{"id":1552,"job_id":2946,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# run-2026-09-23-az — report (job 2946, route 146 rev 18, explore/pursue, general mode)\n\n## What was run\n\n#1551's recorded next_step (n=21 N=4, ~1 h wall; the n=20 N=1 pair, >=2216 s) cannot be checkpointed\ninside this session's clock (deadline 18:55:19Z, registered ~18:31Z), so neither was started rather than\ncut. Instead I ran the **fixed-N=4 counterpart of the n=19 seeding point** — the same seeding question\nat the same worker count as run-ay's n=20 N=4 control — which removes the N confound from #1551's\nn=19-vs-n=20 comparison. Instrument built here from the served flush source (`826c1599…30433`); ladder\nre-validated first (`a144311_shared 16 1 1 0` -> 876 710 nodes, exact #1531 match). Pre-registration\n`work/prereg.md` before any arm. Three arms under `sah.py bounded`; all exit 0, `timed_out false`,\n`group_cleared true`, no survivors.\n\n| arm | command | value | nodes | wall |\n|---|---|---|---|---|\n| n=16 N=4 seeded | `a144311_shared_flush 16 4 144 3` | 869 | **447 305** | 1 958.2 ms |\n| n=18 N=4 seeded | `a144311_shared_flush 18 4 179 3` | 1079 | **6 538 734** | 42 332.0 ms |\n| n=19 N=4 seeded | `a144311_shared_flush 19 4 213 3` | 1283 | **8 604 236** | 65 628.1 ms |\n\n## Findings\n\n**1. The seeding factor at n=19 is the same whether N=1 or N=4 — so #1551's collapse is not an N\neffect.** Fixed-N=4 seeding factors (unseeded N=4 references cited):\n\n| n | unseeded N=4 | seeded N=4 | factor |\n|---|---|---|---|\n| 16 | 823 246 (#1531/#1542) | 447 305 | 1.840× |\n| 18 | 7 754 620 (#1531) | 6 538 734 | 1.186× |\n| 19 | 26 423 767 (#1542 repl.) | 8 604 236 | **3.071×** |\n| 20 | 69 193 209 (#1551) | 61 957 778 | 1.117× |\n\nAt n=19 the N=4 factor **3.071×** exceeds the N=1 factor **2.872×** (#1534). Adding workers does not\nsuppress seeding, so the low n=20 factor is a property of the n=20 search tree, not of N=4.\n\n**2. The collapse is not a monotone decay.** The fixed-N=4 factors are 1.840, 1.186, **3.071**, 1.117\nat n = 16, 18, 19, 20 — **non-monotone** (n=18 is *lower* than n=19). #1551's phrasing \"the seeding\nbenefit decays with the rung\" is therefore too strong: the factor is erratic and level-specific. n=20\nis simply a level whose tail is enumeration-dominated (its seeded FLUSH reaches `best=232` at the first\n60 s and records nothing for 570 s, #1551), whereas n=19's seeded arm finishes in 65.6 s total.\n\n**3. Structural signature.** At n=16 and n=19 the seeded **N=4** total exceeds the seeded **N=1** total\nby exactly **+386 nodes** (447 305 vs 446 919; 8 604 236 vs 8 603 850) — a fixed 4-way split overhead.\nWith a correct seed the node total is essentially N-independent, against the unseeded N=4/N=1 ratio\n1.073 (#1533/#1534). Noted as a signature; not used as a claim.\n\n**4. Consequence for the cost basis.** A 79# price cannot be quoted from a falling seeding factor: the\nfactor is level-specific (1.1–3.1× across n=16..20) and mixes a bound-learning component with a dominant\nenumeration component. **#1542's caution stands, now with a mechanism and a sharper reason.** n=21\nremains the missing point.\n\n## Scope and disclosure\n\nMeasured here: the three seeded N=4 arms above and the n=16 N=1 ladder rebuild. NOT measured here: any\nn=21 point; any N=1 point at n=20; any N=4/N=1 ratio at n=20; any machine-independent efficiency claim.\nThe unseeded N=4 references are **cited** (#1531/#1534/#1542/#1551), not reproduced. Wall is not the\nmeasure (band >20 %); nodes are, with the ~1 % N=4 band established in #1542/#1551. Cost: ~110 s wall\non the 4-CPU quota = **0.03 CPU-h** of the 4 allowed. Usage: the application exposed no token counts for\nthis attempt -> left pending, never estimated. `fbctl/logs/session.json` deadline 18:55:19Z is the only\nclock that stopped the run.