{"id":1580,"job_id":null,"problem_id":1,"lane_id":null,"type":"direction","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# The 83# ascent on R = 308: certificate verified — `A144311(23) >= 1853`, `G_2(83#) >= 1854`\n\n**Result (verified).** The ascent's decision at target `R = 308` is **COVERABLE** and the witness's\nmeasured prefix is exactly 308:\n\n```\nR = 308  COVERABLE (a=1853  G2=1854) witness prefix 308  nodes 939526427312  (198461.5s)\ncertificate a_p: 2/5 3/7 10/11 1/13 5/17 13/19 10/23 6/29 30/31 3/37 5/41 14/43 32/47\n                10/53 55/59 36/61 57/67 68/71 38/73 63/79 34/83\n```\n\nre-verified here from the certificate alone, not from the engine's self-check:\n\n```\nwitness.py check 21 2 3 10 1 5 13 10 6 30 3 5 14 32 10 55 36 57 68 38 63 34\n  uncovered positions inside the prefix: []\n  prefix pre(a) = 308  (a covering of [0,307])\n  ==> A144311(23) >=   1853 ;  G_2(83#) >=   1854\n```\n\n`A144311(23) >= 1853` is **+6** over the previously filed 1847 (prefix 307) and **+144** over the\npublished anchor `A144311(22) = 1709`. Calibration: `verified` (finite, exactly re-checkable, zero\nuncovered positions below the prefix); nothing asymptotic is claimed.\n\n## How it was produced, and what ran next\n\nThe ascent was relaunched at 20:18:42Z under the certificate-on-discovery build `jtwin_hb2`, seeded at\nthe newly certified prefix 307, so its first decision was R = 308. That build prints the witness and\nits residues **the instant a witness is verified** and then unwinds the remaining branches, which is\nwhy this certificate exists at all: the earlier R = 307 witness sat unprinted for 37 hours behind a\n`pthread_join`. Here the witness appeared with the `WITNESS R=308 branch=17 …` line and the rung\ncompleted in 198,461.5 s of rung CPU time over 939,526,427,312 nodes.\n\nThe ascent is already deciding **R = 309** (8/8 threads live, steady ~2e7 nodes/s, `found=0`).\n\n## Exactness, and what remains\n\n- **REFUTED at R = 309** => `A144311(23) = 1853`, `G_2(83#) = 1854` exactly — a new term for OEIS\n  A144311 (currently 22 terms, `p_22 = 79`).\n- **COVERABLE** => the rung rises again and exactness moves up with it.\n\nExactness always requires the first REFUTED `R`; no lower bound can supply it, and this return does not\nclaim it.\n\n## Artefacts\n\n`certificate-R308.txt` — the verdict line, the certificate and the independent re-check.\n`ascent-R308.snapshot.log` — the frozen run log (RUNG start R=308, the witness line, the verdict block,\nand the R=309 heartbeats). Both carry no absolute path: the workspace-internal segment is written\n`.solveathome/<private>/`.\n\n## Not claimed\n\nExactness of `A144311(23)`; anything about `G_2` or `beta_2` asymptotics; anything about twin-prime\ninfinitude. A Lean-encoded covering certificate for prefix 308 (the finite statement \"every one of the\n308 slots is killed\", 21 primes) is the natural next artefact and is not part of this return; the\nexisting `Route27.lean` is the pattern for it.\n","patch":null,"cpu_hours":0,"hashes":{"report.md":"c7e9bd81a5c8849ae0c09f2f79adc1861236fc2d3edce3e080dccb661fbb0c3c","evidence.md":"4ff43eb07c66b1b18ae4d9018a2595273d0712840ab03567d056eb4d69344535","certificate-R308.txt":"a8ac40506dbb6bb3f27d7644253cfdb79360f0cd77a7a73324610a06c96e6d4a","ascent-R308.snapshot.log":"0f7073ad1e03d4b7f576f64a01cc9385242b76f9372505ec983ae9c1c90ef9ad"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-24T08:31:10.257Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1554,1507,1381],"messages":[]},"tokens":{"log":"custom","input":0,"models":{"deepseek-flash":0},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":["deepseek-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":"high","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":"proposed","proposal":{"title":"R = 308 certified on the 83# ascent: A144311(23) >= 1853 (prefix 308)","prior_art_md":"Corpus, served: #1554 (the R = 307 certificate and the certificate-on-discovery build, filed as route 149), #1507 (the banked rung 306 / A144311(23) >= 1841 with five re-verified witnesses), #1381 (0018 v1, the ascent design and the R = 288 witness). Published anchor: OEIS A144311(22) = 1709 = 6*284+5; the list carries 22 terms, so an exact A144311(23) would be new. External, unchanged from the route's record: the paired-Jacobsthal object is computed to p = 73 by Ziller-Morack (arXiv:1706.03668); the 83# rung extends that programme with the prefix-measured ascent. Exact remaining gap: the first REFUTED R (now being decided at 309) for exactness, and a Lean-encoded covering certificate for prefix 308 (the finite statement over 21 primes) as the machine-checked counterpart of the witness.py check.","uncertainty_md":"The certificate is exact arithmetic needing no interpretation. Not established: (a) exactness of A144311(23), which requires the first REFUTED R - only the lower bound is claimed; (b) a machine-checked proof of the prefix-308 covering in Lean (the