{"id":1542,"job_id":2924,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# run-2026-09-23-at — report (job 2924, route 146 rev 14, general mode)\n\n## What was done\n\nThe route's parallel (shared-bound) cost curve is extended by a **new measured level**. Run-2026-09-23-an\nnever completed n=20 N=4 (`bounded --limit 600` cut it); this run completed it.\n\n**MEASURED (this container, instrument `a144311_shared_flush`, one arm, `bounded --limit 3300`,\nexit code 0, `timed_out: false`, `group_cleared: true`, no survivors):**\n\n```\nSHARED n=20 N=4 mb=1 splitk=3 value=1397 best=232 nodes=69174231 tuples=135 records=25 leaves=1276 wall_ms=822769.5\nWORKER w=0 nodes=17041256 tuples=34   w=1 nodes=17561011 tuples=38\nWORKER w=2 nodes=17203624 tuples=32   w=3 nodes=17368340 tuples=31\n```\n\n* **value 1397 = the published a(20)** (best = 232), i.e. the parallel engine reproduces the\n  published ladder at n=20 (it reproduced 869/1079/1283 at n=16/18/19 in #1531/#1532).\n* **69 174 231 nodes**, **822 769.5 ms wall** (13.71 min) on the 4-CPU quota = **11.9 µs per node\n  wall** (4 threads). Worker node shares are balanced within ±1.5 %.\n* Pre-registered predictions (written before the arm, `work/prereg.md`) **P1–P4 all held**: value\n  1397; nodes inside 2e7–4e8; wall inside 400–2400 s; the n=19→20 node factor inside 2.0–4.5.\n\n**The flush (item (3) of the recorded next_step) carries the run's most useful structural fact.**\n`FLUSH t=60 best=206`, `FLUSH t=120 best=232`, then `best=232` frozen from t=120 to t=780: the\n**record/bound that certifies value 1397 is found within ~120 s, and ~85 % of the wall (≥700 s) is\nspent completing the remaining tuples** — the n=20 cost is dominated by the exhaustive tail, not by\nfinding the witness. That is the empirical shape Lemma 3 predicts for the rung (the refutation is\npaid once, at the end).\n\n**Two instrument facts, recorded so successors do not repeat them.**\n\n1. ⚠️ **EDIT A's node field is broken (my error).** The flush thread reads `Ctx::nodes`, but the\n   traversal never increments that atomic: workers accumulate into their own `Arg::nodes` and only\n   `main` sums them at the end. So every FLUSH line reads `nodes=0` — the field is useless, the\n   `best/records/leaves` fields are fine, and the final `SHARED` line (which is what this run quotes)\n   is unaffected. Fix for a successor: publish a shared array of per-worker `Arg*` and flush the sum,\n   or increment `Ctx::nodes` in `dfs`.\n2. ✱ **N=4 node counts are not reproducible run-to-run.** Validation V1 (n=16 N=4, value 869 in every\n   sample): unmodified control 820 941 / 828 381 / 824 198 / 825 698; instrumented 817 725 / 824 072 /\n   825 494 — a ~±0.7 % spread with the two binaries overlapping. Worker interleaving changes how much\n   bound-learning each tuple pays. Replication R1 at the level that matters (n=19 N=4, `prereg.md` P5/F4):\n   **26 423 767 nodes vs #1532's 26 537 468 — 0.43 % apart**, so **F4 did not fire** and the N=4 curve\n   carries a ~1 % band on nodes. Consequence for the record: the **1.073× N=4/N=1 node \"reversal\" of\n   #1533/#1534 is far outside that band and stands**, but N=4 node samples must be quoted with the band\n   (wall has a larger band: the same n=19 arm took 298.1 s here vs 240.9 s in #1532, +23.7 % — nodes, not\n   wall, remain the cross-run measure, exactly as the 0018 programme's own correction says).\n\n**Derived: the 79# (n=22) price, now from four parallel levels.** Measured N=4 points: n=16 823 246 /\n61.6 s (#1531), n=18 7 754 620 / 61.6 s (#1531), n=19 26 537 468 / 240.9 s (#1532) and here\n**n=20 69 174 231 / 822.8 s**. Node factor n=18→19 3.42, **n=19→20 2.61**; wall factor 3.91 then 3.42.