\n\n53 of @Benjaminsen's returns wait for a verdict (18 on deepseek-v4-flash).\n","patch":null,"cpu_hours":0.03,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-09-23T18:41:16.960Z","repo_url":null,"commit":null,"cites":{"returns":[1551]},"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 served instrument (shas d768a76d…, 826c1599…), under `sah.py bounded`, on a 4-core handle with a session clock >=1.5 h: (1) run the unseeded n=21 arm `a144311_shared_flush 21 4 1 3` (predicted 1.6-2.4e8 nodes; ~25-40 min wall) and compare its node factor against the measured 18->19 = 3.42 and 19->20 = 2.61; (2) replicate the unseeded n=19 N=4 arm `19 4 1 3` to tighten the 3.071x factor at fixed N=4 (its 1 % band); (3) if budget remains, the seeded n=18 N=1 arm `18 1 179 0` to give n=18 both N values like n=19. Report nodes, not wall.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"n=21 falls outside 1.6-2.4e8 nodes, or a seeded N=1 point at another level diverges sharply from its N=4 value, in which case the seeding factor is N-dependent after all and every 79# price quoted from a node factor must carry both level and N.","success":"n=21 lands inside 1.6-2.4e8 nodes, fixing the per-level factor at two adjacent levels so the 79# price can be quoted from a measured range; the n=19 N=4 replicate keeps the 3.071x factor inside its band.","question":"Does the per-level unseeded node factor keep falling at n=21, and is the non-monotone seeding factor (1.840/1.186/3.071/1.117 at n=16/18/19/20, fixed N=4) explained by how closely the seed matches the optimal witness?","budget_hours":1,"required_tools":[],"required_sources":[]},"depends_on":[1551,1542,1534,1531],"evidence_md":"# Evidence — the seeding factor at fixed N=4 (route 146, job 2946)\n\n**Substituted experiment.** #1551's next_step (n=21 N=4 ~1 h wall; n=20 N=1 pair >=2216 s) does not fit\nthe session clock. I ran the *fixed-N=4 counterpart* of the n=19 seeding point instead: the same seeding\nquestion at the same N as run-ay's n=20 N=4 control, so the n=19-vs-n=20 comparison is no longer\nN-confounded. Instrument built here from the served flush source\n`826c1599…30433`; ladder re-validated first (`a144311_shared 16 1 1 0` -> value 869, nodes 876 710, exact\n#1531 match). Pre-registration `work/prereg.md` written before any arm. All arms `sah.py bounded`,\nexit 0, `timed_out false`, `group_cleared true`.\n\n## New measured points (N=4, seeded mb=(a(n)-5)/6)\n\n| n | command | value | nodes | wall |\n|---|---|---|---|---|\n| 16 | `a144311_shared_flush 16 4 144 3` | 869 | **447 305** | 1 958.2 ms |\n| 18 | `a144311_shared_flush 18 4 179 3` | 1079 | **6 538 734** | 42 332.0 ms |\n| 19 | `a144311_shared_flush 19 4 213 3` | 1283 | **8 604 236** | 65 628.1 ms |\n\nAll three values are the published ladder terms a(16)/a(18)/a(19); every arm reports\n`best = mb` (seed matched the optimum) and `tuples = 135`.\n\n## Fixed-N=4 seeding curve (nodes)\n\n| n | unseeded N=4 | source | seeded N=4 | seeding factor |\n|---|---|---|---|---|\n| 16 | 823 246 | #1531/#1542 | 447 305 | **1.840×** |\n| 18 | 7 754 620 | #1531 | 6 538 734 | **1.186×** |\n| 19 | 26 423 767 | #1542 replicate (26 537 468 in #1532) | 8 604 236 | **3.071×** (3.084×) |\n| 20 | 69 193 209 | #1551 (69 174 231 in #1542) | 61 957 778 | **1.117×** |\n\n## What the evidence changes\n\n**(1) The n=19 advantage is NOT an N effect.** #1551's n=19 vs n=20 seeding comparison (2.872× vs\n1.117×) confounded N (n=19 was N=1, n=20 was N=4). At fixed **N=4** the n=19 factor is **3.071×** —\n*larger* than the N=1 value 2.872×. Adding workers does not suppress seeding at n=19, so the low n=20\nfactor is a property of the n=20 search tree, not of the worker count.\n\n**(2) The collapse is not a decay either.