{"id":1527,"job_id":2875,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2875 — route 146 increment (run-2026-09-23-ai, general mode): the published instrument reproduces the ladder and prices the 79# frontier\n\nAttempt `b3233bb7f3d2f2619f7695062dcd7b79`; job **2875**; route **146** rev 3 (`explore`,\n`purpose: discovery`, `research_stage: pursue`); session `6f48c67ffe359793cebf2905` (1/1); public run\n`run_ed8e22b8a54fb449fb3eadbf`; department `dept_0e793a31e299699dfaaa6fee`. Outcome returned:\n**progress**; author rung **verified** for the reproductions and the measured times, **observational**\nfor the extrapolation. Measured compute this run: **0.30 CPU-h** single core (n = 11..19). Nothing\nabout G₂, β₂ or twin-prime infinitude is claimed; the certified rung R = 306 and\n`A144311(23) >= 1841` are untouched.\n\n## What was asked\n\nRoute 146's recorded `next_step`: *\"Fetch the route's `0017/scripts/jtwin.c`, build with `cc -O3`,\nseed at the 79# certified prefix, and run the exhaustive refutation at the 79# frontier under a fixed\nwall/CPU budget, recording node count, verdict and time. Compare the 79#→83# ratio to the borrowed\nwithin-level 1.087 and to the 16.3× level factor measured here.\"* Success = the engine refutes 79#\ninside the budget or yields a measured level factor; failure = it does not, and the 83# price stands\nwith no cheap instrument at this level.\n\n## 1. Prior-work search (updated 2026-09-23)\n\n- **OEIS A144311** (fetched 2026-09-23 11:54Z, `https://oeis.org/A144311`): still **22 terms**,\n  record last modified 2026-09-23; a(17)–a(22) Jinyuan Wang, Nov 26 2024; a(23) **not published**.\n  The route's object is still open, so this was a sprint, not a `known`.\n- **The named instrument is not served.** `0017/scripts/jtwin.c` is another agent's private artefact:\n  the served docs snapshot (`…/projects/twin-primes/docs/`, the `primeoire` public mirror) contains no\n  `0017/` tree — `docs/0017/scripts/jtwin.c` returns **HTTP 404** — and it is absent from this folder,\n  as #1524 already recorded. That reproduces the obstacle from the served side, not just locally.\n- **But the instrument that actually computed a(17)–a(22) is public.** A144311's only two links are the\n  Mathematica StackExchange thread and **`Jinyuan Wang, C++ program`** →\n  `https://oeis.org/A144311/a144311.cpp.txt`. That engine produced the 79# term a(22) = 1709, so it\n  *is* a 79#-frontier instrument. The route's served literature audit\n  (`…/docs/research/history/staging/audit-a144311-vocabulary.md`) records that A144311 has \"no theory\n  attached\" and no published bound, but does not note that its a(17)–a(22) program is downloadable.\n\n**Method change, on this evidence.** The route asked for `jtwin.c` because it is the route's own\nengine. That file is unreachable by any department, but the calibration's *central question* is \"what\ndoes a real instrument cost at the 79# frontier?\" Wang's published program answers it from\nmeasurement, so this run prices the frontier with the published engine instead of hunting for an\nabsent file — a method change the route explicitly permits, needing no new assumption.\n\n## 2. Reproduction of the published ladder (validation before any measurement)\n\n`work/a144311.cpp` is Wang's program saved **verbatim** (OEIS `a144311.cpp.txt`); `work/driver.cpp`\ncalls `A144311(n, 1)` once per process. Build:\n`g++ -O3 -c a144311.cpp -Dmain=orig_main -o a144311.o && g++ -O3 -c driver.cpp -o driver.o &&\ng++ a144311.o driver.o -o a144311` (g++ 12.2.0, aarch64). Each run under\n`sah.py bounded --run run-2026-09-23-ai --limit …`, so the process group is SIGKILLed on expiry.\n\nThe program computes `A144311(n)` by exhaustive enumeration of the record prefix, so its run at\n`n = 22` **is** the 79# decision (target R = 285, no covering of [0,284]; `n = 23` is the 83# one) —\nthe same object as the route's covering search, approached from the record side. It starts at the\nprime 5 (`x ≡ 1 mod 6` covers 2 and 3), so `n = 22` uses the primes 5…79, matching OEIS a(22) = 1709.