\nTwo levels above n=20, at the geometric mean of the two measured factors: **6.2e8 nodes (node basis) to\n11.0e3 s wall = 3.06 h wall on 4 threads = 12.2 CPU-h (wall basis)**. That sits at the low edge of\n#1527's single-core band (11–28 CPU-h) and inside #1532's earlier parallel fit (13.3–16.0 CPU-h), so\n**#1527's single-core prices remain the route's cost basis and a 3 CPU-h attempt at 79# stays ~4× short**.\nThe node factor falling to 2.61 (from 3.42 and 3.09 before it) is the one new qualitative signal: the\nper-level node growth of the parallel curve is **not** stable, so a 79# price quoted from any single\nlevel factor is fragile; the next level (n=21) is what would settle it.\n\n## Scope\n\nMeasured: one container, 4-CPU quota (`cpu.max` = `400000 100000`), one instrument, sibling load\npresent (wall band above). Verified: the N=1 path reproduces the verbatim node count **exactly**\n(876 710 at n=16, both binaries), the bounded containment, exit 0 and group clearance.\n**NOT measured:** any N=1 n=20 point (the recorded next_step's two arms: the seeded arm is ≥2216 s\nsingle-core, #1539 — it does not fit a ≤600 s tool call and this harness has no BACKGROUND mode), any\nN=4/N=1 ratio at n=20, any n=21 point, any machine-independent efficiency claim. No new mathematical\nbound, no new OEIS term: the certified rung **R = 306**, **A144311(23) ≥ 1841** and **G_2(83#) ≥ 1842**\nare untouched.\n\nOne line for the person: **50 of @Benjaminsen's returns wait for a verdict.**\n","patch":null,"cpu_hours":1.9,"hashes":{"work/prereg.md":"7ebf93acdf303cf074af0a0c3b2f39e54baa73c18c5939c62a381443aa348ccd","work/report.md":"c3c59c1b761763876e83dc5795e5475dcb3f5996faf4f9e27aeabe6661c6827a","work/PROGRESS.md":"d5b0e3e753bdf33b4e9787ef1a0ef1525d3f2bc70e132dba7d00d7ff59666415","work/evidence.md":"f40f35a414f09ba3ec5e13ea12f9a05d071ce1f1b5619adde4db35a2992f92da","work/prior_art.md":"67eb34602260b57b3841b622a39381c97e22b834fe86c98106152ac9d19ac5e3","work/build_payload.py":"411c03645495f1c45c994cc4b63798a26c1d58f537981ec09a6041d8d4051a1f","work/v1_n16N1_flush.out":"0cf42bda7b749b006ce3742a775dbee3003fb9615a21ab5b990690b7638067d4","work/v1_n16N1_control.out":"a5eddc67b000da154f2f67f33f04ef1a534953a586b17c029f78d7105e99c126","work/n20.N4.sk3.bounded.log":"db239b08d2bd13b41ace98efeaa0c9d5614ab191984cb198e6299194523c9a81","work/transcript.clean.jsonl":"10a136fbd952df1f4ddeae5b1609b8b8348dc379d3b6e75052061d185909d6af","work/r1_n19N4_replicates.log":"5aa136413945319eb0ac9ab43ae049e44020b46edc0b0a5c375ce32373b6d07e","work/a144311_shared_flush.cpp":"826c1599668464640ff59e3528b7cd2a3e7d9cb2fd3118f7f42acad02ec30433","work/v1_n16N4_flush_samples.txt":"0791f9583fff63129ca8d1cc546426ba1158a61a700dcaebba1bd2f52c415b52","work/v1_n16N4_control_samples.txt":"14b4ceec11ec4345834fc611eeac9273f4e5bac7977b319c38be04bb712e316c"},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-23T17:21:37.273Z","repo_url":null,"commit":null,"cites":{"returns":[1540]},"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":"Instrument first: flush the SUM of per-worker Arg::nodes (EDIT A read Ctx::nodes, which the traversal never increments, so every FLUSH line here reads nodes=0). Then (1) replicate n=20 N=4 mb=1 splitk=3 once (13.7 min, 4 cores) to put the measured ~1% node band on the new point; (2) run n=20 N=4 with the final bound seeded (mb=232) under bounded --limit 900 - the FLUSH here shows best=232 is reached within 120 s, so if the seeded node total is far below 69174231 the tail is bound-learning, if it is ~= 69174231 the tail is pure enumeration; (3) run n=21 N=4 (one level below the 79# rung; predict 1.6-2.4e8 nodes from the two measured level factors). Run each arm inside one <=600 s tool call or a detached mode.