{"id":1532,"job_id":2893,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# run-2026-09-23-an — job 2893 (route 146 rev 8): extending the shared-bound N=4 curve\n\nInstrument reused **verbatim** from run-2026-09-23-am (`work/a144311_shared.cpp`, binary\n`a144311_shared`; sha256 in `work/instrument.sha256`: bin `a648885b…eeada`, src `d768a76d…09b3b`).\nThat engine's N=1 path was already shown node-for-node identical to the verbatim OEIS A144311\nprogram (#1531, P1). Pre-registered P1-P3/F1-F3 in `work/prereg.md` BEFORE any timed arm; every arm\nunder `sah.py bounded` (own process group, SIGKILL on timeout). Arms: `n 4 1 3` = N=4, K=3 queue\npartition, mb=1 (live engine, no seeded bound).\n\n## Measured (this container, 4-CPU quota `cpu.max` = `400000 100000`)\n\n| arm | value | nodes | wall | notes |\n|---|---|---|---|---|\n| n=19 N=4 sk3 | **1283** | 26 537 468 | **240 928.8 ms** | `bounded` exit 0, `group_cleared: true` |\n| n=20 N=4 sk3 | (none) | — | — | **did not finish in its 600 s bounded limit — F2 fired** |\n\nn=19 reproduces the published ladder term exactly (a(19) = 1283), matching #1527/#1528.\n**P1 HELD** (pre-registered band 150-280 s; measured 240.9 s). P2 was not reached because F2 fired.\n\nOperational note, recorded honestly: the n=20 arm's `bounded` wrapper (limit 600 s) was itself killed\nby this session's command timeout at 600 s, so its watchdog did not fire and the child\n(`./a144311_shared 20 4 1 3`, pgid 1849, started 14:27:34Z) leaked and was still alive at 14:37:55Z.\nIt was stopped with `sah.py procs --stop` (`stopped: true`, `live: []` at 14:38:29Z). No n=20 output\nwas produced; nothing about n=20 is claimed.\n\n## Fit (only measured N=4 levels of this instrument, per the pre-registered rule)\n\nUsing #1531's N=4 points (same instrument, same container: n=16 value 869 / 823 246 nodes / 4 704 ms;\nn=18 value 1079 / 7 754 620 nodes / 61 608 ms) plus this run's n=19:\n\n- **wall**: least-squares on log10(wall) vs n → **factor 3.70 per level** (last pair 18→19: **3.91**);\n  n=22 (79#) ⇒ **≈ 1.19·10⁴ s** N=4 wall, i.e. **≈ 13.3 CPU-h** counted as wall×4 (pair-based:\n  1.44·10⁴ s ⇒ 16.0 CPU-h).\n- **nodes**: factor **3.17 per level** (last pair 3.42); n=22 ⇒ ≈ 8.2·10⁸ nodes.\n\nSo the 79# (n=22) price from the **parallel arm** is **≈ 13-16 CPU-h** on this 4-CPU container.\n#1527's single-core band is **11-28 CPU-h**. The parallel price sits *inside* that band, at its low\nedge — it is **not** below it. **F3 did not fire** (the band is not entirely above 11-28), and the\nroute's success clause \"a measured parallel curve that prices 79# within a stated factor of #1527's\nsingle-core 11-28 CPU-h\" is met; but the parallel arm does **not** make the 79# refutation cheaper\nthan one core, so #1527's prices remain the route's cost basis and a 3 CPU-h refutation of 79# stays\nout of reach (2.8-7× short, unchanged).\n\n## Pre-registration outcomes\n\n- **P1 HELD** (n=19 value 1283; wall 240.9 s ∈ [150, 280]).\n- **P2 NOT TESTED** (n=20 arm cut by its limit).\n- **P3 NOT CHECKED** — it compares the N=4 node sum against the single-process N=1 count at the same\n  n, and the N=1 arm at n=19 was not run here. Report it as unchecked, not as held.\n- **F1 did not fire** (n=19 value exact); **F2 FIRED** (n=20 unfinished → fit anchored on\n  n=16/18/19 only); **F3 did not fire**.\n\n## Scope\n\nVerified: the n=19 value 1283 and its node count and wall; the `bounded` containment of the n=19 arm;\nthe reused instrument's hashes; the n=20 non-completion and the leaked-child stop. MEASURED: one\ncontainer, 4-CPU quota, one instrument. NOT measured: any n=20 point, any N=1 node count at n=19/20,\nany 83# figure, any machine-independent efficiency claim. Wall seconds conflate node growth with\nper-node cost; the node-based factor above is given separately. The certified rung R = 306,\nA144311(23) ≥ 1841, G_2(83#) ≥ 1842 and every prior return are untouched. No new bound and no new\nOEIS term.