{"id":1360,"job_id":2738,"problem_id":1,"lane_id":4,"type":"explore","user_id":34,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2738 — the pre-registered gate on return #1356's next step: **FAILED**\n\nRung: `measured`. The search results are measured at their stated budgets; the closure results\nare complete finite enumerations (exhaustion is a proof for the stated move count, and each\nfile says so in its own `proof_of_negative` field). No claim here is above its evidence.\n\n## 1. What the gate was, and why it is a real test\n\nReturn #1356's `next_step` was: *gate the direct run-length maximiser on recovering\nA144311(22) = 1709 at n = 22 with a 100 % target; only if it passes, spend budget at n = 25.*\n\nAt n = 22 the value is **published and exact** (Wang 2024, ladder a(17..22)), so a hole-free\nwindow of length 1709 exists there and only an optimal configuration reaches it. Success\nwould mean \"this instrument can reach a known exact value at all\"; failure means the binding\nlimit is the *search*, not the object, and the mechanism is not the source of the n = 25 bar.\nThe gate could have passed — that is what makes failing informative.\n\n## 2. Level control (a real one, and it fired)\n\nEvery n = 22 number below is produced with the prime set truncated to 22 primes, re-checked by\neach instrument's own printed level (`{\"level\": 22, \"primes\": 22}` on stderr). The control is\nnot cosmetic, and it is loud rather than graceful: handing a 22-residue tuple to the scan\nwithout `--level 22` aborts with `IndexError` and exit 1 instead of silently answering a\ndifferent question — verified again at 2026-09-20T18:48Z, exit 1.\n\nIt also caught a real artifact defect of mine, disclosed in §6.3: the direct maximiser echoes\nthe caller's residue list, so its level-22 output file carried 25 residues. The optimised\nstate is the first 22; the 1157-run is a level-22 value of that state, re-measured\ndeterministically by the scan and pointwise by the independent checker (`level22-240s-trunc22.json`,\n`scan-level22-trunc22-L2M.json`, `rc-mine-1157.json`).\n\n## 3. Measurements\n\n| # | measurement | budget | result |\n| --- | --- | --- | --- |\n| G1 | proxy descent (holes in the best 1709-window over 20,000 offsets) | 120 s | **5 holes**, window start 437; holes 844, 1072, 1264, 1654, 2086 |\n| G2 | the same, chained, then 540 s under the job object | 720 s, 12,338 iterations, 3,703 restarts | **still 5 holes** — the floor of this mechanism |\n| G3 | what that state actually is: longest covered run at level 22 over 2,000,000 offsets | 0.01 s | **431** (start 1655) = **25 %** of 1709 |\n| G4 | exact residual-hole closure on G1/G2's best window | 1,568 / 61,078 / 2,369,699 nodes | **no solution** for ≤ 2, ≤ 3, ≤ 4 moves on distinct primes — exhaustion, so a **proof of the negative** for K ≤ 4; `best_holes_seen` stayed 5, i.e. no single move even reduces the count |\n| G5 | direct run-length maximiser at n = 22 (the pre-registered instrument; state filed with #1356) | 240 s | **1157** / 1709 = **67.7 %**; scan and independent checker both give 1157 exactly, bounding holes 34 and 1192 |\n| (reference, #1356) | the same maximiser at n = 25 | 540 s, 1,973 restarts | no run > 2027; random descents top out at 1319 |\n\nThree further rows were added because they are on the served record and cost no compute; they\nare what turns \"my instrument is weak\" into \"this class of mechanism is weak here\".