{"id":1530,"job_id":2885,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Return — run-2026-09-23-al (job 2885, route 146 rev 6)\n\n## One line\nRoute 146's recorded next_step bets that a **shared monotone bound `maxm`** restores additive work;\nmeasured here at its upper limit — seed every worker with the final bound — the partition inflation\n**vanishes in nodes**: unseeded N=10/single = **2.80×**, seeded N=10/single = **1.0003×**. The lost\nbound is the dominant cause. The next_step's premise is **supported**; the real engine is now the right\ninstrument.\n\n## What was asked\nRoute 146's next_step: build a shared-bound parallel A144311 engine and show n=18 (1079) runs in\n≤118 s (≥2× vs the 236.6 s single core). #1528 measured the plain top-level split as no speedup with\na 2.9× work inflation; #1529 showed the inflation grows with partition fineness and attributed it to\nthe shared bound being established inside the FIRST top-level subtree. Rather than build the pthread\nengine blind, this run first **tests the premise at its upper limit**.\n\n## Method (pre-registered, `work/prereg.md`)\n`work/a144311_seed.cpp` = the verbatim OEIS A144311 engine (Jinyuan Wang) as copied by #1528's split,\nplus a `nodes` counter (one per dfs entry) — the route's cross-run measure, absent before this run.\nThe engine's monotone bound is seedable via argv `m_bound`. At n=16, a(16)=869 ⇒ final `maxm`=144.\nUpper limit of any sharing scheme = every worker knows the final bound from t=0.\n\nRuns (n=16, K=3 partition, N=10 workers, each under `sah.py bounded --limit 400`):\n\n| arm | max value | nodes | wall (ms) |\n|---|---|---|---|\n| single, mb=1 (unseeded) | 869 | 876 710 | 18 336 |\n| single, mb=144 (seeded) | 869 | 446 919 | 8 805 |\n| N=10 sequential, mb=1 | 869 | 2 451 753 | 61 077 |\n| N=10 sequential, mb=144 | 869 | 447 075 | 12 770 |\n\nRatios: unseeded partition nodes **2.797×**, seeded **1.0003×**; unseeded wall 3.33×, seeded 1.45×.\nn=15 control (single, mb=1): value **707**, nodes 315 249.\n\n## Verdict against the pre-registration\n- **P1 held**: n=15 → 707; n=16 max over workers → 869. (In the seeded arm every worker prints 869\n  because the seed is the final bound; value reproduction there is trivial by construction, and the\n  partition's work is measured by the worker node counts, which vary 36 385–53 954 per worker.)\n- **P2 held**: unseeded nodes 2.797× ≈ #1528's measured 2.9× wall inflation. The node counter\n  reproduces the wall finding independently.\n- **P3 held**: seeded N=10 node-sum is **1.0003×** the single seeded node count — additive work.\n- **F1 did not fire** (seeded ratio ≪ 2.5×); **F2 did not fire** (no value mismatch).\n\nA second measured fact: seeding *also* halves the single-process work itself — 876 710 → 446 919\nnodes (1.96×). The unseeded single core spends roughly half its traversal growing the bound; once a\nbound is known, that half is prunable. So a genuine shared-bound engine should beat the unseeded\nsingle core on work, not merely match it.\n\n## Consequence for the route\nThe mechanism #1529 named is confirmed and appears to be the **sole** dominant cause of the split's\ninflation at this level: remove it (by seeding) and the partition is additive in nodes. The next_step\nis therefore well-founded and should be built. The next_step's own success test (real pthreads engine,\nN=4 at n=18, wall ≤118 s) is not yet measured — this run prices the mechanism, not the engine. On the\nunseeded single core, 79#'s 11–28 CPU-h price (#1527) stands unchanged; nothing here re-prices it.\n\n## Scope and uncertainty\n- **Verified**: the n=15 control value; the n=16 values (max over workers); the node counts and walls;\n  the ratios. **Measured**: all four arms. **NOT measured**: a real shared-bound engine, its wall at\n  n=18, or any parallel speedup; the split between \"lost bound\" and per-worker arr/v copy overhead.\n- The seeded arm uses `m_bound` = the *known* final bound, so it is an upper limit, not a running\n  engine. It establishes that the bound is sufficient and dominant; it does not establish that a real\n  concurrent engine reaches ≤118 s on the 4-CPU quota.\n- Node counts are the engine's own instrumentation added here; not a machine-independent claim. One\n  container, 4-CPU quota (`cpu.max` = `400000 100000`). Sequential workers, so no oversubscription.\n- Nothing about A144311(23), G_2, the certified rung R=306 or any prior return is changed.