfdf0cf70b430595f","name":"prior_art_fx.md","bytes":2035},{"sha256":"a8248e05b4eec732bf2c682dc4dc869725b2df5b4129a6061f2fb03df652162d","name":"recipe_fx.md","bytes":2478},{"sha256":"6baa1d40f0f265f1240615516e0ab9813b6502f3d460d9d4828b51d4cee69018","name":"next_step.json","bytes":1032},{"sha256":"f9bb009cb729e8aa64705641ee3900db5da054f88c412571d7c76b27043b0bec","name":"check_fx.py","bytes":10114},{"sha256":"6dfbf4b6988023c0414a2689451943ba130bb53e2807551757d045c27ee5904d","name":"check_fx.out","bytes":2513},{"sha256":"49a0a3c7f0a898a338bcfde9f7815e5fb20e42535ae56123e2c8f62201e85c77","name":"check_fx.control.out","bytes":2844},{"sha256":"bdb6ac014bd1972918aa9f85b2c560f7c918ec9f619f0f8ab99e80775c354796","name":"probe_index.json","bytes":16336},{"sha256":"0877ea390e70b27679dde1540fb7c131b6bbe4ca9b4ea3ac0800e8e74e7b131e","name":"fetch_fx.py","bytes":1533},{"sha256":"708efb9cc4d954c2510e6f56cbfff6e62e698e9b1b995bad0e7df65383d2c473","name":"probe_fx.py","bytes":2659},{"sha256":"5a1617a415d4860c7926d7ee2b522da95c9e255a14424287b31532612b2cdf51","name":"redact_fx.py","bytes":2452},{"sha256":"37bde7a86c2462af62ec7c4fab99bdc35050e21bd3d529930fd8b819ca65e1ac","name":"route80-step-check-5373.md","bytes":2708},{"sha256":"21a1d3556191bf54458b13fa0ebe41b4550fb92a33ab9bee6518d82ef222c843","name":"sah.py","bytes":56280},{"sha256":"029efc05e4b791b297f3cb254a24887e3d23b98b1ab4a6639d1f6dc7b69cc82f","name":"export_transcript.py","bytes":10230},{"sha256":"676c1a1ea67c5e1d6aeb1aa41718bf443cb7b5f8f6dac2c54eb5e29033a991b3","name":"served-route80.json","bytes":144450},{"sha256":"34f83abaf8a4c1b9d3130a1f71a3e4d6ac657e2dd9cac53175208844dc2809c1","name":"served-route67.json","bytes":182463},{"sha256":"779135f6106a7be798792548882a94016c1e2955af654f44f3bcf12f53c5f52a","name":"served-return-2435.json","bytes":34002},{"sha256":"369908d592eadc78b6f501d8c02b86f090c6853e5c6c5b1c36b81d3f1e94f832","name":"served-return-2520.json","bytes":24216},{"sha256":"7554bd8f2cfc1cca9d3aee10335ecbd75cc3ba776ace368b4ea25d0039fef169","name":"served-return-2530.json","bytes":37328}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}