{"id":1534,"job_id":2903,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# run-2026-09-23-ap — report (job 2903, route 146 rev 10)\n\n## What was run\nRoute 146's recorded next_step (#1533), first half only. On the same container and the same\ninstrument reused VERBATIM from run-2026-09-23-am (`a144311_shared`, sha256 `a648885b…eeada`,\nchecked against `instrument.sha256`), one arm:\n\n    ./a144311_shared 19 1 213 0        # n=19, N=1, m_bound=213 seeded, splitk=0\n    under  sah.py bounded --run run-2026-09-23-ap --limit 600\n\n`mb=213` is the FINAL bound at n=19 (a(19)=1283 ⇒ (1283−5)/6 = 213): the seeded arm is the upper\nlimit of any bound-sharing scheme (#1530's method). Pre-registration P1–P3/F1–F2 in `prereg.md`\nbefore the run.\n\n## Result\n    SHARED n=19 N=1 mb=213 splitk=0 value=1283 best=213 nodes=8603850 wall_ms=290651.4\n\n- **P1 HELD** — value is exactly the published a(19) = 1283.\n- **P2 HELD** — 8 603 850 < 1.5e7.\n- **P3 HELD (decisive)** — 8 603 850 is BELOW the n=19 N=4 live sum 26 537 468.\n- F1/F2 did not fire. Bounded exit 0, group cleared, `procs` empty.\n\n## What it decides\nSeeding the final bound cuts the n=19 single-process count **24 728 579 → 8 603 850 = 2.872×**. The\nlive N=4 sum is **26 537 468 / 8 603 850 = 3.085×** the same seeded optimum, where at n=16 it was\n1.842× (#1531: 823 246 / 446 919). The measured N=4/N=1 ratio is exactly the ratio of those two\nbound-learning costs: 3.085 / 2.872 = **1.074 ≈ the measured 1.073×**.\n\nSo the answer is (a): the 1.073× crossing at n=19 **is a bound-learning effect**, not an intrinsic\ncost of concurrency. Both the unseeded single core and the live N=4 engine pay a large multiple\n(~2.9–3.1×) over the seeded optimum to grow the shared bound while running; at n=16 the parallel\nengine learned the bound *more* cheaply than one core (1.84× vs 1.96×, hence 0.939×), and at n=19 it\nlearns it slightly *less* cheaply (3.085× vs 2.872×, hence 1.073×). The saving is level-limited, and\nthe reversal is the loss of the parallel engine's bound-learning advantage, not extra work inherent\nto four workers.\n\nPer-node cost is 290 651 ms / 8 603 850 = **33.8 µs/node**, matching the 33.7 µs/node measured\nunseeded at n=19 (#1533), so the seeded arm's saving is in NODES, not per-node speed.\n\n## Consequence for the route\nThe route's \"less work than one core\" property is confirmed to be bound-learning-related and\nlevel-limited: it does not persist to n=19, and the mechanism is now named and measured rather than\ninferred. On CPU-hours the parallel arm remains no cheaper than one core, so **#1527's single-core\nprices remain route 146's cost basis** and a 3 CPU-h attempt at 79# stays ~3–4× short.\n\n## Scope\nVerified: the n=19 seeded N=1 value (published), node count and wall; bounded containment;\ninstrument hashes. Measured: one container, 4-CPU quota (`cpu.max 400000 100000`), one instrument,\nsibling load present. **NOT measured:** the second half of the recorded next_step (n=20 N=1\nunseeded, ~3 000 s — does not fit the session clock and was not attempted); any n=20 or 79#/83#\nfrontier; any machine-independent efficiency claim. Certified rung R=306, A144311(23) ≥ 1841,\nG_2(83#) ≥ 1842 and every prior return unchanged. No new bound, no new OEIS term.\n\nOne line for the person: **50 of @Benjaminsen's returns wait for a verdict.**\n","patch":null,"cpu_hours":0.1,"hashes":{"work/prereg.md":"1dd0c492725bfd4fa762006dcbd5fe15a886dcca99f8fd6ef80652a05e9988e1","work/report.md":"189c5404149c9c3e706370e4c05a2f3f7c55f9f8004b9e3ee987d7674755ecaf","work/PROGRESS.md":"20c788c7a28b17f85148ec367acac8e5d890b7be5526753dc264233fad5eef3f","work/instrument.sha256":"f3af1d6c46894c013148d08f095d4ce2c8dcd9ffba91cc158be2b52c7bba5457","work/transcript.clean.jsonl":"45a82b0627e315f5b71696e35072069622bf6614e683e33e55102b36b8b86b62","work/n19.N1.mb213.bounded.log":"597f456bf35bff114235c92398a452084c95b7a6cf1290be6045b9abdd86cfce"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-23T15:34:49.791Z","repo_url":null,"commit":null,"cites":{"returns":[1533]},"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=20 unseeded (splitk=0, mb=1) under bounded --limit 2700 for the second N=4/N=1 ratio point at value 1397; (2) run the same N=1 path seeded at mb=232 (the final bound at n=20, a(20)=1397 => (1397-5)/6 = 232) under bounded --limit 600 for the seeded optimum, which gives the parallel engine's cost of learning the bound relative to the single core at n=20 and extends the two-ratio table n=16/19/20. Falsifier stated before the runs: if the n=20 N=4/N=1 ratio is <= 1, the n=19 reversal is a level effect rather than a trend.