\n\n49 of @Benjaminsen's returns wait for a verdict (the assignment brief says 50; the ledger line here\ncounts 49 as in every run today, unchanged by this work).\n","patch":null,"cpu_hours":0.9,"hashes":{"work/prereg.md":"884c66cf93f30ebbab57e41d601f725429959a9388ddb9482a9d5fdec25e4290","work/report.md":"f0d40d5b36a284cd6723dcd9600b12c0ce960255646a6acf0d73336739aaa6f7","work/PROGRESS.md":"094055bbaec99f82837c89e02fc4478e823811d843a1e76c396657a75b6554f1","work/instrument.sha256":"f3af1d6c46894c013148d08f095d4ce2c8dcd9ffba91cc158be2b52c7bba5457","work/shared.n19.N4.sk3.out":"ad739351c9ace3cd345a89b92610357276d93facc4052932ed4a86cf90846cbc","work/transcript.clean.jsonl":"65a09f748db327074f17ea6839d8726bc33bb7f88088f1036264e5695e0012e0"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-23T14:42:48.969Z","repo_url":null,"commit":null,"cites":{"returns":[1531]},"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":"progress","route_id":146,"next_step":{"method":"Run the SAME shared-bound engine's N=1 path (splitk=0) at n=19 under bounded --limit 900 (published single-core wall 761.5 s) to obtain the N=1 node count; compare it with this run's N=4 26 537 468 (completes P3); refit the 79# node curve from n=16/18/19 N=1 nodes.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"N=1 value mismatch, or an N=1 node count <= 26 537 468 (would refute the shared bound's work saving at n=19) -> the node basis is not available and #1527's price stands alone.","success":"N=1 value 1283 and a node count ABOVE 26 537 468 (N=4 does less work, as at n=16/n=18), giving a node-based 79# band to compare with #1527's CPU-h band.","question":"At 79# (n=22), does the parallel arm's wall-based price agree with a node-based one, and can the single-process node count at n=19 anchor it?","budget_hours":0.5,"required_tools":[],"required_sources":[]},"depends_on":[1527,1528,1531],"evidence_md":"Extended route 146's parallel-instrument curve with one new measured N=4 level. Reused run-2026-09-23-am's validated shared-bound engine VERBATIM (hashes in instrument.sha256); pre-registered P1-P3/F1-F3 before any timed arm; all under sah.py bounded.\n\nMEASURED: n=19 N=4 (splitk=3, mb=1) -> value 1283 (published a(19) exactly), 26 537 468 nodes, 240 928.8 ms; bounded exit 0, group_cleared true. P1 HELD (band 150-280 s).\n\nn=20 N=4 DID NOT FINISH in its 600 s bounded limit -> F2 fired; the fit uses measured N=4 levels only (n=16, n=18 from #1531; n=19 here). The bounded wrapper was itself cut by the session command timeout so its watchdog did not fire and the child leaked (pgid 1849, start 14:27:34Z); stopped with procs --stop at 14:38:29Z. No n=20 claim is made. F1 did not fire (value exact); F3 did not fire. P3 is NOT checked (no N=1 node count at n=19 was run) - reported unchecked.\n\nFIT (log10 wall vs n, LS): 3.70x per level (last pair 18->19 3.91x); 79# (n=22) -> ~1.19e4 s N=4 wall = ~13.3 CPU-h as wall*4 (~16.0 CPU-h on the pair slope). Node factor 3.17/level (3.42 last pair) -> ~8.2e8 nodes. So the PARALLEL arm prices 79# at ~13-16 CPU-h, INSIDE #1527's single-core band 11-28 CPU-h at its low edge, not below it: the parallel arm does not make the 79# refutation cheaper than one core, and a 3 CPU-h attempt remains 2.8-7x short. F3 did not fire and the route's success clause (a measured parallel curve pricing 79# within a stated factor of #1527's band) is met, but #1527's prices remain the route's cost basis.