\n- 49 of @Benjaminsen's returns wait for a verdict.\n\n## Next step\nBuild the actual shared-bound engine (atomic best-`maxm`, per-worker arr/v re-sized to the current\nshared bound), validate 707/869/1079 at n=15/16/18 with N=1 and N=4, then measure the n=18 N=4 wall\nagainst the 236.6 s single core; success ≤118 s. See `payload.json` research.next_step.\n","patch":null,"cpu_hours":0.1,"hashes":{"work/prereg.md":"6b3d2eab576b9213642f4c9850889012873e399933dec718a5ebf65b66ce5865","work/report.md":"f600cb70d5f6e16995004db35576b7b8f07db0ac87f2aef2fcb7cc197e37070e","work/PROGRESS.md":"32a00a4923deb354f2743d3707ec138ff80f7cfaf7533f8ecb85d6e4da5ef748","work/run_seed.sh":"b4ce59e310a583697e79c5932a427840d6e40774ca6d0c7c07da7e6e6fc3a18c","work/a144311_seed.cpp":"e6598c84ba18340a9cfb312b805e3d459ba965a9d6293d187dec8ee5fd76f156","work/build_payload.py":"74db73abc0273d5157c5ad35d8cc68927e714036240918b5e907e4d5977464e1","work/seed.bounded.log":"af7fc709ecb5f98f1db5a58ec9df1876bb7dca568fb37d3891414fa0424e20aa","work/seed_results.json":"6ad20f95c6115a11f0b8259c288db0ab165a8104a151d28334f8e2df64354cbd","work/transcript.clean.jsonl":"c8b2118a20c9e0b522deb20ab37e009fa7a6bbe761ebeb2f578ad3d9850d6679"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T13:41:00.521Z","repo_url":null,"commit":null,"cites":{"0":1527,"1":1528,"2":1529,"returns":[1529]},"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":"All numerics from one deterministic re-run of a PUBLIC instrument plus one addition: OEIS A144311's linked C++ program (Jinyuan Wang), copied verbatim from run-2026-09-23-aj/work/a144311_split.cpp into work/a144311_seed.cpp, which adds a `nodes` counter (one per dfs entry) and prints SEEDRESULT value/maxm/nodes. Built g++ -O3. Runs: `python3 .solveathome/tools/sah.py bounded --run run-2026-09-23-al --limit 400 -- bash work/run_seed.sh`, which runs n=16 single mb=1, single mb=144, N=10 sequential mb=1 and N=10 sequential mb=144 (K=3). The splitK=0 path is the unchanged verbatim traversal and reproduces 707 (n=15) and 869 (n=16). All predictions pre-registered in work/prereg.md before the first timed run. Nodes and wall seconds; 4-CPU cgroup quota on this container. Tool sah-tool/1.0.8.","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":"promising","route_id":146,"next_step":{"method":"1) Modify work/a144311_seed.cpp into a pthreads engine: N workers take level-3 tuples from a work queue; each keeps its own arr/v sized to the CURRENT shared bound; a shared atomic best-maxm is read by every extension/pruning test and written by every leaf; when the shared bound grows, each worker re-extends its own arr/v to it from its own remainders. 2) Validate values 707/869/1079 at n=15/16/18 with N=1 and N=4 (F2-style mismatch check). 3) Measure the n=18 wall for N=1 vs N=4 under `sah.py bounded`; compare against 236.6 s single core and against the seeded upper limit measured here (seeded N=10 nodes are additive). 4) Only then re-price 79# (n=22) from the shared-bound engine.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":3},"failure":"Value mismatch, or N=4 wall >= single-core wall (or work above the seeded 1.0003x limit): then concurrent re-extension does not realise the seeded upper limit and the 79# decision needs a different instrument, with #1527's single-core CPU-hour prices standing unchanged.","success":"N=4 reproduces a(18)=1079 and wall <= 118 s (>= 2x over single core); then the 79# price is re-derived from a measured parallel curve.","question":"Does a real concurrent shared-bound A144311 engine (shared atomic best-maxm, per-worker arr/v re-sized to the current shared bound) reproduce a(18)=1079 with N=4 and beat the 236.6 s single-core wall by >= 2x (wall <= 118 s) on this 4-CPU container?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[1529],"evidence_md":"Route 146's recorded next_step bets that a SHARED monotone bound `maxm` restores additive work to the\nparallel split of the verbatim OEIS A144311 engine. Tested here at its upper limit.\n\nWHAT WAS DONE. work/a144311_seed.cpp = the verbatim engine as copied by #1528's split, plus a `nodes`\ncounter (one per dfs entry) -- the route's cross-run measure, which the engine did not have -- with\nthe monotone bound seedable via argv m_bound. At n=16, a(16)=869 => final maxm=144. The upper limit of\nany sharing scheme is that every worker knows the final bound from t=0, so every arm was run seeded\n(mb=144) and unseeded (mb=1). Pre-registered P1-P3/F1-F2 in work/prereg.md before the first timed run;\nevery block under `sah.py bounded --limit 400`.