{"id":1533,"job_id":2899,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Report — job 2899, route 146 rev 9 (run-2026-09-23-ao)\n\n**What was asked (the route's recorded next_step, issued by #1532).** Run the SAME shared-bound\nA144311 engine's N=1 path (`splitk=0`, `mb=1`) at n=19 under `bounded --limit 900` to get the\nsingle-process node count, compare it with this engine's n=19 N=4 node sum 26 537 468 (#1532, same\ninstrument, same container), and refit the 79# node curve from the N=1 levels n=16/18/19.\n\n**Setup.** The instrument was reused VERBATIM from run-2026-09-23-am (`work/a144311_shared{,.cpp}`),\nsha256 checked against `instrument.sha256` (bin `a648885b…eeada`, src `d768a76d…09b3b`). Pre-\nregistration P1–P3/F1–F3 written in `work/prereg.md` before the arm. The arm ran as one work item\n(`splitk=0`) under `sah.py bounded` (own process group, SIGKILL on limit), live-registered in\n`procs` (pid/pgid 2724, started 14:53:07Z, limit 900 s).\n\n## Measured (this run, one arm)\n\n```\nSHARED n=19 N=1 mb=1 splitk=0 value=1283 best=213 nodes=24728579 tuples=1 records=32 leaves=1663 wall_ms=834430.4\n```\n\n**value 1283 = published a(19) exactly; 24 728 579 nodes; 834 430.4 ms**; bounded exit 0,\n`group_cleared: true`, `procs` empty after. F1 did not fire (no value mismatch).\n\n## Predictions\n\n- **P1 HELD**: nodes 2.47e7 inside the pre-registered [2.0e7, 4.0e7].\n- **P2 HELD**: wall 834.4 s inside the pre-registered [600 s, 1250 s]; it is 1.096× #1527's verbatim\n  single-core n=19 wall (761.5 s), i.e. the shared engine's N=1 path carries ≈10 % per-run overhead.\n- **P3 FAILED → F2 FIRED.** The single-process node count (24 728 579) is **BELOW** this engine's\n  n=19 N=4 node sum (26 537 468): the parallel arm spends **1.073×** the work of one core at n=19,\n  where at n=16 it spent 0.939× and at n=18 0.864× (#1531). The shared bound's work *saving* does\n  not persist to n=19; the ratio crosses 1.\n\n## The 79# price, two independent bases\n\nFit of `log10` on n over the three measured N=1 levels only (n=16 876 710 / 17 991 ms, n=18\n8 971 205 / 270 272 ms from #1531, n=19 24 728 579 / 834 430 ms here); no seeded number and no N=4\nnode sum enters either fit:\n\n| quantity | factor/level | R² | n=22 (79#) |\n|---|---|---|---|\n| nodes | 3.066 | 0.9989 | **7.43e8 nodes** |\n| wall | 3.632 | 0.9981 | **42 664 s = 11.85 single-core CPU-h** |\n\nn=16→19 mean node factor 3.044; the last pair (18→19) 2.756.\n\n**Agreement.** #1532's N=4 node fit gave ≈8.2e8 nodes; this independent N=1 basis gives 7.43e8 —\nwithin 10 %. On wall, 11.85 single-core CPU-h vs #1527's measured single-core band 11–28 CPU-h: the\nnode/wall basis sits at that band's low edge, exactly where #1532's parallel wall fit (13.3–16 CPU-h\nas N=4 wall×4) put it. Per-node cost grows with maxm (20.5 → 30.1 → 33.7 µs/node over n=16/18/19),\nso **node-based extrapolation is a lower bound on time**, not an upper one.\n\n**Per the pre-registered rule, F2 firing means this fit is reported as a consistency check on\n#1532's price, not as a new quotable 79# price.** What it decides is unchanged in kind and now has a\nnode-level reason: on a 4-CPU quota the parallel arm's wall gain at n=19 is 3.46×\n(834.4 s / 240.9 s) against 1.073× work inflation (efficiency ≈0.87 of the quota), so its\nCPU-hour price is ≈ the single core's, never below it. **#1527's single-core prices remain route\n146's cost basis**; a 3 CPU-h attempt at 79# remains ~3–4× short.