\n\n| # | measurement | source | result |\n| --- | --- | --- | --- |\n| G6 | the **producing** instrument's own n = 22 calibration row (the instrument that produced the served n = 25 state 2027) | `check-2043.out.json` (#1121), `levels.calibration.22` | target 1709, **`covered: false`, `holes_best: 3`**, 10,800 steps, 18 s each |\n| G7 | the producer's own n = 22 **best run**, independently reproduced here | same file, `best_run_residues` + `best_run_x` | **1301** = 76.1 % of 1709. This run's scan finds exactly 1301 starting at offset **418**; `runcheck/2` confirms all 1301 offsets **and** all 1301 absolute integers covered with both neighbours holes (`length_is_exact: true`); the CRT placement of the tuple equals the recorded `best_run_x` exactly |\n| G8 | **route 90's own mechanism** (fixed target + exact residual-hole repair) applied to the producer's 3-hole n = 22 plateau, window start 52 | 39 / 1,511 / 58,884 / 2,293,087 nodes | **no solution** for ≤ 1, ≤ 2, ≤ 3, ≤ 4 moves — exhaustion at each K, so proofs; `best_holes_seen` stayed 3, i.e. **no single move even reduces the count** |\n| G9 | the producer's ladder: does exact recovery happen at all? | same file, `levels.calibration` | **yes at n = 16 (869) and n = 17 (965)**, exactly and within 18 s; then 1, 3, 2, 2, 3 holes at n = 18, 19, 20, 21, 22. Exact recovery is demonstrated up to n = 17 and not at 18 or above |\n\nG8 is the row that matters most for route 90: it takes the *stronger* instrument, at a level\nwhere the answer is published, and applies the route's own pre-registered repair step to its\nown plateau — and the repair closes nothing.\n\nOne more consequence worth stating plainly: the producer's 3-hole state has a longest covered\nrun of **545** (this run's scan, `scan-prod22-L2M.json`), while its 1301-run lives in a\n*different* state of the same level. The proxy-misalignment finding of #1356 therefore\nreproduces inside the producing instrument's own output file, which keeps both fields. The\n3-hole count is not a rung toward a longer run; it is a fact about a window.\n\n## 4. Verdict, and why it is decisive rather than another negative\n\n**The gate failed.** Two independent instruments and the route's own exact-repair step all fail\nat a level where the exact answer is known and published:\n\n* my direct maximiser reaches 67.7 % of 1709 (G5), and its proxy variant's plateau has a\n  431-run (G3);\n* the instrument that produced the record state reaches 76.1 % (G7) and cannot cover the\n  1709-window at all in its own 18 s calibration (G6);\n* exact residual-hole repair closes neither my 5-hole plateau nor the producer's 3-hole\n  plateau within 4 moves — by exhaustion, not by timeout (G4, G8).\n\nSo the n = 25 reading (2027, unimproved) is a statement about **this class of instrument**,\nand the failure branch of the pre-registered step fires *as written*: no budget is spent at\nn = 25, and the constructive branch of route 90 needs a different producer. The candidate\nspace is now narrower than \"try harder\": G9 shows the class's exact recovery is demonstrated\nonly to n = 17, and route 73's own records put Wang's program in records mode at 1289 at\nn = 25 against the 2027 already on the record — so the remaining candidates are Wang's exact\nprogram run to *completion* (not records mode) and route 73's complete branch-and-bound, both\nof which are exact-computation programs rather than searches.\n\nTwo things are added to the record beyond \"no witness\":\n\n1. **The gate's own design was worth its cost.** Without it, \"our maximiser gets 2027 at\n   n = 25\" reads like evidence about the object. With it, the same number is calibrated\n   against a level where the truth is known, and it is not evidence about the object.\n2. **The failure has a boundary, not a shrug.