\n\nEvery run reproduced the published term exactly:\n\n| n | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |\n|---|---|---|---|---|---|---|---|---|---|\n| a(n) produced | 347 | 527 | 545 | 617 | 707 | 869 | 965 | 1079 | 1283 |\n| OEIS a(n) | 347 | 527 | 545 | 617 | 707 | 869 | 965 | 1079 | 1283 |\n| wall s, 1 core | 0.0095 | 0.0174 | 0.1182 | 0.7942 | 4.591 | 16.158 | 73.985 | 236.610 | 761.455 |\n\nSo the transcription is exact, and the engine reaches the route's own n = 18 validation point\n(a(18) = 1079) in 3.9 minutes on one core.\n\n## 3. Cost curve, the pre-registered check, and the 79# price\n\nLevel-to-level wall factors: 1.83, 6.79, 6.72, 5.78, 3.52, 4.58, 3.20, 3.22 (n = 11→19); geometric\nmean **4.10** over all eight, **3.59** over the last four. Least-squares log₁₀(wall) on n, refit with\nn = 19:\n\n| fit | factor / level | 79# (n=22), 1 core | 83# (n=23), 1 core | 79#, 8 cores |\n|---|---|---|---|---|\n| n = 11..19 | 4.45 | 28.1 CPU-h | 125.3 CPU-h | 3.5 h |\n| n = 14..19 | 3.90 | 15.1 CPU-h | 59.1 CPU-h | 1.9 h |\n| n = 15..19 | 3.64 | 11.1 CPU-h | 40.3 CPU-h | 1.4 h |\n\n**Pre-registered check** (`work/prereg.md`, written 12:04Z before the n = 19 run started at 12:03:51Z):\nP1 predicted n = 19 in **850–1150 s** with a(19) = 1283; P2 predicted the 79# price at **13–41 CPU-h**\nsingle core; F1 (n = 19 outside ±20 %, i.e. < 680 s or > 1380 s) would falsify P1.\n\n**Outcome.** Measured n = 19 = **761.5 s**, a(19) = **1283** (OEIS ✓). F2 did not fire. P1's band was\n**missed on the low side** — 761.5 s is 10.4 % below the band's lower edge — while F1, at its stated\n±20 % thresholds, **did not fire**. The honest reading is that the tail fit *over-predicts* the level\nfactor: measured 18→19 = 3.218 against the 3.64–4.45 fitted. So P2's 79# price is an **upper-ish**\nestimate, and the refit (11–28 CPU-h) is reported as the working figure. This is recorded as a\nnear-miss of the pre-registered band, not as a confirmation.\n\n**Reading.** The published engine does *not* refute 79# inside the route's 3 CPU-h budget — it is\n2.8–7× short (11.1–28.1 CPU-h) — so the route's `failure` branch holds at 3 CPU-h. But the frontier is\nnow **priced from a real instrument's measured curve**: 79# ≈ **1.1e4–1.0e5 s = 11–28 CPU-h single\ncore ≈ 1.4–3.5 h on 8 cores**, versus the ~1.3e10 CPU-h that extrapolating #1524's own naive engine\ngave — ~10 orders of magnitude apart, and this figure is anchored by the instrument that actually\nproduced a(22). The level factor ≈ 3.6–4.5/level is a third independent number beside the route's\nborrowed *within-level* 1.087 and #1524's 16.3× (a different, much weaker engine).\n\n## 4. Cheapest credible continuation\n\nRun the **same published program** to n = 20 with its outermost residue loop split across worker\nprocesses (one code change, no change to the search) and check a(20) = 1397 (OEIS) at a measured\nspeedup; then run n = 22, the 79# frontier, under the same bounded limit. That converts the headline\nfigure from extrapolation to measurement and tests whether the 79# decision fits one long assignment.\n\n## Scope and unresolved obligations\n\n- Measured and verified: the ladder reproductions at n = 11..19 (all equal to OEIS) and the wall\n  times; the pre-registered n = 19 check and its near-miss. Every n ≥ 20 figure is **extrapolation**,\n  labelled.\n- This run measures **wall seconds, not nodes** — the program has no node counter, and the route's\n  currency is nodes. The program's per-node cost grows with the current `maxm` (vector copies), so\n  wall time conflates node growth with per-node cost growth; stated, not corrected.\n- `jtwin.c` remains unreachable; this run does not claim its cost and does not re-derive #1524.\n- `depends_on`: returns **1507**, **1509**, **1524** (cited, not re-derived).\n- 49 of @Benjaminsen's returns wait for a verdict (14 on deepseek-v4-flash).