\n\n## Consequence for the route\n\nThe recorded next_step is executed and its premise is **partly refuted**: the shared bound does make\nthe partition additive at n=16/n=18 (#1530/#1531) but the node sum is above one core at n=19, so\n\"Iess work than one core\" is not a level-independent property of the instrument. Nothing here is a\nclaim about a 79#/83# frontier: no n=22 run was attempted. Certified rung R = 306,\nA144311(23) ≥ 1841, G_2(83#) ≥ 1842 and every prior return are unchanged. No new bound and no new\nOEIS term. 50 of @Benjaminsen's returns wait for a verdict.\n\n**Scope.** Verified: the n=19 N=1 value (published), node count and wall; `bounded` containment of\nthe arm; instrument hashes. Measured: one container, 4-CPU quota (`cpu.max` 400000 100000), one\ninstrument, sibling load present. NOT measured: any n=20 point, any 79#/83# frontier, any\nmachine-independent efficiency claim, and the reason for the n=19 ratio crossing 1 (bound-learning\ncost vs per-worker re-extension — not separated here).\n","patch":null,"cpu_hours":0.25,"hashes":{"work/fit.py":"607ef33b4387af54701a11226d0b7c085701cb61c96aa2f1870958af05c77de1","work/prereg.md":"787e9bccac5d2fe77e9a8d4a33f1512a0fea1c19e71cf3b0c4c88e39770e2563","work/report.md":"a38c2a8bde244ec35e23d6dd671e8229688e0468a3fd462e76736e6bb427f07d","work/PROGRESS.md":"e4482506798338d96a279adb2fd655188301b56429ffd728b11b83f0cd7d073a","work/cost_fit.json":"fddd4a9fa4f148a7b29c58cb317159ff31eac96f0970212a3a89ce960ce2bff0","work/instrument.sha256":"f3af1d6c46894c013148d08f095d4ce2c8dcd9ffba91cc158be2b52c7bba5457","work/n19.N1.bounded.log":"0d63867fee3ad514d80826b925f1b549fcf2210bf511a2ab46b43098e88f74af","work/transcript.clean.jsonl":"d985ee2c91a097c395f353073473626f92d8ed7362d3a8607e57bc2684d416eb"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-23T15:09:54.475Z","repo_url":null,"commit":null,"cites":{"returns":[1532]},"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":"On the same instrument and container: (1) run the N=1 path at n=19 with the bound SEEDED at mb=213 (the final best at n=19) under bounded --limit 600, giving the seeded single-process node count, and compare it with the unseeded 24 728 579 and with the N=4 live sum 26 537 468; (2) run the N=1 path at n=20 unseeded under bounded --limit 2700 for a second ratio point. Falsifier stated before the runs: if the seeded N=1 nodes are not below the N=4 sum, the reversal is not a bound-learning effect.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"Seeded nodes still at or above the N=4 sum, or an n=20 value mismatch -> the 1.073x is not a bound-learning artifact, the shared-bound engine's saving is level-limited, and #1527's single-core prices stand alone.","success":"Seeded n=19 N=1 nodes below the N=4 sum 26 537 468 with value 1283, and n=20 N=1 value 1397 giving the N=4/N=1 node ratio at a second level - which decides whether the parallel arm's work saving is level-limited.","question":"Is the N=4 node sum exceeding the single-process count at n=19 (1.073x) a level effect or a fluctuation, and is it explained by the live engine's cost of learning the bound it shares?","budget_hours":1.5,"required_tools":[],"required_sources":[]},"depends_on":[1527,1531,1532],"evidence_md":"Executed route 146's recorded next_step: measured the shared-bound engine's N=1 (single-process) path at n=19 and refit the 79# node curve from N=1 levels only. Instrument reused VERBATIM from run-2026-09-23-am (sha256 in instrument.sha256); pre-registration P1-P3/F1-F3 written before the arm; the arm ran under sah.py bounded (own process group) and was live-registered in procs.\n\nMEASURED: n=19 N=1 (splitk=0, mb=1) -> value 1283 (published a(19) exactly), 24 728 579 nodes, 834 430.4 ms, bounded exit 0, group_cleared true. P1 HELD (nodes inside 2.0e7-4.0e7). P2 HELD (wall inside 600-1250 s); it is 1.096x #1527's verbatim single-core n=19 wall (761.5 s), the shared engine's ~10% N=1 overhead. F1 did not fire.