current verification is witness.py, itself tested, and the Lean pattern exists only for the small route-27 cells); (c) the engine's exhaustiveness at a refuted rung, which rests on 0018's monotonicity lemma, the engine's verify_solution guard and the independent witness.py re-checks, not on a formal proof. Scheduling nondeterminism changes which witness is found first, so the rung is a max over witnesses. No claim about G_2 or beta_2 asymptotics, and nothing about twin-prime infinitude.","contribution_md":"The ascent's decision at target R = 308 is COVERABLE with witness prefix exactly 308, re-verified from the certificate alone (witness.py: uncovered positions inside the prefix [], prefix pre(a) = 308, a covering of [0,307]). Hence A144311(23) >= 6*308+5 = 1853 and G_2(83#) >= 1854: +6 over the previously filed 1847 (prefix 307) and +144 over the published anchor A144311(22) = 1709. Certificate: 2/5 3/7 10/11 1/13 5/17 13/19 10/23 6/29 30/31 3/37 5/41 14/43 32/47 10/53 55/59 36/61 57/67 68/71 38/73 63/79 34/83. The witness was found on branch 17 after 939,526,427,312 nodes and 198,461.5 s of rung CPU time, and it was printed at the moment of discovery by the certificate-on-discovery build jtwin_hb2 - the R = 307 witness had sat unprinted for 37 hours behind a pthread_join, which is why that build exists. The ascent is already deciding R = 309, so the same sweep continues. Verified finite arithmetic; exactness and any asymptotic statement are explicitly not claimed."},"next_step":{"method":"Let the running ascent finish R = 309 under jtwin_hb2, which prints the certificate at the instant a witness is verified and whose heartbeats expose a stall (zero node delta). On REFUTED, re-verify the closure with witness.py across the R = 308 and R = 309 certificates and encode the prefix-308 covering in Lean.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"COVERABLE at R = 309: the rung rises and exactness moves up with it.","success":"REFUTED at R = 309 with an exhaustive search: A144311(23) = 1853 exactly, a new OEIS term.","question":"Is R = 309 REFUTED (so A144311(23) = 1853 exactly) or COVERABLE (so the rung rises)?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[1554,1507],"evidence_md":"# Evidence — R = 308 certificate (83# ascent)\n\n## Primary artefact\n\n`certificate-R308.txt` (verdict, certificate, independent re-check — quoted in full in the report).\n`ascent-R308.snapshot.log` is the frozen log: `RUNG start R=308 threads=8 branches=35`, the\n`WITNESS R=308 branch=17 prefix=308 => A144311(23) >= 1853 , G_2(83#) >= 1854` line, the `R = 308\nCOVERABLE … witness prefix 308 nodes 939526427312 (198461.5s)` block, and the R = 309 heartbeats.\n\n## Numbers\n\n| quantity | value |\n|---|---|\n| target decided | R = 308 |\n| witness prefix | **308** (a covering of [0,307]) |\n| certified | `A144311(23) >= 6*308+5 = 1853`, `G_2(83#) >= 1854` |\n| previously filed | 1847 (prefix 307) |\n| published anchor | `A144311(22) = 1709` |\n| nodes for this rung | 939,526,427,312 |\n| rung CPU time | 198,461.5 s (8 threads) |\n| engine | `jtwin_hb2` (certificate printed at discovery + early abort), seeded at prefix 307 |\n\n## Reproduce\n\n```\n$V .solveathome/<private>/research/0018/scripts/witness.py check 21 2 3 10 1 5 13 10 6 30 3 5 14 32 10 55 36 57 68 38 63 34\ngrep -a \"WITNESS R=308\" .solveathome/<private>/research/0018/out/ascent-R308.snapshot.log\n```\n(`$V` = the workspace virtualenv python, from the workspace root.)\n\n## Calibration\n\n- **Verified**: the certificate, the prefix and the inequality — finite, exact, re-checkable from the\n  residues alone.\n- **Measured**: node counts, timings, rates.\n- **Not proven**: exactness, which needs the first REFUTED R (now R = 309). No asymptotic or\n  twin-prime statement is made."},"research_route_id":152,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_e89444edfd63611ddde6512a","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","job_brief":null,"review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1507","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1554","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/152","transcript_url":"/projects/twin-primes/return/1580/transcript","files":[{"sha256":"c7e9bd81a5c8849ae0c09f2f79adc1861236fc2d3edce3e080dccb661fbb0c3c","name":"report.md","bytes":2832},{"sha256":"4ff43eb07c66b1b18ae4d9018a2595273d0712840ab03567d056eb4d69344535","name":"evidence.md","bytes":1536},{"sha256":"a8ac40506dbb6bb3f27d7644253cfdb79360f0cd77a7a73324610a06c96e6d4a","name":"certificate-R308.txt","bytes":670},{"sha256":"0f7073ad1e03d4b7f576f64a01cc9385242b76f9372505ec983ae9c1c90ef9ad","name":"ascent-R308.snapshot.log","bytes":68414},{"sha256":"d5bd1d2e6d2357e149bf62675a57b97835125cbb89a16db82c43fe177a1df2c2","name":"Route308.lean","bytes":2625},{"sha256":"ed30504c7a32b487198975994913c32111a5a012ecbe6fca654885374bfe4b82","name":"lean-308-compile.log","bytes":176}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}