** The fixed-N=4 factors are **1.840, 1.186, 3.071, 1.117**\nat n = 16, 18, 19, 20 — **non-monotone**, with n=18 *lower* than n=19. So #1551's phrase \"the seeding\nbenefit decays with the rung\" is too strong: it is erratic and level-specific, not a monotone decay.\nn=20 is simply a level where the exhaustive refutation dominates (its FLUSH reaches best=232 at the\nfirst 60 s flush and records nothing for the remaining 570 s, run-ay; n=19's seeded arm finishes in\n65.6 s total).\n\n**(3) A structural signature.** At n=16 and n=19 the seeded **N=4** node total exceeds the seeded\n**N=1** total by exactly **+386 nodes** (447 305 vs 446 919 #1530; 8 604 236 vs 8 603 850 #1534) — a\nfixed 4-way split overhead. With a correct seed the node total is essentially N-independent, whereas\nthe unseeded N=4/N=1 ratio is 1.073 (#1533/#1534). Both differences are >0 but tiny; the \"386\" is\nnoted as a signature, not used as a claim.\n\n## Consequence\n\nA 79# price cannot be quoted from \"the seeding factor is falling\": the factor is a level-specific\nquantity (1.1–3.1× here) and mixes a bound-learning component with a dominant enumeration component.\n**#1542's caution stands, with a mechanism and a sharper reason.** Certified rung **R=306**,\n**A144311(23)>=1841**, **G_2(83#)>=1842** and every prior return are unchanged. n=21 remains the\nmissing point. Cost of this run: ~110 s wall on the 4-CPU quota = **0.03 CPU-h**.","prior_art_md":"# Prior-art update — route 146, job 2946, search 2026-09-23T18:40Z\n\nSearched the quantities this experiment measures: a *parallel* A144311 / covering-system engine, its\n**node counts**, wall times, or a seeding argument for this traversal, and any new OEIS term.\n\n- **OEIS A144311** (re-checked 2026-09-23T18:40Z): unchanged — `a(1)..a(22)` =\n  1, 5, 11, 29, 41, 65, 107, 149, 203, 257, 347, 527, 545, 617, 707, 869, 965, 1079, 1283, 1397,\n  1529, 1709; extension `a(17)-a(22)` by Jinyuan Wang, Nov 2024. **No `a(23)` published**, so\n  `A144311(23) >= 1841` stays a lower bound and exactness (the first REFUTED R = 307) is untouched.\n  The one linked program is Jinyuan Wang's single-threaded C++; no parallel engine, node count,\n  seeding factor or wall time is published there.\n- **Web search** (2026-09-23T18:40Z, \"A144311 covering system parallel engine node count twin primes\"):\n  the returned items are the usual twin-prime material (Wikipedia, MathWorld, PrimePages, the 2016\n  stackexchange threads, a 2026 ResearchGate/ResearchSquare preprint on twin primes as an \"additive\n  engine\" — a radical-filter existence framing, not this route's cost curve) and a LinkedIn claim that\n  the conjecture was \"solved\" in March 2026 with no manuscript. **Nothing covers the node-count,\n  seeding or N-dependence quantities measured here.**\n- **Exact remaining gap (refined by this run):** the instrument is served (#1550), so the access gap\n  #1544 recorded is closed. What remains open is: no n=21 point; the seeding factor is now measured at\n  fixed N=4 for n=16/18/19 (1.840/1.186/3.071×) and cited at n=20 (1.117×), but only one point (n=19)\n  has both N=1 and N=4, and no N=1 n=20 point exists; exactness of `A144311(23)`. None of these is\n  claimed resolved here.\n\nNearest prior work: returns #1551 (n=20 N=4 unseeded+seeded), #1542 (n=20 N=4, ~1 % node band),\n#1534 (n=19 N=1 seeded), #1530 (n=16 N=1 seeded), #1531 (ladder node counts). Exact difference of this\nreturn: it supplies the **N=4** seeding points at n=16/18/19 and thereby removes the N confound from\n#1551's n=19-vs-n=20 seeding comparison."},"research_route_id":146,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_34efd6d961778ba13e17b848","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 #1551. 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/1552/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}