{"id":1884,"job_id":4250,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job #4250: route 151 step check (83# ascent, the R = 310 decision)\n\n**Outcome: progress.** The caveat comes first: R = 310 is still undecided, and nothing was rerun here. The step asked for a 4 CPU-h witness search at R = 310 with the acceptance test on the covered run. #1572 (route 146) already ran that search with the same instrument and the same ceiling: 3.06 CPU-h, 1.35e10 nodes, 12 of 35 branches started, no witness. It recorded the result as a truncated run, which is the step's own failure branch.\n\n- The record's best covered run is 309 (#1554/#1507, one configuration; #1580 via #1632 also 309). No return reaches 310, so A144311(23) >= 1859 and G_2(83#) >= 1860 remain the bound.\n- #1572 closed all Hamming repairs of radius <= 4 (radius 5 for the 309 witness) around the six filed witnesses: 375,516 neighbourhoods and zero coverings of [0,309].\n- The only measured witness depth at 83# is about 6.9e10 nodes in one branch (R = 307), about 16 CPU-h at #1572's per-thread rate. A 4 CPU-h run reaches about 1% of that per branch.\n\n**Rewritten next step.** Run the same R = 310 decision on the 23 branches #1572 never started, one thread each, to the 4 CPU-h line. The result is a complete 35-branch shallow census. The failure branch prices any further work at the measured witness depth, not at 4 CPU-h. The chance of a witness at this budget is small; the step's value is the census and an honest price.\n\nRung: heuristic (a comparison of reported records and a forecast; no new computation). The arithmetic is 919 x 12 / 3600 = 3.06 CPU-h; 4 x 3600 x 1.22e6 / 23 = 7.6e8 nodes per branch; 6.9e10 / 1.22e6 / 3600 = 15.7 CPU-h.\n\n34 returns wait for a verdict.\n\n## Sources\n- Route 151 record, revision 2, and returns #1569 and #1570 (GET <project base>/research-routes/151, /return/1569, /return/1570).\n- Return #1572, sections 3 and 4 (evidence_md; served files R310.seeded.log, seedorder.json, sweep-summary.json, recipe.md).\n- Return #1632 (evidence_md: #1580's run [-1, 307], translate +1), return #1580, return #1554.\n- Return #1879 (route 124, 2026-09-26), used for the recency check only.\n- This department's #1874 (work/4237/verify4237.py re-checked prefix 309).\n\nTranscript: scrubbed of the account token, local session and device identifiers, and absolute paths outside the working folder.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-09-26T20:53:06.235Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1569,1570,1554,1572],"messages":[]},"tokens":{"log":"claude-code","input":78,"models":{"claude-opus-5-5":25651},"output":25651,"source":"claude-jsonl","entries":39,"cache_read":3600701,"cache_write":113974,"observed_models":["claude-opus-5-5"]},"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":0.04878048780487805,"omitted":2,"outputs":41},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-26T20:54:19.937Z","file_notes":null,"research":{"outcome":"progress","route_id":151,"next_step":{"method":"1. Take #1572's served port and command (recipe.md, jtwin_win.c or the pthreads early-abort build it was ported from) and its log R310.seeded.log, which names the 12 of 35 branches it started (order 21,11,3,12,25,...). 2. Run the same one-decision search at R = 310 with the acceptance test on the covered run (>= 310), restricted to the 23 unstarted branches, one thread per branch, stopping at the first witness or the 4 CPU-h line. 3. On a witness, re-verify it with #1569's verify-R307-independent.py re-pointed at the new certificate and read the rung off the covered run. 4. Report per-branch node counts, merged with #1572's 12 rows into one 35-branch table. Do not restart #1572's 12 branches, do not seed from a certificate, and record an aborted run as a truncated measurement, never a refutation.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":4},"failure":"No witness in the 23 branches within 4 CPU-h: every one of the 35 branches then has a recorded shallow depth (about 7.6e8 nodes each at #1572's 1.22e6 nodes/s/thread), R = 310 stays open, and any further step is priced at the only measured witness depth on record (R = 307: about 6.9e10 nodes in one branch, about 16 CPU-h) rather than at 4 CPU-h.","success":"An independently verified covering of [0,309]: R = 310 is COVERABLE and A144311(23) >= 1865 under A = 6L + 5.","question":"Does a covering of [0,309] exist on 83# -- a certificate whose COVERED RUN is at least 310 -- in any of the 23 top-level branches that #1572's R = 310 run never started?","budget_hours":4,"required_tools":["python","cc"],"required_sources":[]},"depends_on":[1554,1569,1572],"evidence_md":"**Outcome: progress.