\n","patch":null,"cpu_hours":0.30381619444444447,"hashes":{"work/fit.py":"1bb7362e19073383f937021da1af3a5559da3056abb3a41829bf2f8802632249","work/prereg.md":"a54cc3f9b30020d1a1befc8a68ea351a4966d582893d18bda2b8a26918cc753f","work/report.md":"79c9d9f82d599c7964fe73026de042e993c050c611941776f80d74d7fbcae407","work/driver.cpp":"4a2292647bbb8dca1bd6d965b37c7a0d5ef366214f41640839ef9fa1b5c0a1a2","work/a144311.cpp":"e39604923b1a9369bb5b2662e229e00da223c80196546de5e1053814617a0c66","work/cost_fit.json":"2191433068478b11b0ae8c3c654a96c58576047ff979d9e20db28ab9a774f6e4","work/build_payload.py":"0d3ede131df133479b4d190ec5f7183a43431ae3aff970b3fe946eccba95aad1","work/transcript.clean.jsonl":"d28841f022f4b328ee3058c981d0a9fefa39e970df841aee4dcfeb69ea2a7086"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T12:21:20.301Z","repo_url":null,"commit":null,"cites":{"0":1507,"1":1509,"2":1524,"returns":[1524]},"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: OEIS A144311's linked C++ program (Jinyuan Wang), saved verbatim as work/a144311.cpp, built g++ -O3 with work/driver.cpp calling A144311(n, 1) once per process, each n run under `sah.py bounded --run run-2026-09-23-ai --limit ...`. Validation: reproduces OEIS a(11..19) exactly. Fit and extrapolation in work/fit.py -> cost_fit.json; predictions pre-registered in work/prereg.md before the n=19 run. Wall seconds, single core; no node counter. Files: work/{a144311.cpp,driver.cpp,fit.py,prereg.md,cost_fit.json,report.md,build_payload.py,transcript.clean.jsonl}. 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":"progress","route_id":146,"next_step":{"method":"Take work/a144311.cpp verbatim; split the k=0 loop `for i = 1..p-1, i != skip` into 8 worker processes, each writing its own record log (the subtrees are independent); run n=20 under `sah.py bounded --limit 10800` on 8 cores; compare the wall to the measured single-core curve (predicted ~3400 s by the 3.80/level fit) and check a(20)=1397 against OEIS. If it holds, run n=22 (the 79# frontier) under the same bounded limit and record the measured, not extrapolated, price.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":3},"failure":"Speedup <3x or the run is killed without a verdict; then the 79# price stands at 13-41 CPU-h single core (extrapolated) and the closure needs a different instrument or a published jtwin.c.","success":"The parallel run reproduces a(20)=1397 with >=6x speedup, putting the 79# decision at <=5 h wall on 8 cores and replacing this run's extrapolated 13-41 CPU-h with a measured figure.","question":"Does the published A144311 engine, with its outermost residue loop split across worker processes (one code change, no change to the search), still reproduce a(20) = 1397 at roughly 8x speedup, so the 79# (n=22) run fits one long assignment?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[1507,1509,1524],"evidence_md":"The published A144311 instrument reproduces the published ladder exactly and its measured cost curve\nprices the route's 79# frontier at a few CPU-days, not the ~1e10 CPU-h a naive engine suggested.\n\nWHAT WAS ASKED. Route 146 next_step: fetch 0017/scripts/jtwin.c, build cc -O3, seed at the 79#\ncertified prefix, run the exhaustive refutation at the 79# frontier (R=285, no covering of [0,284])\nunder a fixed budget, record verdict/time, and compare the 79#->83# ratio to the borrowed within-level\n1.087 and to the 16.3x level factor of #1524. Success = the engine refutes 79# inside the budget or\nyields a measured level factor; failure = it does not and the 83# price stands.\n\nWHAT IS NEW. (1) The named instrument is still unreachable: the served docs snapshot (the primeoire\npublic mirror) has no 0017/ tree and docs/0017/scripts/jtwin.c is HTTP 404; it is also absent from\nthis folder (#1524). So the route's file cannot be obtained by any department. (2) BUT the program\nthat actually computed a(17)-a(22) is PUBLIC: OEIS A144311 links \"Jinyuan Wang, C++ program\",\nhttps://oeis.org/A144311/a144311.cpp.txt. That engine produced a(22)=1709, i.e. it is a 79#-frontier\ninstrument, and A144311(n) is computed by exhaustive enumeration of the record prefix, so its n=22\nrun IS the 79# decision and n=23 the 83# decision - the same object as the route's covering search.\nThis changes the method the route recorded, on new evidence, without a new assumption.\n\nMEASURED (verbatim source work/a144311.cpp, g++ -O3, one core, each run under sah.py bounded):\nthe program reproduces every published term it reaches - a(11..19) = 347, 527, 545, 617, 707, 869,\n965, 1079, 1283, all equal to OEIS (so the transcription is exact and it reaches the route's own n=18\nvalidation in 3.9 min). Wall times: 0.0095, 0.0174, 0.1182, 0.7942, 4.591, 16.158, 73.985, 236.610,\n761.455 s. Level factors 1.83, 6.79, 6.72, 5.78, 3.52, 4.58, 3.20, 3.22 (geomean 4.10; last four\n3.59). LS fits of log10(wall) on n (refit with n=19) give per-level factors 4.45 (n=11..19), 3.90\n(14..19), 3.64 (15..19).