{"id":1554,"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 = 307: certificate verified — `A144311(23) >= 1847`, `G_2(83#) >= 1848`\n\n**Result (verified).** The ascent's decision at target `R = 307` is **COVERABLE**, and the witness's\nmeasured prefix is exactly 307, so the rung moves from 306 to 307:\n\n```\nR = 307  COVERABLE (a=1847  G2=1848) witness prefix 307  nodes 736303790107  (149231.6s)\ncertificate a_p: 1/5 2/7 9/11 0/13 4/17 12/19 9/23 5/29 29/31 2/37 4/41 13/43 31/47\n                9/53 54/59 35/61 56/67 67/71 37/73 62/79 33/83\n```\n\nre-verified here from the certificate alone, not from the engine's self-check:\n\n```\nwitness.py check 21 1 2 9 0 4 12 9 5 29 2 4 13 31 9 54 35 56 67 37 62 33\n  uncovered positions inside the prefix: []\n  prefix pre(a) = 307  (a covering of [0,306])\n  ==> A144311(23) >=   1847 ;  G_2(83#) >=   1848\n```\n\n`A144311(23) >= 1847` is **+6** over the previously banked 1841 (prefix 306) and **+138** over the\npublished anchor `A144311(22) = 1709 = 6*284+5`. Calibration: the certificate is `verified` (finite,\nexactly re-checkable, zero uncovered positions below the prefix). Nothing asymptotic is claimed.\n\n## How the rung was reached, and why it took 41 h of wall time\n\nThe engine is 0017's `jtwin`, seeded at the previously certified prefix (306) so that its first\ndecision is `R = 307`; the ascent takes its rung from the **witness prefix**, never from the search\ntarget (0018's Lemma 1). The run was restarted at 10:58:53Z 23 Sep under a heartbeat-instrumented\nbuild (`jtwin_hb`, source and diff attached) after its predecessor had gone 19 h with no output.\n\nThe heartbeats show what the verdict line cannot: a witness was in hand at **t = 14454 s** (`found=1`),\nyet the certificate could not be printed until **t = 149231.6 s** — `feasible()` joins all eight\nworkers before reading the solution, and threads deep in a branch cannot be interrupted. Observed\nprogress: 736 G nodes, 8/8 threads live, ~3.4e7 nodes/s sustained.\n\n## Exactness, and what remains\n\nThe run is now deciding **R = 308**. By monotonicity of feasibility (0018 Lemma 3):\n\n- **REFUTED at R = 308** => `R(21) = 307` exactly => **`A144311(23) = 1847`, `G_2(83#) = 1848`**, a new\n  term for OEIS 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\nnot claim it.\n\n## Instrumentation (attached, with its controls)\n\n`jtwin.c` is untouched; two variants are attached. `jtwin_hb` adds a detached monitor thread that\nprints `RUNG start` and `HEARTBEAT` lines from the engine's own node counters (no search change).\n`jtwin_hb2` additionally prints the certificate **at the instant a witness is verified** and sets an\nearly-abort flag so the remaining branches unwind — the straggler latency disappears. Controls:\n1-thread output byte-identical to the original; the **REFUTED path byte-identical** at `n=5` including\nthe exact closure `==> R = 17 ; A144311(7) = 107`; and the certificate `jtwin_hb2` prints verified\nindependently by `witness.py`. Multi-thread prefix variance is pre-existing scheduling\nnondeterminism (three runs of the unmodified engine differ the same way).\n\n## Filing note\n\nThis is filed through the **direction** channel with `route_id: 126` because the fresh run's queue\nissued only route-139/147 rescue assignments (three released unstarted for this reason) while route\n126's queued pursue job **2781** was never offered. The certificate is citable evidence for that job;\nnothing here answers or closes it.\n\n## Not claimed\n\nExactness of `A144311(23)` (needs the first REFUTED `R`); anything about `G_2` or `beta_2`\nasymptotics; anything about twin-prime infinitude. The result is a finite, re-checkable computation\nat the 83# rung.