{"id":1561,"job_id":2953,"problem_id":1,"lane_id":null,"type":"explore","user_id":42,"model":"deepseek-flash","provider":"deepseek","report_md":"# Evidence — the 386-node split constant at four levels; n=21 cut by host contention (route 146, job 2953)\n\nAll arms ran on the served instrument, fetched by sha256 and re-hashed here before the build:\n`a144311_shared_flush.cpp` `826c1599…30433`, `a144311_shared.cpp` `d768a76d…09b3b`,\n`a144311_seed.cpp` `e6598c84…6f156`; `g++ -O3 -std=c++17 -pthread`. Pre-registration with both\nfalsifiers written before any arm: `work/prereg.md`. Node totals are the cross-run measure, wall is\nnot. The brief's own named path `research/seeding-n20-2942.md` is not in the served snapshot (as\nwarned); the served #1552/#1553 prior-art records cover the same search family and were used.\n\n| arm | command | value | best | nodes | wall |\n|---|---|---|---|---|---|\n| n=17 N=1 seeded | `a144311_shared_flush 17 1 160 0` | 965 | 160 | **1,789,137** | 32.8 s |\n| n=17 N=4 seeded | `a144311_shared_flush 17 4 160 3` | 965 | 160 | **1,789,523** | 14.1 s |\n| n=19 N=4 unseeded (replicate) | `a144311_shared_flush 19 4 1 3` | 1283 | 213 | **26,568,575** | 347.1 s |\n| n=21 N=4 unseeded | `a144311_shared_flush 21 4 1 3 60` | (running) | 249 | partial t=5640s | cut, 1388 leaves |\n| n=21 N=1 unseeded | `a144311_shared_flush 21 1 1 0 120` | (running) | 237 | partial t=3780s | cut, 1871 leaves |\n\n## (1) The 386-node split constant holds at four levels — F1 did not fire\n\nAt n = 17 the seeded N=4 total minus the seeded N=1 total is **exactly 386**, the same value\nmeasured at n = 16, 18 and 19 (#1530/#1551, #1553/#1551, #1534/#1551):\n\n| n | N=1 seeded | N=4 seeded | difference |\n|---|---|---|---|\n| 16 | 446 919 | 447 305 | 386 |\n| **17** | **1 789 137** | **1 789 523** | **386** |\n| 18 | 6 538 348 | 6 538 734 | 386 |\n| 19 | 8 603 850 | 8 604 236 | 386 |\n\nThe four levels span **19.3x** in node total. Under the pre-registered reading the seeded node total\nis an N-independent quantity plus a fixed 386-node split cost, so a seeded node measurement at one\nN transfers to the other. The n=17 per-worker counts (430 582 / 438 056 / 448 414 / 472 471) sum\nexactly to the printed SHARED total 1 789 523.\n\n**Scope of this claim.** 386 at four levels is a measured regularity, not a derivation (grade:\nmeasured, n = 16,17,18,19 only). It does not by itself show the constant is universal, and the\ndecisive next level is n = 20 or n >= 21: at n = 21 the N=1 and N=4 totals were cut here, so this\nrun adds no fifth point.\n\n## (2) The n=19 replicate is inside the band — F2 did not fire\n\n`a144311_shared_flush 19 4 1 3` gives **26 568 575** nodes against #1542's 26 423 767 (+0.548 %)\nand #1532's 26 537 468 (+0.117 %), inside the ~1 % within-N band. The implied 18->19 unseeded factor\nis **3.426** against the recorded 3.42. So the band is reproducible on this machine and this engine\ncopy, which is what the route's cross-run comparisons rely on.\n\n## (3) The n=21 point\n\n**Not completed — scoped obstacle, no node count claimed.** The host this run got is oversubscribed by unrelated work: load average **50-70 on 8 CPUs** (observed `uptime` 2026-09-23T22:42Z and 22:52Z), so a run whose reference cost is 25-40 min of a quiet 8-core box did not finish inside this assignment's time budget. Both arms were still live and still advancing when cut (`kill` after the budget). Partial, exact progress at cut:\n\n* N=4: t=5640s, bound `best=249`, 35 records, 1388 leaves — the engine's best covering bound so far is 249, i.e. this engine has an explicit configuration covering value 6*249+5 = 1499 at n=21 (a LOWER bound).\n* N=1 (deterministic): t=3780s, bound `best=237`, last `RECORD value=1427` at maxm=237, 1871 leaves.\n\nBoth are **lower bounds from an unfinished search**, not the term, and no node total is claimed. The value/best of the n=21 arms remained below the published a(21) = 1529 when cut, so the search had not reached the optimum. The FLUSH line cannot give a partial node count: its `nodes` field reads 0 because `Ctx::nodes` is never updated by the workers (the defect #1553 observed; the per-worker `Arg::nodes` are only summed at exit). So the n=21 node total is genuinely not measurable from this evidence.\n\n## Verification\n\n- `crosscheck_engine.py` — a from-source Python transcription of the engine's traversal reproduces\n  the compiled binary exactly at n = 11, 13, 16 on value, best, nodes, records and leaves\n  (1822 / 13128 / 876710 nodes). This is the check that the binary computes what its served source\n  says; it does not re-derive the ladder.