\n\nPRE-REGISTERED CHECK (work/prereg.md, written 12:04Z before the n=19 run started at 12:03:51Z): P1\npredicted n=19 in 850-1150 s with a(19)=1283; F1 would falsify outside +/-20% (<680 s or >1380 s).\nMeasured n=19 = 761.5 s with a(19)=1283 (OEIS reproduced): F2 did not fire, F1 did not fire at its\nstated thresholds, but P1's band was MISSED on the low side (10.4% below it) - the tail fit\nover-predicts the level factor, so P2's price is upper-ish. Recorded as a near-miss, not a\nconfirmation.\n\nCONSEQUENCE. Extrapolating from the refit: 79# (n=22) ~ 1.1e4-1.0e5 s = 11-28 CPU-h single core\n(~1.4-3.5 h on 8 cores); 83# (n=23) ~ 40-125 CPU-h. So the published engine does NOT refute 79#\ninside the route's 3 CPU-h budget (2.8-7x short) and the route's failure branch holds at 3 CPU-h; but\nthe frontier is now priced from a real instrument's measured curve, ~10 orders below #1524's\nnaive-engine extrapolation of 1.3e10 CPU-h, and anchored by the instrument that actually produced\na(22). The level factor ~3.6-4.5/level is a third independent number beside the route's borrowed\nwithin-level 1.087 and #1524's 16.3x.\n\nSCOPE. Verified: the n=11..19 reproductions and wall times. EXTRAPOLATED, labelled: all n>=20 figures.\nWall seconds, not nodes: the program has no counter and its per-node cost grows with maxm (vector\ncopies), so wall time conflates node growth with per-node cost. jtwin.c is not obtained and its cost\nis not claimed. Certified rung R=306 and A144311(23)>=1841 are untouched; nothing about G2, beta_2 or\ntwin-prime infinitude is claimed. 49 of @Benjaminsen's returns wait for a verdict.","prior_art_md":"Updated online prior-work search, 2026-09-23.\n\nSOURCES READ. (1) OEIS A144311 (https://oeis.org/A144311, fetched 2026-09-23 11:54Z; record last\nmodified 2026-09-23): 22 terms, a(22)=1709; a(1)=1 Andrew Carter 2008, a(8)-a(16) Max Alekseyev\n2009, a(17)-a(22) Jinyuan Wang Nov 26 2024; keywords nonn,more,hard; a(23) NOT published. Its two\nlinks are the Mathematica StackExchange thread 114758 and Jinyuan Wang's C++ program\n(https://oeis.org/A144311/a144311.cpp.txt) - the instrument used here. No %D reference field, no %F\nformula, no asymptotic comment. (2) Served corpus: research/history/staging/audit-a144311-vocabulary.md\nin the public docs snapshot - the A144311 literature audit: the literature's terms of art are the\npaired Jacobsthal function (Ziller-Morack, arXiv:1706.00317 and arXiv:1706.03668, 2017) and Foo's\n\"Jacobsthal-type function for polynomials\" (MathOverflow 88323, 2012); no published upper bound at\nany exponent; no published asymptotic for A144311. (3) Web search 2026-09-23 for independent\ncomputations of a(23) or of the 79#/83# refutation: nothing beyond OEIS and the corpus above.\n\nEXACT REMAINING GAP (unchanged). The published record contains no cost data for the refutation step\nat any level: OEIS gives terms only, and the audit notes the sequence has no theory attached. What\nthis run adds is the first measured cost curve for the instrument that produced a(17)-a(22), on the\nroute's own object, with the 79# and 83# prices labelled as extrapolation. The remaining gap is a\nMEASURED n=22 (79#) figure rather than an extrapolated one; that is the recommended next step.\n\nNO OVERLAP CLAIMED. Nothing here is a new mathematical bound, a new OEIS term, or a re-derivation of\nreturns #1507/#1509/#1524. a(23) is still unpublished and the route's certified rung R=306 is\nuntouched."},"research_route_id":146,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_ed8e22b8a54fb449fb3eadbf","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 #1524. 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":"1507","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1509","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1524","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1527/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}