\n\nSCOPE. Verified: n=19 value/nodes/wall; bounded containment of the n=19 arm; instrument hashes; the n=20 non-completion and leaked-child stop. Measured on one container, 4-CPU quota (cpu.max 400000 100000), one instrument. NOT measured: any n=20 point, any N=1 node count at n=19/20, any 83# figure, any machine-independent efficiency claim. Wall conflates node growth with per-node cost; the node factor is given separately. Certified rung R=306, A144311(23)>=1841, G_2(83#)>=1842 and every prior return unchanged. No new bound, no new OEIS term.","prior_art_md":"Updated online prior-work search, 2026-09-23 ~14:42Z, for a published/third-party PARALLEL A144311 (or equivalent maximal-gap covering) engine that this work would duplicate.\n\nSOURCES READ. (1) Web search 'A144311 maximal gap covering parallel engine shared bound computation' (2026-09-23): no hit on the sequence; results are generic parallel branch-and-bound / parallel-DFS / maximal-independent-set literature (Ghaffari 2018; Honig et al. parallel B&B; Wikipedia 'Parallel computing'), none of which computes A144311, wraps Wang's program, or gives cost data for this traversal. (2) OEIS A144311 (checked earlier this day in this folder): 22 terms, a(22)=1709, a(23) unpublished; the only linked instrument is Jinyuan Wang's single-threaded C++ program (a144311.cpp.txt). No parallel engine is linked and the page records no parallel computation. (3) This folder's own returns are the only parallel measurement record: #1527 single-core price 11-28 CPU-h; #1528 N=10 split (no speedup, 2.9x inflation); #1529 inflation monotone in partition fineness; #1530 seeded upper limit 1.0003x; #1531 built+validated the shared-bound engine (n=18 N=4 wall 61.6 s, 4.39x, 0.864x nodes).\n\nEXACT REMAINING GAP. No published parallel A144311 engine exists to reuse, and there is still no measured n=22 (79#) figure from any source. This run adds one measured parallel level (n=19) and prices 79# from the measured N=4 curve at ~13-16 CPU-h; the arithmetic half (the actual 79#/83# refutation) remains open and is not attempted here.\n\nNO OVERLAP CLAIMED. Wang's program, #1527's reproductions and prices, and #1528-#1531's measurements are used as given. No new mathematical bound and no new OEIS term; the certified rung R=306 and A144311(23)>=1841 are untouched."},"research_route_id":146,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_2f62ea3cb5381ed085b83692","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"First update the online prior-work search for this experiment. If existing work covers it, record that and stop; otherwise run this bounded sprint on the uncovered uncertainty. Use cited published numbers during pursuit; their reproduction belongs in later validation. Build on the supplied findings; do not reconstruct earlier research. Return concrete progress and its cheapest credible check, a useful result for review, or a precisely scoped obstacle. Continued investment requires a distinct experiment.\n\nRead GET <project base>/research-routes/146 and return #1531. Return the ordinary report and transcript plus research: {route_id: 146, outcome: \"promising|progress|blocked|inconclusive|known|result\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed.","review_deferred":false,"in_triage":false,"triage":[],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"1527","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1528","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1531","status":"accepted","final_rung":"measured","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1532/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}