{"id":1524,"job_id":2861,"problem_id":1,"lane_id":null,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2861 — return report (run-2026-09-23-af, explore, route #146, general mode)\n\nSession context: this run **recovered** the interrupted predecessor `run-2026-09-23-ae`\n(attempt `01c9d99c…`, expired 07:15:13Z after its session ended) under this joining\ninstruction via `X-Recover-Attempt`; the server re-issued the same job #2861 to a new attempt\n`7674cfb4…` in a new session. The predecessor had left only a half-built solver (`cover.c` +\na compiled `cover`); no report or payload. Setup, identity (`deepseek/deepseek-v4-flash` /\n`unmeasured`), and local readiness (**45/45**, `sah-tool/1.0.8`) were re-run this session.\n\n## What I ran\n\nThe route's recorded `next_step` is the **79# instrument calibration**: refute the 79#-level\nfrontier (primes 5..79, `A144311(22) = 1709 = 6·284+5`), where the answer is *published*, inside\n3 CPU-h, and measure the level-to-level node ratio. 0017's engine (`jtwin.c`) is not present in\nthis department folder (it lives in the route's own artefacts on the server), so this run builds\nand exercises the **generic complete solver** arm only: an independent exact DFS covering engine\n(`work/cover.c`) with the counting-capacity bound as pruning.\n\nDesign and falsifier written before the runs: the engine is trustworthy iff its exhaustive\nREFUTED verdicts land exactly on the published frontier at small levels; the calibration\nsucceeds iff the 79# frontier refutes inside the budget (3 CPU-h).\n\n## Result — the independent engine is exact but the growth rate closes the 79# target (scoped negative)\n\n**The engine reproduces the published ladder exactly at the levels it reaches.** At n = 9, 10, 11\nthe exhaustive REFUTED verdicts land on the exact frontiers `R = pre+1` implied by OEIS\n(`a(9)=203, a(10)=257, a(11)=347`); every run matches (`all_oracle_matches: true`):\n\n| n | max prime | frontier R | nodes | wall | nodes/s |\n|---|---|---|---|---|---|\n| 9 | 23 | 34 | 684 461 | 9 ms | 76 M |\n| 10 | 29 | 43 | 10 850 591 | 126 ms | 86 M |\n| 11 | 31 | 58 | 182 430 255 | 2 065 ms | 88 M |\n\n**Measured level-to-level node factor ≈ 16.3×** (segment factors 15.85, 16.81 — measured on two\nintervals only, and labelled as such). This is the level-to-level quantity the route needs; it is\nnot the route's 1.087, which is a *within-level* factor per +1 R.\n\n**The 79# frontier was NOT reached.** `cover 61 180` (the n = 18 frontier) ran under\n`sah.py bounded --limit 300` and was killed at the wall limit (`timed_out: true`,\n`group_cleared: true`) with no verdict. Extrapolating the measured 16.33× factor and the measured\n88.3 M nodes/s single-core rate (all labelled extrapolation, not measurement):\n\n| level | extrapolated frontier nodes | single-core hours |\n|---|---|---|\n| 61# (n=18) | 5.6e16 | 1.8e5 h (≈20 y) |\n| 79# (n=22) | 4.0e21 | 1.3e10 h (≈1.4e6 y) |\n| 83# (n=23) | 6.5e22 | 2.1e11 h |\n\nSo **this** generic complete solver does not reach the 79# refutation inside 3 CPU-h — it is off\nby ~13 orders of magnitude even allowing only the two measured intervals. A generic solver of\nthis shape is not the cheap instrument the route hoped for; any viable one must be a genuinely\ndifferent search (0017's engine, or a learned/CDCL encoding with strong propagation), not a\nstraightforward DFS.\n\n## Scope and what this does NOT settle\n\n- **Verified:** the engine's exhaustive REFUTED verdicts equal the published frontiers at\n  n = 9, 10, 11 (three independent exact checks against OEIS); the node counts and rate above.\n- **Measured:** the ≈16.3× level node factor and the 79#/83# extrapolation.\n- **Not answered:** whether *0017's* engine refutes the 79# frontier in 3 CPU-h. That arm of the\n  calibration needs the route's own `jtwin.c`, absent from this folder; the re-pricing question\n  the route actually asked stays open on that side.\n- **Not claimed:** any change to the certified rung (R = 306), to `A144311(23) >= 1841`, or to\n  the route's `>=176.7 core-h` price for the 83# frontier decision. Nothing here is a new\n  mathematical bound; it is an instrument-cost measurement.\n- One incidental defect found and fixed locally in the reused solver: the printed\n  `a144311_index` label was `n_primes+3`; it should be `n_primes+2` (primes 5..p_n are the last\n  n−2 of the first n), corrected in `work/cover.c`.\n\n## Cheapest credible check/next step\n\nObtain 0017's `jtwin.c` (the route's own artefact) and run **its** 79# frontier refutation under\na fixed budget, comparing its node count at 79# against its own 83# R = 285 count (36.4G). That\nis the missing half of the calibration and is cheap on the route's side; the generic-solver arm is\nnow closed negative by this measurement.\n\nAccounting: 0.13 CPU-h actually consumed (one 300 s bounded run + the sub-3 s frontier runs);\none watched process, all `group_cleared: true`. One line for the person: **49 of @Benjaminsen's\nreturns wait for a verdict.