** Exact recovery is achieved at n = 16 and\n   n = 17 in 18 s by the producing instrument; the same instrument fails from n = 18 up. That\n   is where a reviewer should look next, and it is a much sharper statement than \"the search\n   did not find it\".\n\n## 5. What this does NOT claim\n\nNo witness, at n = 22 or anywhere else: this job produces no run longer than 1301 at n = 22 and\nno run at all at n = 25. `a(25) >= 2027` is unchanged and no better lower bound is offered. The\npublished ladder, the identity G2 = A144311 + 1, both bars and the route's own floors (#1149,\n#1147) are untouched. K = 5 closure was **not** attempted at either plateau — at this\ninstrument's measured node rate (2.29M nodes in 46 s) the K = 5 tree is ~42x larger, i.e.\n≈30 min per state, which was not spent. So \"no closure for K <= 4\" is exact and \"no closure at\nall\" is not claimed. No claim is made that 2454 is unreachable; only that these instruments do\nnot reach it, with a measured scale attached.\n\n## 6. Defects, disclosed\n\n1. **`closer.py`'s monotone prune** (from #1356's work) was first written to forbid the hole\n   count exceeding the starting count; it refused every branch and returned `nodes: 1`. A\n   checker that cannot branch is not a negative, and the run looked like a fast proof. Caught\n   because the node count was absurdly small, not by inspection. Everything reported here uses\n   `--monotone 0` (complete enumeration); the monotone mode survives only as a labelled bound\n   and its own output says `proof_of_negative: false`.\n2. **Level handling in `cover90max.py` output** (this job). Lowering the level optimises the\n   first 22 residues but echoes the caller's 25-residue list into `start_residues` and\n   `best_residues`, so a level-22 result was stored in a 25-residue shape. The run value is\n   level-22-correct (re-verified deterministically), but the artifact was ambiguous and a\n   reviewer could have read it as an n = 25 result. Fixed by truncating to the current prime\n   count on output and stamping the level; the corrected state is served alongside.\n3. **A false negative I nearly filed** (this job). My first independent check of the producer's\n   1301-run reported *not reproduced*: I tested the recorded `best_run_x` as if it were an\n   offset. Reading the producer's own `verify_run` first showed that `best_run_x` is the CRT\n   placement while the run is the *offset* interval; re-checked at offset 418 under both\n   readings it is exactly 1301, and the CRT placement reproduces the recorded number to the\n   digit. Framework lesson: read the producer's verification code before declaring\n   non-reproduction — the difference was a convention, not a discrepancy, and a filed negative\n   would have been wrong.\n","patch":null,"cpu_hours":0.25,"hashes":{"closer.py":"1a9dd7c79e35173828584927d9826a0228f026657c356b5843a91d7ec67e1e7b","cover90.py":"9688dab40b616c72b3d1783037027b353855b501ce9c849b795670eb2870ff83","runcheck.py":"a11f7b99711c426c5ec3b179a6df94a65037ce688c5840c8ad1f97a25f9f2f36","cover90max.py":"1de45097f3e1905e1b336e0b218eff3c9c61857d43e6693a63cf05036167fcb2","gate22-a.json":"76f741aa0e5a8f2e679505e2006d1edf12e9470efac5d7f962a2c0a74c9ab8cc","gate22-b.json":"329a0927a3b9043c7dff5213e5f1ed60f74d26802f3d8b80e51826629383a789","gate22-c.json":"7c9f132c0198e09db2faaeddd844936053113c78ed1be22220e4fd113d56309c","cover90scan.py":"b8a454c76e06e05ce421950f342bfd8dcec2dc0f408a68a3a52236e119d57fc8","cover90search.py":"5038688c41bcf861a0dcd17d4ff74ea18748e712515f004622232b1629592aef","rc-mine-431.json":"12bf10f1d1d8c2d3de66d3bb1de4810025e7e9a8fb771339567d1e29ded147ad","level22-240s.json":"c6d44ff462a3e510deafbc4f1287daecc8c731ccacebd6b6b54ab61c188d0818","prod22-state.json":"d22135dbfd3269a496f0be385d7ef8904386d80f3ee0d4184d2abd29f3312bd4","rc-mine-1157.json":"df86fcbbad21305af2de50d516dc6c64fd0efe07b9ad69cc8ddc7cf3ad4f322e","rc-prod-1301.json":"288377c414aac1471d28f30f42239256655028111ca19259fdc0fdfa07c06d35","rc-served-2027.json":"24da391ad62290b1d217922fac77106df7c327ace41c0d59d3ecaadf882e332a","close-prod22-K1.json":"ec2fa3a9c48785ab84187e9ec32cf81e8a0a7da4fa1e11a83d815cc6baf1bd2c","close-prod22-K2.json":"297f26daef3299c9bd8eef9cbf3a0d5dc1286a27bfa4261767342ee38142d355","close-prod22-K3.json":"15a564525f8311f3695eb9882e36a1f89e6ab8cc038259431198374f108a0fda","close-prod22-K4.json":"6267ecbdecc07b6ecbb0ab501ebf7ed051e2f2a11bb36e82765264112aabfbad","prod22-runstate.json":"70a970e4a1f12f4dc7760723086b7a731a5853f4f9d0eda6f82dfb8b087e7135","scan-prod22-L2M.json":"9cf616f9eb45a699c622256cb66884ea8afa4a63b32088db89c9f26cfa319064","served-residues.json":"a535b6e6af4f4ed882771e4ed6a31f545dac251ad148dca3455ef077eb0ad986","close22-sound-K2.json":"fb9969a5b4e454b538a5f942c6068d7aec1b906e18ff1e0c76802c374fed19dd","close22-sound-K3.json":"69a3c176c4013ca6cbf90eff99de1ea39e03f5f6f92974f3bb84dce7063654ea","close22-sound-K4.json":"45466bc1ef36081a3e79c4ad36eec08b6cba757b8c17944b00e17fa6fbcbff65","scan-gate22-c-L2M.json":"6d34ebcb9ed63435ac5fc8f51517c6d75b4a5a9a07396eb9663046dbe3dbbcbf","scan-prod22-run-L2M.json":"bbeb8ef3d3eb57df94742112ebf66b22396d4f8d08789bd1e5550a142d1b758f","level22-240s-trunc22.json":"9884aa2aba047503250dc2c7399d7adcb9a8ab068e4f77b705ad2c34c3fbedbd","scan-level22-trunc22-L2M.json":"e623504246d468666b96689ad09b50eb3bba5a3ec6478245606361ce8707b847","12bf10f1d1d8c2d3de66d3bb1de4810025e7e9a8fb771339567d1e29ded147ad":"rc-mine-431.json","15a564525f8311f3695eb9882e36a1f89e6ab8cc038259431198374f108a0fda":"close-prod22-K3.json","1a9dd7c79e35173828584927d9826a0228f026657c356b5843a91d7ec67e1e7b":"closer.py","1de45097f3e1905e1b336e0b218eff3c9c61857d43e6693a63cf05036167fcb2":"cover90max.py","24da391ad62290b1d217922fac77106df7c327ace41c0d59d3ecaadf882e332a":"rc-served-2027.json","288377c414aac1471d28f30f42239256655028111ca19259fdc0fdfa07c06d35":"rc-prod-1301.json","297f26daef3299c9bd8eef9cbf3a0d5dc1286a27bfa4261767342ee38142d355":"close-prod22-K2.json","329a0927a3b9043c7dff5213e5f1ed60f74d26802f3d8b80e51826629383a789":"gate22-b.json","45466bc1ef36081a3e79c4ad36eec08b6cba757b8c17944b00e17fa6fbcbff65":"close22-sound-K4.json","5038688c41bcf861a0dcd17d4ff74ea18748e712515f004622232b1629592aef":"cover90search.py","6267ecbdecc07b6ecbb0ab501ebf7ed051e2f2a11bb36e82765264112aabfbad":"close-prod22-K4.json","69a3c176c4013ca6cbf90eff99de1ea39e03f5f6f92974f3bb84dce7063654ea":"close22-sound-K3.json","6d34ebcb9ed63435ac5fc8f51517c6d75b4a5a9a07396eb9663046dbe3dbbcbf":"scan-gate22-c-L2M.json","70a970e4a1f12f4dc7760723086b7a731a5853f4f9d0eda6f82dfb8b087e7135":"prod22-runstate.json","76f741aa0e5a8f2e679505e2006d1edf12e9470efac5d7f962a2c0a74c9ab8cc":"gate22-a.json","7c9f132c0198e09db2faaeddd844936053113c78ed1be22220e4fd113d56309c":"gate22-c.json","9688dab40b616c72b3d1783037027b353855b501ce9c849b795670eb2870ff83":"cover90.py","9884aa2aba047503250dc2c7399d7adcb9a8ab068e4f77b705ad2c34c3fbedbd":"level22-240s-trunc22.json","9cf616f9eb45a699c622256cb66884ea8afa4a63b32088db89c9f26cfa319064":"scan-prod22-L2M.json","a11f7b99711c426c5ec3b179a6df94a65037ce688c5840c8ad1f97a25f9f2f36":"runcheck.py","a535b6e6af4f4ed882771e4ed6a31f545dac251ad148dca3455ef077eb0ad986":"served-residues.json","b8a454c76e06e05ce421950f342bfd8dcec2dc0f408a68a3a52236e119d57fc8":"cover90scan.py","bbeb8ef3d3eb57df94742112ebf66b22396d4f8d08789bd1e5550a142d1b758f":"scan-prod22-run-L2M.json","c6d44ff462a3e510deafbc4f1287daecc8c731ccacebd6b6b54ab61c188d0818":"level22-240s.json","d22135dbfd3269a496f0be385d7ef8904386d80f3ee0d4184d2abd29f3312bd4":"prod22-state.json","df86fcbbad21305af2de50d516dc6c64fd0efe07b9ad69cc8ddc7cf3ad4f322e":"rc-mine-1157.json","e623504246d468666b96689ad09b50eb3bba5a3ec6478245606361ce8707b847":"scan-level22-trunc22-L2M.json","ec2fa3a9c48785ab84187e9ec32cf81e8a0a7da4fa1e11a83d815cc6baf1bd2c":"close-prod22-K1.json","fb9969a5b4e454b538a5f942c6068d7aec1b906e18ff1e0c76802c374fed19dd":"close22-sound-K2.json"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-20T19:06:24.140Z","repo_url":null,"commit":null,"cites":{"returns":[1356]},"tokens":{"log":"custom","input":144474,"models":{"deepseek-v4-flash":106976},"output":106976,"source":"custom-jsonl","entries":1,"cache_read":14747776,"cache_write":0,"observed_models":["deepseek-v4-flash"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe — job #2738: reproduce the gate verdict\n\nCPython 3 + numpy 2.4.4, single thread. Wall clock below ≈ 17 minutes for G1–G5 plus the\nclosure runs; G6–G9 read the served state and cost no compute beyond the scans (seconds).\n\nInput: `check-2043.out.json` — the route's declared n = 25 state, sha256\n`0d77773d01631d9eb70b76b18588c13b1d76b2bca5a0e4ff22b52c5887630600` (the bytes\n`GET <project base>/return/1121` carries; the route record also serves the producing script as\n`evidence/1098/check-2043.py`). G6–G9 read its `levels.calibration` block; nothing is recomputed\nfrom it.\n\n`SAH_DETERMINISTIC=1` removes wall clocks, so every *scan*, *closure* and *checker* output\nbelow reproduces byte for byte. The two search artifacts (`gate22-a/b/c`, `level22-240s`) are\ntime-boxed and seeded; they are quoted as protocols with their seeds, and what a reviewer can\nreproduce from them is the *state* they contain, not their own hashes.\n\n## Level control first (expected: 22 primes; the unscoped call aborts, exit 1)\n\n    python cover90scan.py --residues gate22-c.json --level 22 --L 2000000 --out scan-gate22-c-L2M.json\n    python cover90scan.py --residues gate22-c.json --L 2000000 --out /dev/null      # IndexError, exit 1\n\n## G1/G2 — the proxy floor at n = 22 (expected `best_window_holes_from_scratch` 5)\n\n    python cover90search.py --level 22 --X 20000 --R 1709 --seconds 120 --seed 4 --out gate22-a.json\n    python cover90search.py --level 22 --X 20000 --R 1709 --seconds 180 --seed 4 --start gate22-a.json --out gate22-b.json\n    python cover90search.py --level 22 --X 20000 --R 1709 --seconds 540 --seed 21 --start gate22-b.json --out gate22-c.json\n\n## G3 — what that state is (expected `longest_run` 431, start 1655)\n\n    python cover90scan.py --residues gate22-c.json --level 22 --L 2000000 --out scan-gate22-c-L2M.json\n\n## G4 — the exact closure of my plateau (expected: no solution at K = 2, 3, 4)\n\n    python closer.py --residues gate22-b.json --start 437 --R 1709 --K 2 --monotone 0 --level 22 --out close22-sound-K2.json\n    python closer.py --residues gate22-b.json --start 437 --R 1709 --K 3 --monotone 0 --level 22 --out close22-sound-K3.json\n    python closer.py --residues gate22-b.json --start 437 --R 1709 --K 4 --monotone 0 --level 22 --node-cap 5000000 --out close22-sound-K4.json\n\n`--monotone 0` enumerates every candidate set, so exhaustion is a proof for that K;\n`--monotone 1` is a bound only and says so in its own `proof_of_negative: false`.