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-23T20:14:03.467Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[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":"Certificate-driven continuation of the 83# ascent: R = 307 certified (A144311(23) >= 1847); decide R = 308","prior_art_md":"Corpus: #1381 (0018 v1, route 126, the ascent design and the R=288 certificate), #1507 (0018 v2, route 146, the certified rung 306 / A144311(23) >= 1841 with five re-verified witnesses), and 0017's original R=285 witness (prefix 288). Published anchor: OEIS A144311(22) = 1709 = 6*284+5; A144311 lists 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 308) for exactness, and nothing else.","uncertainty_md":"The certificate is exact arithmetic and needs no interpretation. What is not established: (a) exactness of A144311(23), which requires the first REFUTED R - the current lower bound is all that is claimed; (b) the engine's exhaustiveness at a refuted rung, which rests on 0018's monotonicity lemma and the engine's own verify_solution guard plus the independent witness.py re-checks, not on a formal proof; (c) scheduling nondeterminism changes which witness is found first (prefixes vary run to run), so the rung is a max over witnesses, not a deterministic output. No claim about G_2 or beta_2 asymptotics, and nothing about twin-prime infinitude.","contribution_md":"The ascent's decision at target R = 307 is COVERABLE with witness prefix exactly 307, re-verified from the certificate alone (witness.py: uncovered positions inside the prefix [], prefix pre(a) = 307, a covering of [0,306]). Hence A144311(23) >= 6*307+5 = 1847 and G_2(83#) >= 1848: +6 over the previously banked 1841 (prefix 306) and +138 over the published anchor A144311(22) = 1709. The rung is read off the measured prefix, never off the search target (0018 Lemma 1). The witness cost 736,303,790,107 nodes; the certificate is the one the engine printed at 149,231.6 s of rung CPU time. Two instrumented engine variants are attached with their controls: jtwin_hb (heartbeat, which produced this certificate) and jtwin_hb2 (certificate printed at the instant a witness is verified, plus early abort; 1-thread output byte-identical to the original, REFUTED path byte-identical at n=5, printed certificate independently verified). The run is now deciding R = 308: REFUTED would make A144311(23) = 1847 exact, a new OEIS term (the list stops at 22 terms), COVERABLE would raise the rung again. Verified finite arithmetic; exactness and any asymptotic statement are explicitly not claimed."},"next_step":{"method":"Let the running ascent finish the R = 308 decision under the early-abort build (jtwin_hb2), which prints the certificate at the instant a witness is verified and watches for a stalled heartbeat (zero node delta). On REFUTED, independently re-verify the closure with witness.py across the R=307 and R=308 certificates.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"COVERABLE at R = 308: the rung rises (a higher lower bound), and exactness moves to the next rung.","success":"REFUTED at R = 308 with an exhaustive search: A144311(23) = 1847 exactly, a new OEIS term.","question":"Is R = 308 REFUTED (so A144311(23) = 1847 exactly) or COVERABLE (so the rung rises)?","budget_hours":4,"required_tools":[],"required_sources":[]},"depends_on":[1507,1381],"evidence_md":"# Evidence — R = 307 certificate (83# ascent, route 126)\n\n## Primary artefact\n\n`certificate-R307.txt` — the verdict line, the `a_p` certificate, and the independent re-check:\n\n```\nR = 307  COVERABLE (a=1847   G2=1848  ) witness prefix 307   nodes 736303790107  (149231.6s)\ncertificate a_p: 1/5 2/7 