**\n","patch":null,"cpu_hours":0.13,"hashes":{"work/cover.c":"b9092fa7efe0f9040c3714af2e1f1946df7cfbefc274de11fa57216b2ae4491f","work/prereg.md":"12bd6dda641e49e1cb42c387b305e07ea608af6ed724a883cfe70be25391c4c3","work/report.md":"0d0d524a78317568e858ec81032d50eaad55c33d9292c0e3d54712e94d18c58b","work/measure.py":"073bfe4a15c48852b18e8094207f6a985389a2d7dba1231a8e3eaaf1c6149aac","work/build_payload.py":"3faeb497c350867021cdcecd10130a5a16b36769bd702dc5b434251aa07427fd","work/cost_measurement.json":"7fe742544177ee5aa6f4160f73ede760f3cedf82dcb2d8696517e680ce098c5e","work/transcript.clean.jsonl":"08d133cd6148025462d6aab1ff990f283995a88ee4b0a84522682941f4dd5659"},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-09-23T11:10:37.718Z","repo_url":null,"commit":null,"cites":{"0":1507,"1":1509,"returns":[1509]},"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":"0.13 CPU-h; offline and deterministic (C compiler + stdlib Python). Build: cc -O3 -o work/cover work/cover.c. Validate: work/cover 23 34 ; work/cover 29 43 ; work/cover 31 58  (all REFUTED, matching a(9)=203, a(10)=257, a(11)=347). Measurement/extrapolation: python3 work/measure.py -> work/cost_measurement.json. Bound the frontier attempt: python3 .solveathome/tools/sah.py bounded --run run-2026-09-23-af --limit 300 -- work/cover 61 180  (killed at 300 s, no verdict; group_cleared true). Byte-stable JSON on stdout, no timing on stdout.","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":"Fetch the route's 0017/scripts/jtwin.c, build with cc -O3, seed at the 79# certified prefix, and run the exhaustive refutation at the 79# frontier under a fixed wall/CPU budget, recording node count, verdict and time. Compare the 79#->83# ratio to the borrowed within-level 1.087 and to the 16.3x level factor measured here.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"0017's engine also fails to refute 79# inside the budget; the 83# frontier price stands and no cheap instrument exists at this level.","success":"0017's engine refutes 79# inside the budget and yields a measured level-to-level node ratio, re-pricing the 83# frontier from data.","question":"Does 0017's jtwin engine refute the 79# frontier (R=285, no covering of [0,284]) inside a fixed budget, and what is its 79# node count against its own 83# R=285 count of 36.4G nodes?","budget_hours":3,"required_tools":[],"required_sources":[]},"depends_on":[1507,1509],"evidence_md":"Instrument cost of the route's 79# calibration, generic-solver arm. An independent exact DFS covering engine (work/cover.c, capacity-pruned) reproduces the published frontiers exactly at n=9,10,11 (REFUTED at R=pre+1 for a(9)=203, a(10)=257, a(11)=347; all three match OEIS). Measured frontier node counts: n=9 684,461; n=10 10,850,591; n=11 182,430,255, at 88.3M nodes/s single core. Level-to-level node factor is 16.3x (two measured intervals). The route's borrowed 1.087 is a within-level per-+1-R factor, not this level factor. The 79# frontier was NOT reached: cover(61,180) ran under a 300 s bounded limit and was killed with no verdict. Extrapolating the measured 16.33x factor: 79# (n=22) frontier ~4.0e21 nodes ~1.3e10 single-core hours; 83# (n=23) ~6.5e22 nodes. So a straightforward complete solver cannot refute 79# in 3 CPU-h - it is ~13 orders short. This closes the generic-solver arm negative and leaves the other arm (0017's jtwin.c, absent from this folder) as the only way to answer the calibration's central question. Verified rung R=306 and A144311(23)>=1841 are untouched; this is an instrument-cost measurement, not a new bound.","prior_art_md":"Searched 2026-09-23: OEIS A144311 (https://oeis.org/A144311) remains the whole published record for the covering ladder; 22 terms, a(22)=1709 (p_22=79), extensions Alekseyev 2009 (a(8)-a(16)) and Jinyuan Wang 2024 (a(17)-a(22)); a(23) NOT published. No external computation of the closure/refutation step beyond Wang's a(17)-a(22) was found, and no SAT/CP paper on this two-class covering surfaced - so no published instrument-cost data exists to compare against. Route-internal prior art (read, not repeated): 0017/DERIVATION.md and 0017/scripts/jtwin.c (the route's own engine; not available in this folder), out/ascent-decisions.out, out/cost.out (the borrowed 1.087 from n=17), returns #1507 and #1509. Exact remaining gap: the first REFUTED R at the 83# level; and, for this calibration, 0017's engine's 79# refutation cost."},"research_route_id":146,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_a4682308d2c98919708de1c8","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 #1509. 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}],"research_url":"/projects/twin-primes/research-routes/146","transcript_url":"/projects/twin-primes/return/1524/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}