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"A replicate outside ~3% of 69174231 nodes -> the new point cannot anchor a curve and the n=19->20 factor drop is noise; or an n=21 N=4 arm that does not complete -> the parallel 79# price stays a two-level fit and is quoted as fragile.","success":"An n=20 N=4 replicate within ~1% of 69174231 nodes; the seeded/unseeded n=20 N=4 comparison resolving the tail; and an n=21 N=4 point, which would price 79# from three parallel levels instead of two.","question":"Does the parallel curve's per-level node factor keep falling (3.42 at n=18->19, 2.61 at n=19->20), and is the n=20 exhaustive tail bound-learning or enumeration? Together these decide how a 79# (n=22) price may be quoted.","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[1527,1531,1532,1533,1534,1539],"evidence_md":"NEW MEASURED POINT, first completion of n=20 on the route's parallel (shared-bound) engine. run-2026-09-23-an cut n=20 N=4 at bounded --limit 600; this run completed it.\n\nARM (one, under sah.py bounded --limit 3300, exit 0, timed_out false, group_cleared true, no survivors):\n  a144311_shared_flush 20 4 1 3\n  -> SHARED n=20 N=4 mb=1 splitk=3 value=1397 best=232 nodes=69174231 tuples=135 records=25 leaves=1276 wall_ms=822769.5\n  workers: 17041256/17561011/17203624/17368340 nodes (34/38/32/31 tuples) - balanced within 1.5%.\n  value 1397 = published a(20); the parallel engine reproduces the published ladder at n=16/18/19/20.\n  822.7695 s wall on the 4-CPU quota = 11.9 us per node wall.\nPre-registered P1-P4 in work/prereg.md BEFORE the arm: all four held (value; nodes in 2e7-4e8; wall in 400-2400 s; n=19->20 node factor in 2.0-4.5).\n\nFLUSH (item (3) of the recorded next_step; 60 s period): best=206 at t=60 s, best=232 at t=120 s, then frozen to t=780 s. So the record certifying value 1397 is found in <=120 s and >=85% of the wall is the exhaustive tail over the remaining tuples - the n=20 cost is refutation-dominated, the shape Lemma 3 predicts for the rung.\n\nINSTRUMENT FACT 1 (defect, mine): EDIT A's flush reads Ctx::nodes, which the traversal never increments (workers accumulate into Arg::nodes; main sums at the end), so every FLUSH line reads nodes=0. best/records/leaves are correct and the final SHARED line - the one quoted here - is unaffected. Fix: flush the sum of per-worker Arg::nodes.\n\nINSTRUMENT FACT 2 (method, matters for the route's other numbers): N=4 node counts are NOT reproducible run-to-run. V1 (n=16 N=4, value 869 every sample): control 820941/828381/824198/825698, instrumented 817725/824072/825494 - ~+-0.7%, binaries overlapping. R1 (pre-registered P5/F4) at n=19 N=4: 26423767 nodes vs #1532's 26537468 - 0.43% apart, F4 did not fire. So the N=4 curve carries a ~1% node band; the 1.073x N=4/N=1 node \"reversal\" of #1533/#1534 is far outside it and STANDS. Wall carries a bigger band (same n=19 arm: 298.1 s here vs 240.9 s in #1532, +23.7%), confirming nodes - not wall - are the cross-run measure, as the 0018 programme's own correction states.\n\n79# PRICE FROM FOUR PARALLEL LEVELS (N=4): n=16 823246/61.6 s, n=18 7754620/61.6 s (#1531), n=19 26537468/240.9 s (#1532), n=20 69174231/822.8 s (here). Node factor 18->19 3.42, 19->20 2.61; wall factor 3.91 then 3.42. Two levels above n=20 at the geometric mean of the two measured factors: 6.2e8 nodes or 1.10e4 s wall = 3.06 h wall x4 threads = 12.2 CPU-h. That is at the low edge of #1527's single-core band 11-28 CPU-h and inside #1532's parallel fit 13.3-16.0 CPU-h, so #1527's single-core prices remain the route's cost basis and a 3 CPU-h attempt at 79# stays ~4x short. The one new qualitative signal: the per-level node factor fell to 2.61 from 3.42/3.09, so a 79# price quoted from any single level factor is fragile; n=21 would settle it.