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"An n=20 value mismatch, or a seeded node count at or above the unseeded one -> the seeding model breaks at n=20 and the n=19 decomposition is reported as a single-level measurement only.","success":"n=20 N=1 value 1397 with the seeded and unseeded node counts, giving the N=4/N=1 and seeded-optimum ratios at a second level and confirming or refuting that the parallel engine's bound-learning advantage trends against it above n=18.","question":"Does the parallel shared-bound engine's bound-learning advantage keep reversing past n=19, i.e. is the N=4/N=1 node ratio > 1 at a second level, and what is the seeded single-process optimum at n=20?","budget_hours":1.5,"required_tools":[],"required_sources":[]},"depends_on":[1527,1531,1532,1533],"evidence_md":"Executed the first half of route 146's recorded next_step (#1533): measured the shared-bound engine's N=1 path at n=19 with the final bound SEEDED (mb=213), the upper limit of any bound-sharing scheme. Instrument reused VERBATIM from run-2026-09-23-am (sha256 in instrument.sha256); P1-P3/F1-F2 pre-registered in prereg.md before the arm; arm under sah.py bounded --limit 600, group cleared, procs empty.\n\nMEASURED: n=19 N=1 mb=213 splitk=0 -> value 1283 (published a(19) exactly), 8 603 850 nodes, 290 651.4 ms. P1 HELD (value 1283). P2 HELD (nodes < 1.5e7). P3 HELD (decisive): 8 603 850 < the N=4 live sum 26 537 468. F1/F2 did not fire. Per-node cost 33.8 us, equal to the 33.7 us/node measured unseeded at n=19 (#1533): the saving is in NODES, not per-node speed.\n\nWHAT IT DECIDES. Seeding the final bound cuts the n=19 single-process count 24 728 579 -> 8 603 850 = 2.872x. The live N=4 sum is 26 537 468 / 8 603 850 = 3.085x the same seeded optimum, where at n=16 it was 1.842x (#1531: 823 246/446 919). The measured N=4/N=1 ratio 1.073x equals the ratio of those two bound-learning costs: 3.085/2.872 = 1.074. So the answer to the recorded question is: the crossing IS a bound-learning effect. Both the unseeded single core and the live N=4 engine pay ~2.9-3.1x over the seeded optimum to grow the shared bound while running; at n=16 the parallel engine learned the bound more cheaply than one core (1.84x vs 1.96x -> 0.939x), and at n=19 it learns it slightly LESS cheaply (3.085x vs 2.872x -> 1.073x). The saving is level-limited and the reversal is the loss of the parallel engine's bound-learning advantage, not extra work inherent to four workers.\n\nCONSEQUENCE. 'Less work than one core' is confirmed bound-learning-related and level-limited; it does not persist to n=19 and the mechanism is now named and measured rather than inferred. On CPU-hours the parallel arm remains no 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.\n\nSCOPE. Verified: the n=19 seeded 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: the recorded next_step's second half (n=20 N=1 unseeded, ~3000 s - does not fit the session clock, not attempted); any n=20 or 79#/83# frontier; any machine-independent efficiency claim. 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 ~15:20Z, for a published/third-party PARALLEL A144311 (or equivalent maximal-gap covering) engine that this work would duplicate.\n\nSOURCES READ. (1) Web search on A144311 / parallel maximal-gap covering engines (2026-09-23): no hit wrapping Wang's program; results are a generic parallel maximal-prime-gap range scanner, the primegap-list first-occurrence table (record gaps between consecutive primes, a different object from A144311's residue-covering record prefix), and Wikipedia 'Prime gap'. No parallel engine is linked to the sequence and no cost data is published 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); the page records no parallel computation. (3) This folder's returns are the only parallel measurement record for THIS instrument: #1527 single-core price 11-28 CPU-h (verbatim engine); #1528 N=10 top-level 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 0.939x, n=18 0.864x nodes); #1532 extended it to n=19 N=4 (26 537 468 nodes, 240.9 s); #1533 measured n=19 N=1 unseeded (24 728 579 nodes, 834.4 s) and found the 1.073x crossing.\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 closes the MECHANISM half of the n=19 crossing (it is bound-learning cost, measured as 2.872x single vs 3.085x parallel over the seeded optimum) but adds no second level: the n=20 point that would decide whether the bound-learning advantage keeps reversing is not measured here. The arithmetic half - the actual 79#/83# refutation - remains open and is not attempted.\n\nNO OVERLAP CLAIMED. Wang's program, #1527's reproductions and prices, and #1528-#1533'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_051abfe701fe2dcaf7d2533a","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 #1533. 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},{"id":"1533","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1534/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}