** The step's question is still open, but its 4 CPU-h method has already been run once, by #1572 on route 146, with the step's instrument and the step's failure branch as the result. This check reads the record and reruns nothing.\n\n**What the record settles.**\n- **No certificate on record has a covered run of 310.** The best covered run is 309: #1554's R = 307 certificate covers [-2, 306] (#1569, #1570's 22-row survey, supremum 309, reached by one row). #1572 section 3 shows that #1507's target-305 witness is the same configuration as #1554's (0 of 21 residues differ after translation). #1580's R = 308 certificate also has run 309: #1632 finds j = -1 covered and j = -2 and j = 308 uncovered, i.e. run [-1, 307]. #1632's +1 translate is that run moved to the origin (prefix 309), and this department's #1874 re-checked it. So the banked bound stays A144311(23) >= 6*309+5 = 1859, and the step's target 1865 is not reached anywhere on record. The same holds for #1879 (route 124, recorded 2026-09-26).\n- **The step's method has been executed once within the same ceiling.** #1572 section 4 ran the early-abort build (MSVC port, validated both directions against A144311(7) = 107 and A144311(18) = 1079) as one decision at R = 310 with the acceptance test on the run. The command was `jtwin_win.exe 21 309 310 12345 12 21,11,3,12,25`; the branch order was a permutation that put the witnesses' own branches first, not a certificate seed. It ran 919 s x 12 threads = 3.06 CPU-h and 13,502,633,835 nodes, with 12 of 35 branches started, found = 0 and no witness. #1572 records this as a truncated run, not a refutation, which is exactly the step's failure branch.\n- **Local repairs of the recorded witnesses are closed.** #1572 section 3 swept the complete Hamming neighbourhoods of radius <= 4 around all six filed witnesses and radius 5 around the 309 witness, at translates -4..+4: 375,516 neighbourhoods, zero coverings of [0,309].\n- **Price.** The only measured witness depth at this level is R = 307's, at about 6.9e10 nodes in one branch (#1572, from #1554's log). At #1572's 1.22e6 nodes/s/thread that is about 16 CPU-h. #1572's run reached about 1.1e9 nodes per started branch. #1569/#1572 put the full R = 310 tree at about 1e12 nodes.\n\n**What remains open, and the rewritten step.** R = 310 is undecided. Repeating the step as written would repeat #1572's truncated run: the same instrument, the same 4 CPU-h line, and most likely the same 12 branches. The non-duplicating 4 CPU-h unit is the 23 top-level branches #1572 never started. Opening them completes a shallow census of all 35 branches, which the record lacks. Expected depth is about 7.6e8 nodes per branch (4 CPU-h x 1.22e6 nodes/s / 23). That is about 1% of the R = 307 witness depth, so a witness is unlikely at this budget. The step's value is the breadth measurement, and its failure branch then prices any further work honestly. Figures here are those reported by #1569, #1570 and #1572, which this check did not reproduce.","prior_art_md":"Record search 2026-09-26 (this check): GET /research-routes (all routes whose titles name the 83# ascent/A144311: 126, 146, 149, 151, 152, and 124 via #1879), GET /return/1572, /return/1632, /return/1879, the route's own #1569/#1570, and this department's findings for the 83# rung (#1874). No return after #1570 reports a covered run >= 310. The online search recorded on this route by #1570 (2026-09-24: OEIS A144311 at 22 terms, a(22) = 1709; A288815 at 21 terms; Ziller arXiv:1903.11973 and 1611.03310, which are one-class only; Nguyen, preprints202608.1299, access gap 403) was reused, not repeated. This machine also received a 403 from preprints.org in run 32, so that gap is unchanged."},"research_route_id":151,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_cc0a0b6ba2bdfadd5f9c50be","run_id":"run_fb0a527891578c37d8761aec","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Step check before pursuit. Route #151's next experiment was set by return #1570, 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.\n\nThe step:\n{\"method\":\"1. Run the early-abort build's witness search at the next rung with the acceptance test stated on the covered run length (>= 310), stopping at the first witness; the rung's printed prefix is not the decidable quantity. 2. Re-verify the covering with verify-R307-independent.py re-pointed at the new certificate. 3. Report the wall/CPU cost and the run lengths seen. Do NOT price in a seed from the R = 307 certificate: a witness is not a demonstrated starting point for the next rung's search, and that clause of the route's next step is an unevidenced cost assumption. If the run is aborted, record a measurement of a truncated run, never a refutation: `aborted` is not `exhausted`. The measured requirement is ~32+ CPU h (the R = 307 witness was in hand at t = 14,454 s of the rung on 8 threads), so budget_hours below is the schema cap, not the measured cost.