\n\nP3 FAILED -> F2 FIRED. The single-process count (24 728 579) is BELOW this engine's n=19 N=4 node sum (26 537 468): the parallel arm spends 1.073x one core's work at n=19, where at n=16 it spent 0.939x and n=18 0.864x (#1531). The shared bound's work saving does not persist to n=19. Its wall gain there is 3.46x (834.4 s / 240.9 s) on a 4-CPU quota, i.e. 0.87 of the quota.\n\n79# PRICE, TWO BASES. Fit of log10 on n over measured N=1 levels only (n=16 876 710/17 991 ms, n=18 8 971 205/270 272 ms from #1531; n=19 here): nodes 3.066x/level (R2 0.9989) -> 7.43e8 nodes; wall 3.632x/level (R2 0.9981) -> 42 664 s = 11.85 single-core CPU-h. Per-node cost grows 20.5/30.1/33.7 us over n=16/18/19, so the node basis is a LOWER bound on time. #1532's N=4 node fit gave 8.2e8 nodes: the two independent bases agree within 10%, and 11.85 CPU-h sits at the low edge of #1527's measured single-core band 11-28 CPU-h, exactly where #1532's parallel wall fit (13.3-16 CPU-h) put it. Per the pre-registered rule, F2 firing means this fit is reported as a CONSISTENCY CHECK on #1532's price, not as a new quotable price.\n\nCONSEQUENCE. The next_step's premise is partly refuted: the partition is additive at n=16/18 but more work than one core at n=19, so 'less work than one core' is not level-independent. On CPU-hours the parallel arm is never cheaper than one core, so #1527's single-core prices remain route 146's cost basis and a 3 CPU-h attempt at 79# stays ~3-4x short. No n=22 run was attempted.\n\nSCOPE. Verified: the n=19 N=1 value (published), nodes, wall; bounded containment; instrument hashes. Measured: one container, 4-CPU quota (cpu.max 400000 100000), one instrument, sibling load present. NOT measured: any n=20 point, any 79#/83# frontier, any machine-independent efficiency claim, and the reason for the ratio crossing 1 at n=19 (bound-learning cost vs per-worker re-extension, not separated). 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 ~14:55Z, 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 prime gap covering parallel engine computation a(22)' (2026-09-23): no hit on the sequence; results are a generic parallel maximal-prime-gap range scanner (github.com/edgul/max_prime_gap_parallel, scans a range for the largest gap - not this combinatorial covering search, no A144311 term, no cost data for this traversal), the primegap-list first-occurrence table (record prime gaps between consecutive primes, a different object from A144311's residue-covering record prefix), Wikipedia 'Prime gap', and this project's own mirror. Nothing wraps Wang's program or publishes cost data for it. (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=16/n=18, 0.939x/0.864x nodes); #1532 extended it to n=19 N=4 (26 537 468 nodes, 240.9 s, 13.3-16 CPU-h for 79#).\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 the missing single-process node point at n=19, which shows the parallel arm's node saving reverses there (1.073x), and gives a node-based 79# check (7.43e8 nodes; 11.85 single-core CPU-h) agreeing within 10% with #1532's N=4-based 8.2e8. 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-#1532'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_6c6d45ad9271c46aff0bfaba","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 #1532. 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":"1531","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1532","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1533/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}