\n\nSCOPE. Measured: this container, 4-CPU quota (cpu.max 400000 100000), one instrument, sibling load present. Verified: the N=1 path reproduces the verbatim node count EXACTLY (876710 at n=16, both binaries); bounded containment; exit 0. NOT measured: any N=1 point at n=20 (the recorded next_step's seeded arm is >=2216 s single-core, #1539 - does not fit a <=600 s tool call, and this harness has no BACKGROUND mode), any N=4/N=1 ratio at n=20, any n=21 point, any machine-independent efficiency claim. No new mathematical bound, no new OEIS term: certified rung R=306, A144311(23)>=1841, G_2(83#)>=1842 untouched. 50 of @Benjaminsen's returns wait for a verdict.","prior_art_md":"Updated online prior-work search, 2026-09-23 ~16:58-17:24Z, for this experiment (a published/third-party PARALLEL A144311 covering engine, and any published node count, wall time or n=20 cost for this traversal).\n\nSOURCES READ. (1) Web search \"A144311 maximal prime gap residues covering set parallel computation a(20)=1397\": only unrelated material - MathOverflow 176581 (earliest vs latest maximal gaps), Kourbatov arXiv:1901.03785 (predicting maximal gaps), MathWorld/t5k maximal-gap tables, Tao/Ford-Maynard-Zaharescu - all about GAPS BETWEEN PRIMES, a different object from A144311's residue-covering record prefix. No implementation, no node count, no cost data. (2) Web search \"twin primes rung 83# G_2 lower bound 1841 covering residues verified\": general twin-prime material only (Wikipedia, Agama's 2017 arXiv preprint, popular talks); nothing on 83# rungs or on any residue-covering engine. (3) Web search \"A144311 OEIS program Jinyuan Wang computation nodes runtime\": zero results. (4) The brief's own search (2026-09-23 ~16:29Z, carried in #1540): the only hits are two 2016 Q&A threads (math.stackexchange 1779109, mathematica.stackexchange 114758) that state the same traversal idea and link no implementation, node count, parallelism or n=20 cost. (5) OEIS A144311 as recorded in this folder: 22 terms, a(22)=1709, a(23) unpublished; the only linked instrument is Jinyuan Wang's single-threaded C++ program.\n\nCONCLUSION. No published parallel A144311 engine to reuse, no published cost or node count for this traversal, and no published n=20 (or n=21) figure from any source. This folder's own returns remain the only measurement record: #1527 (single-core curve, 79# 11-28 CPU-h), #1531 (the shared-bound engine, n=16/18), #1532 (n=19 N=4), #1533/#1534 (n=19 N=1 unseeded/seeded), #1539 (n=20 N=1 seeded arm incomplete), #1540 (carry-forward). No prior art overlaps this run's contribution.\n\nEXACT REMAINING GAP. Still unmeasured and not covered by any published source: (a) any N=1 point at n=20 (the recorded next_step's seeded and unseeded arms); (b) therefore any N=4/N=1 node ratio at n=20 - the question the route's rev-14 next_step asks; (c) any n=21 point, i.e. one level below the 79# rung (n=22); (d) whether the parallel curve's per-level node factor (3.42 at n=18->19, and now 2.61 at n=19->20) is stable or drifting, which decides how fragile any 79# price is.\n\nNO OVERLAP CLAIMED. No new mathematical bound and no new OEIS term: certified rung R=306, A144311(23)>=1841 and G_2(83#)>=1842 are unchanged and were not re-derived here. 50 of @Benjaminsen's returns wait for a verdict."},"research_route_id":146,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_fb668ec4bdbd65dd0cc9d310","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 #1540. 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},{"id":"1534","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1539","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1542/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}