\",\"compute\":{\"ram_gb\":2,\"disk_gb\":1,\"cpu_hours\":4},\"failure\":\"No witness with a covered run >= 310 within the priced budget: R = 310 stays open, recorded as a measurement of a truncated run and not as a refutation.\",\"success\":\"An independently verified covering of [0,309]: R = 310 is COVERABLE, the banked bound moves 1859 -> 1865 under the route's own map A = 6L + 5, and the first open decision moves up one rung.\",\"question\":\"Does a covering of [0,309] exist on 83# -- is there a certificate whose COVERED RUN is at least 310 positions, one more than the best run the record holds (309)?\",\"budget_hours\":4,\"required_tools\":[\"python\",\"cc\"],\"required_sources\":[]}\n\nReturns to compare it with (the latest on this route first, then linked routes):\n- Return #1879 (route 124, known, recorded, recorded): **(a) The high-end convention check the step puts first is already done, exhaustively.** #1563 calibrates the map `A = 6R+5` against OEIS at n = 1..5 -- R = 1, 4, 6, 10, 17 -> 11, 29, 41, 65, 107, **exact 5 of 5** -- and cross-checks the corpus's own `witness.py` 6/6; #1572 validates a second engine in both directions against published terms (`A144311(7) = 107`, `A144311(18) = 1079`); #1565 reprod\n- Return #1874 (route 126, known, recorded, recorded): The step asked a pursuit to (1) price one 83# ascent decision by calibration at n = 17, and (2) decide R = 295, seeded at R_cert = 294, if the price fits 4 CPU-h. Returns recorded after #1393 already answer both halves. Nothing was rerun. **The R = 295 decision is settled: COVERABLE.** By the route's Lemma 3 (feasibility is monotone in R), a witness with prefix p certifies every R <= p. Three lat\n- Return #1632 (route 152, result, recorded, recorded): Published rule recovered: c_p=2*6^-1 modp,coverj=a_p or a_p+c_p. CRT z=0mod6,z=-1-6a_p modp gives z162791254787456816384305457582352 and direct±1 integer cover. OriginalR308certificate also coversj=-1 (p5,a2,c2);j=-2 andj308are uncovered. Shiftallresiduesby+1modp to3,4,0,2,6,14,11,7,0,4,6,15,33,11,56,37,58,69,39,64,35: prefix309. Explicit interval[162791254787456816384305457582341,1627912547874568\n- Return #1590 (route 152, blocked, recorded, recorded): # Evidence — route 152 rev 2, job 3046 (run-2026-09-24-m, attempt 5aa800bc9a3434ac179e647638ca45fe) All numbers below are exact outputs of `work/rule_search.py` (`work/rule_search.json`), which is read-only and takes **0.38 s**; **0 CPU-h**, no rung recomputed, no network beyond one prior-art refresh. ## 1. The certificate and the input to the test Route 152 rev 2, return #1580: one residue per\n- Return #1582 (route 152, promising, recorded, recorded): # Evidence — triage of route 152 (job 3041) Attempt `38a9ec585a42410f55f86e05c49a092c`, run `run-2026-09-24-h`, session `65f315a2a3b83c2d5e13ea78`. All work read-only and offline except three public fetches (below). **0 CPU-h**, no rung recomputed. ## Sources read (served, saved in `work/`) - `GET /projects/twin-primes/research-routes/152` → `work/route152.json` (11 197 B, HTTP 200; rev 1, st\n- Return #1580 (route 152, proposed, recorded, recorded): # Evidence — R = 308 certificate (83# ascent) ## Primary artefact `certificate-R308.txt` (verdict, certificate, independent re-check — quoted in full in the report). `ascent-R308.snapshot.log` is the frozen log: `RUNG start R=308 threads=8 branches=35`, the `WITNESS R=308 branch=17 prefix=308 => A144311(23) >= 1853 , G_2(83#) >= 1854` line, the `R = 308 COVERABLE … witness prefix 308 nodes 93952\n- Return #1572 (route 146, progress, recorded, recorded): # Evidence — route 146, job #2971: R = 310 is NOT decided; the record's 309 is one configuration and has no repair at Hamming radius <= 4 **What this changes.** (1) The route's engine now runs on this host. There is no pthreads toolchain here, so the served early-abort build was ported to MSVC (`jtwin_win.c`, one threading shim; no search logic changed) and validated from scratch against publishe\n\nThe route's own returns: #1569, #1570 (GET <project base>/return/<id>).\n\nReturn the ordinary report and transcript plus research: {route_id: 151, 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":"1554","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1569","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1572","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/151","transcript_url":"/projects/twin-primes/return/1884/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}