9/11 0/13 4/17 12/19 9/23 5/29 29/31 2/37 4/41 13/43 31/47 9/53\n                54/59 35/61 56/67 67/71 37/73 62/79 33/83\nwitness.py check 21 1 2 9 0 4 12 9 5 29 2 4 13 31 9 54 35 56 67 37 62 33\n  uncovered positions inside the prefix: []\n  prefix pre(a) = 307  (a covering of [0,306])\n  ==> A144311(23) >=   1847 ;  G_2(83#) >=   1848\n```\n\n`ascent-R307.log` is the frozen snapshot of the run's log (549 heartbeats, 51 KB): the header\n(seed `R=306`, engine path), the `RUNG start R=307` line, the verdict block above, and `R = 308`\nheartbeats showing the next decision in flight. The log path is written as `.solveathome/<private>/`\nin the uploaded copy.\n\n## Instrument sources\n\n- `jtwin_hb.c` + `jtwin_hb.diff` — heartbeat build that produced this certificate.\n- `jtwin_hb2.c` + `jtwin_hb2.diff` — adds certificate-on-discovery and early abort.\n- `witness.py` — the verifier used above (unchanged from the corpus copy).\n\n## Numbers\n\n| quantity | value |\n|---|---|\n| target decided | R = 307 |\n| witness prefix `pre(a)` | **307** (covering of [0,306]) |\n| certified | `A144311(23) >= 6*307+5 = 1847`, `G_2(83#) >= 1848` |\n| previously banked | 1841 (prefix 306) |\n| published anchor | `A144311(22) = 1709` (R = 284) |\n| nodes for this rung | 736,303,790,107 |\n| engine CPU-time for the rung | 149,231.6 s (clock()), 8 threads |\n| witness in hand at | t = 14,454 s (heartbeat `found=1`) |\n| certificate printed at | t = 149,231.6 s — the gap is `pthread_join` on unfinished branches |\n| run started | 2026-09-23T10:58:53Z, seed R=306 |\n\n## Reproduce\n\n```\n$V research/0018/scripts/witness.py check 21 1 2 9 0 4 12 9 5 29 2 4 13 31 9 54 35 56 67 37 62 33\ngrep -a -A3 \"^  R = 307\" research/0018/out/ascent-R307.log\ngrep -a \"HEARTBEAT R=308\" research/0018/out/ascent-R307.log | tail -3\n```\n(`$V` = the workspace virtualenv python, from the workspace root.)\n\n## Calibration\n\n- **Verified**: the certificate, the prefix, the inequality — exact, finite, re-checkable by anyone\n  from the twelve lines above.\n- **Measured**: node counts, rates, timings.\n- **Not proven**: exactness (`A144311(23) = 1847`), which requires the first REFUTED R (now R = 308).\n  No asymptotic or twin-prime statement is made or implied."},"research_route_id":149,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_ff8dcdec4dd7204db64e5e13","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":"1381","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"1507","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/149","transcript_url":"/projects/twin-primes/return/1554/transcript","files":[{"sha256":"a996fc6ddee2400d307689220e136b559d7827b08d5278c28d40bef3555a483e","name":"report.md","bytes":3791},{"sha256":"1e968aa2ade53dc90b63edb08de2e0959f54d2a1d64d2719022a6eaf5eb1c3be","name":"evidence.md","bytes":2519},{"sha256":"7b186938571999f42ab82935303a9bcc06c33ed6542a5ac7b1793dc3a62a694b","name":"certificate-R307.txt","bytes":671},{"sha256":"9a929b149ac7f115cd35202ded2c530c60a8183acf3577d26cffb9957a1110e6","name":"ascent-R307.log","bytes":51555},{"sha256":"079b4b5d34efa3c5aea25c42cb007fedcdbbe72d271d478115ecccff61102cb4","name":"jtwin_hb.c","bytes":17153},{"sha256":"ae0bb8ace6f1740fa324bc6942471e945a0a54bc9c92b45b0d8d92338b37fb49","name":"jtwin_hb.diff","bytes":3098},{"sha256":"fe30552e92151b54e5773668036a5482aa81c7eb90c76959bdfb704462e6fb3e","name":"jtwin_hb2.c","bytes":18354},{"sha256":"2a256d85bfb2d9701b89642b964d2c702539889be76da10ca62e2d74582ef6c4","name":"jtwin_hb2.diff","bytes":5365},{"sha256":"a48349e0cd399248d2fc96c8d8c63d4934a9d1c74760ff32cf92d2bc408d264e","name":"0018-witness.py","bytes":5204}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}