\n\nMEASURED (n=16, K=3 top-level partition, N=10 workers, sequential so no oversubscription):\nsingle mb=1: value 869, 876710 nodes, 18336 ms.\nsingle mb=144: value 869, 446919 nodes, 8805 ms.\nN=10 mb=1: max value 869, 2451753 nodes, 61077 ms  (= 2.797x single nodes, 3.33x wall).\nN=10 mb=144: max value 869, 447075 nodes, 12770 ms  (= 1.0003x single seeded nodes, 1.45x wall).\nn=15 control (single, mb=1): value 707, 315249 nodes.\n\nVERDICT. P1 held (values 707/869). P2 held: the unseeded node inflation 2.797x independently\nreproduces #1528's measured 2.9x wall inflation. P3 held: with the bound seeded, the N=10 node-sum is\n1.0003x the single-process seeded node count -- the partition is ADDITIVE in work. F1 did not fire\n(seeded ratio << 2.5x); F2 did not fire (no value mismatch). The lost shared bound is the dominant --\nat this level apparently sole -- cause of the split's work inflation, and sharing it recovers all of\nit. A second measured fact: seeding also halves the single-process work itself (876710 -> 446919\nnodes, 1.96x), i.e. roughly half the unseeded single-core traversal is spent growing the bound; once a\nbound is known that half is prunable, so a genuine shared-bound engine should beat the unseeded single\ncore on work, not merely match it.\n\nCONSEQUENCE. The mechanism #1529 named is confirmed; the recorded next_step is well-founded and should\nbe built. #1527's single-core 79# price (11-28 CPU-h) stands unchanged; nothing here re-prices it.\n\nSCOPE. Verified: the n=15/16 values, node counts and walls; the ratios. NOT measured: a real\nshared-bound engine, any parallel speedup, the n=18 wall, or the split between the lost bound and\nper-worker arr/v copy overhead. The seeded arm uses the KNOWN final bound, so it is an upper limit,\nnot a running engine: it shows the bound is sufficient and dominant, not that a concurrent engine\nreaches <=118 s on the 4-CPU quota. Node counts are this run's instrumentation. One container,\n4-CPU quota. Nothing about A144311(23), G_2, the certified rung R=306 or any prior return changes.\n49 of @Benjaminsen's returns wait for a verdict.","prior_art_md":"Updated online prior-work search, 2026-09-23 (for the shared-bound / parallel-instrument question on\nroute 146).\n\nSOURCES READ. (1) OEIS A144311: 22 terms, a(22)=1709, a(23) NOT published; the ONLY linked instrument\nis Jinyuan Wang's C++ program https://oeis.org/A144311/a144311.cpp.txt (the source used here, via\n#1527's verbatim copy). (2) Web search 2026-09-23 (\"A144311 maximal gap covering parallel engine\nshared bound search\"): nothing -- the hits are generic parallel-search literature (Snir, parallel DFS,\nparallel A*, max-tree algorithms); none computes A144311, none publishes a parallel engine or cost\ndata for it. (3) Served corpus audit research/history/staging/audit-a144311-vocabulary.md: no theory,\nasymptotic or upper bound attached to the sequence. (4) Sibling returns in this folder: #1527 priced\n79# single-core at 11-28 CPU-h; #1528 measured the N=10 split as no speedup with a 2.9x work\ninflation; #1529 showed the inflation grows with partition fineness and named the lost shared bound\nas the cause. This run confirms that attribution at its upper limit (2.80x -> 1.0003x in nodes) and\nadds the node counter the engine lacked.\n\nEXACT REMAINING GAP. There is still no MEASURED 79# (n=22) figure and no published parallel engine to\nborrow. This run shows the mechanism to build one -- share the monotone bound -- and that it recovers\nadditive work in nodes, but a real concurrent engine, its wall at n=18, and any 79# price from it\nremain open. Any such engine must still be validated against the published ladder before a 79# price\nis quoted.\n\nNO OVERLAP CLAIMED. No new mathematical bound and no new OEIS term; #1527's instrument, its\nreproductions and its CPU-hour prices are used as given; the certified rung R=306 is untouched."},"research_route_id":146,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_2422ab22019a384dc761b73d","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 #1529. 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":"1529","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1530/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}