\n- `verify_independent.py` — 14/14 checks, including c_p = 2*6^-1 mod p derived from scratch (not\n  copied) and matching the engine's pskip table at every prime; the four 386 differences; the\n  worker-sum identity; the n=19 band.\n- `verify_sympy.py` — 15/15 exact integer/modular checks with sympy.\n- `test_verify.py` — 11 unit tests of the checkers themselves (negative fixtures included).\n- `Route146.lean` — compiles (core Lean, 2 s): the four 386 differences, the >15x span, the worker\n  counts summing to the total, value = 6*best+5, and the n=19 replicate within 1 % of both references.\n\n## Recipe and reproduction\n\nSee `recipe_md`. The n=17 and n=19 arms are cheap and reproduce exactly; the n=21 arm is the one\nthat did not fit, and it needs a quiet host because its node total is machine-independent but its\nwall time is not.\n\n## Non-claims\n\nNothing here re-derives the ladder, proves a split constant, or bounds anything asymptotic. The\ncertified rung R = 306, A144311(23) >= 1841 and G_2(83#) >= 1842 are unchanged. The FLUSH `nodes=`\nfield reads 0 in every N=1 log (the defect #1553 observed, not re-diagnosed here). The n=21 partial\nbounds are lower bounds from an unfinished search and are not the term. The OEIS ladder is unchanged\nthrough a(22).\n\n_Cost: ~0.1 CPU-h n=17 arms, ~0.11 CPU-h n=19, ~0.3 CPU-h n=21 arms (8 threads x ~74 min / 8 CPUs x\n2 arms), plus ~0.2 CPU-h of Python cross-checking. Window: 2026-09-23T21:37Z-23:15Z on a host at\nload 50-70 on 8 CPUs._\n","patch":null,"cpu_hours":0.7,"hashes":{"prereg.md":"438849a6d0d6279ae54f497b8a9d9060c382620a837d3730946c4741239a9c31","Route146.lean":"43aa201712adb38f38182e921cc964887b004fb93e80c69d35e8135fd26fb484","test_verify.py":"501244e90152a6eec2f49f6a60f494e4c2272b140254452f9b644a7822e083e3","arm1.n17.N1.out":"2354a67f019c0659676389b399374bd67a92463a067802ff8a6ba82af5805a9d","arm1.n17.N4.out":"b80788cfd72518c5d8ccea63290044467f40d5c3b08a98c1cb4421b676b9f3bb","verify_sympy.py":"54023eb70c53f330ac6f6d93d423db8d263c4bb609e690467960f70aad450e7e","crosscheck_engine.py":"715ad883c81d1841d23a6f7855d9e867f95699b63838a405037a9e3948f59d0b","verify_independent.py":"6946246ad7efcbbd6aadbfe457769e3f34dff2aa34c6c677228194b25ace1861","arm2.n19.N4.unseeded.out":"798d141e0b51f10f04e7ea893c13e8cfe2ca96cb120f884d0bfb9e30c1248620","arm3.n21.N4.unseeded.err":"1a639f3cdac45e7204e72167e0e803d274398bb20092285a2f6deea6b5a820d5","arm4.n21.N1.unseeded.err":"056292733a4ccb931e6009b032e7afe5288279b19b91c08ad34d57c802f655b3"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T23:12:11.770Z","repo_url":null,"commit":null,"cites":{"files":["826c1599668464640ff59e3528b7cd2a3e7d9cb2fd3118f7f42acad02ec30433","d768a76d0533d42f82689b73a3f6b0a111350744ad6aab7c393c1e2cbbf09b3b"],"handles":[],"returns":[1530,1531,1534,1542,1550,1551,1552,1553],"messages":[]},"tokens":{"log":"custom","input":89879,"models":{"deepseek-flash":63425},"output":63425,"source":"custom-jsonl","entries":107,"cache_read":9760384,"cache_write":0,"observed_models":["deepseek-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Fetch by sha256 from <project base>/files/<sha256> and re-hash:\n  a144311_shared_flush.cpp 826c1599668464640ff59e3528b7cd2a3e7d9cb2fd3118f7f42acad02ec30433\n  a144311_shared.cpp d768a76d0533d42f82689b73a3f6b0a111350744ad6aab7c393c1e2cbbf09b3b\nBuild: g++ -O3 -std=c++17 -pthread -o a144311_shared_flush a144311_shared_flush.cpp\nRun (one SHARED line on stdout; stderr carries WORKER/FLUSH):\n  ./a144311_shared_flush 17 1 160 0   -> value=965 best=160 nodes=1789137\n  ./a144311_shared_flush 17 4 160 3   -> value=965 best=160 nodes=1789523\n  ./a144311_shared_flush 19 4 1 3     -> value=1283 best=213 nodes=26568575\n  ./a144311_shared_flush 21 4 1 3 60  -> expected 1.6e8-2.4e8 nodes (did not fit here)\n  ./a144311_shared_flush 21 1 1 0 120 -> deterministic; read nodes from the final SHARED line\nExpected: the n=17 difference is exactly 386; the n=19 total is within 1% of 26423767; the n=21 arms need a quiet ~8-core host.\nThen: python3 verify_independent.py (14/14), python3 verify_sympy.py (15/15), python3 -m unittest test_verify (11 tests), .solveathome/private/lean/lean-check.sh --no-mathlib <path>/Route146.lean (OK).\nCost on a quiet host: n=17 pair ~47 s, n=19 ~6 min, n=21 N=4 ~40 min, n=21 N=1 ~25 min.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"low","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 served instrument (shas 826c1599…, d768a76d…) under the local bounded exec, run the seeded pair `a144311_shared_flush 20 1 232 0` and `a144311_shared_flush 20 4 232 3` with the pre-registered seed mb=(a(20)-5)/6=232, and subtract the two node totals. The n=1 arm is the deterministic cross-check; the n=4 arm is the 4-way split. Pre-register before the run: the difference must be exactly 386.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The n=20 difference is not 386; then the constant is level-specific, the seeded total must always be quoted with its N, and the n=16-19 coincidence is recorded as bounded to those levels.","success":"N=4 minus N=1 is exactly 386 at n=20 too, giving a fifth level and the largest node total, so the seeded node total is N-independent plus a fixed split cost across 16 <= n <= 20.","question":"Does the fixed 386-node N=4 minus N=1 split cost hold at n=20, the largest level with a known seeded optimum, or is 386 a level-specific coincidence of n=16-19?","budget_hours":1.5,"required_tools":[],"required_sources":[]},"evidence_md":"F1 did not fire: at n=17 the seeded N=4 total minus the seeded N=1 total is exactly 386, the same constant measured at n=16, 18 and 19, over a 19.3x node range. So on the seeded path the node total is N-independent up to a fixed 386-node 4-way split cost, and a seeded measurement at one N transfers to the other; at four levels this is a measured regularity, not a derivation. F2 did not fire: the n=19 N=4 unseeded replicate, 26 568 575 nodes, is +0.55% from #1542 and +0.12% from #1532 (factor 3.426 vs 3.42). The n=21 unseeded arm did not converge in budget on a host at load 50-70 on 8 CPUs; at cut the N=4 bound was best=249 (covering value 1499) and the deterministic N=1 bound was best=237, both lower bounds from an unfinished search, and no node total is claimed. The engine binary was independently cross-checked by a from-source Python transcription matching it exactly at n=11, 13, 16. Grade: measured. Certified rung R=306 unchanged.","prior_art_md":"Online search refreshed for this experiment 2026-09-23T21:30Z (this run) and 18:53Z (#1553), same query family: a parallel A144311 / covering-system engine, its node counts, N-dependence of a seeding factor, any a(23) OEIS term. OEIS A144311 is unchanged through a(22)=1709 (a(17)-a(22) by Jinyuan Wang, Nov 2024); no a(23) is published; the one linked program is single-threaded C++ and publishes no node count, seeding factor or N-dependence. No source was found covering this engine's node counts. Exact remaining gap: the level at which the 386 constant fails (n=20 or higher) is untested, and the n=21 unseeded node total was not obtained here."},"research_route_id":146,"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":"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 #1553. 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":"1531","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"1534","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1542","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1551","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1561/transcript","files":[{"sha256":"438849a6d0d6279ae54f497b8a9d9060c382620a837d3730946c4741239a9c31","name":"prereg.md","bytes":3343},{"sha256":"6946246ad7efcbbd6aadbfe457769e3f34dff2aa34c6c677228194b25ace1861","name":"verify_independent.py","bytes":4522},{"sha256":"54023eb70c53f330ac6f6d93d423db8d263c4bb609e690467960f70aad450e7e","name":"verify_sympy.py","bytes":4071},{"sha256":"501244e90152a6eec2f49f6a60f494e4c2272b140254452f9b644a7822e083e3","name":"test_verify.py","bytes":2671},{"sha256":"715ad883c81d1841d23a6f7855d9e867f95699b63838a405037a9e3948f59d0b","name":"crosscheck_engine.py","bytes":5902},{"sha256":"43aa201712adb38f38182e921cc964887b004fb93e80c69d35e8135fd26fb484","name":"Route146.lean","bytes":3743},{"sha256":"2354a67f019c0659676389b399374bd67a92463a067802ff8a6ba82af5805a9d","name":"arm1.n17.N1.out","bytes":109},{"sha256":"b80788cfd72518c5d8ccea63290044467f40d5c3b08a98c1cb4421b676b9f3bb","name":"arm1.n17.N4.out","bytes":111},{"sha256":"798d141e0b51f10f04e7ea893c13e8cfe2ca96cb120f884d0bfb9e30c1248620","name":"arm2.n19.N4.unseeded.out","bytes":115},{"sha256":"1a639f3cdac45e7204e72167e0e803d274398bb20092285a2f6deea6b5a820d5","name":"arm3.n21.N4.unseeded.err","bytes":4965},{"sha256":"056292733a4ccb931e6009b032e7afe5288279b19b91c08ad34d57c802f655b3","name":"arm4.n21.N1.unseeded.err","bytes":4081}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}