\n\n## G5 — the pre-registered instrument, and the level-22 artifact correction\n\n    python cover90max.py --level 22 --X 40000 --seconds 240 --seed 22 --out level22-240s.json --log level22-240s.log\n    python cover90scan.py --residues level22-240s-trunc22.json --level 22 --L 2000000 --out scan-level22-trunc22-L2M.json   # 1157 at 35\n    python runcheck.py  --residues level22-240s-trunc22.json --level 22 --start 35 --length 1157 --out rc-mine-1157.json\n\n`level22-240s.json` stores a 25-residue shape for a level-22 result (§6.2 of the report);\n`level22-240s-trunc22.json` is that state truncated to the 22 primes actually used, and is the\nfile any downstream consumer should read.\n\n## G7/G8 — the producing instrument's own n = 22 numbers, re-verified here\n\nThe two states are copied verbatim out of `check-2043.out.json` (nothing else is taken from\nit), into `prod22-runstate.json` (`levels.calibration.22.best_run_residues`,\n`best_run_x`) and `prod22-state.json` (`levels.calibration.22.residues`).\n\n    python cover90scan.py --residues prod22-runstate.json --level 22 --L 2000000 --out scan-prod22-run-L2M.json   # 1301 at 418, independently\n    python runcheck.py  --residues prod22-runstate.json --level 22 --start 418 --length 1301 --out rc-prod-1301.json\n    python cover90scan.py --residues prod22-state.json  --level 22 --L 2000000 --out scan-prod22-L2M.json        # 545: the 3-hole state\n    python closer.py --residues prod22-state.json --start 52 --R 1709 --K 1 --monotone 0 --level 22 --out close-prod22-K1.json\n    python closer.py --residues prod22-state.json --start 52 --R 1709 --K 2 --monotone 0 --level 22 --out close-prod22-K2.json\n    python closer.py --residues prod22-state.json --start 52 --R 1709 --K 3 --monotone 0 --level 22 --out close-prod22-K3.json\n    python closer.py --residues prod22-state.json --start 52 --R 1709 --K 4 --monotone 0 --level 22 --node-cap 5000000 --out close-prod22-K4.json\n\n`runcheck.py` is a pure-Python checker that shares no code with the scanners or the search; it\ntests the claim twice — offsets `(v + i) mod p in {1, p-1}`, and absolute integers\n`j mod p in {1, p-1}` at the CRT placement `j = x + i` — and reports `length_is_exact` only when\nboth neighbours are holes. It was written after reading the producer's `verify_run`, whose\nresidue convention it matches by construction.\n\n    python runcheck.py --residues gate22-c.json           --level 22 --start 1655 --length 431  --out rc-mine-431.json\n    python runcheck.py --residues served-residues.json     --level 25 --start 227  --length 2027 --out rc-served-2027.json\n\n## Expected outputs and their sha256\n\n| file | sha256 |\n| --- | --- |\n| `gate22-a.json` (seeded search, protocol) | `76f741aa0e5a8f2e679505e2006d1edf12e9470efac5d7f962a2c0a74c9ab8cc` |\n| `gate22-b.json` (seeded search, protocol) | `329a0927a3b9043c7dff5213e5f1ed60f74d26802f3d8b80e51826629383a789` |\n| `gate22-c.json` (seeded search, protocol) | `7c9f132c0198e09db2faaeddd844936053113c78ed1be22220e4fd113d56309c` |\n| `close22-sound-K2.json` | `fb9969a5b4e454b538a5f942c6068d7aec1b906e18ff1e0c76802c374fed19dd` |\n| `close22-sound-K3.json` | `69a3c176c4013ca6cbf90eff99de1ea39e03f5f6f92974f3bb84dce7063654ea` |\n| `close22-sound-K4.json` | `45466bc1ef36081a3e79c4ad36eec08b6cba757b8c17944b00e17fa6fbcbff65` |\n| `scan-gate22-c-L2M.json` | `6d34ebcb9ed63435ac5fc8f51517c6d75b4a5a9a07396eb9663046dbe3dbbcbf` |\n| `level22-240s.json` (seeded search, protocol) | `c6d44ff462a3e510deafbc4f1287daecc8c731ccacebd6b6b54ab61c188d0818` |\n| `level22-240s-trunc22.json` | `9884aa2aba047503250dc2c7399d7adcb9a8ab068e4f77b705ad2c34c3fbedbd` |\n| `scan-level22-trunc22-L2M.json` | `e623504246d468666b96689ad09b50eb3bba5a3ec6478245606361ce8707b847` |\n| `scan-prod22-run-L2M.json` | `bbeb8ef3d3eb57df94742112ebf66b22396d4f8d08789bd1e5550a142d1b758f` |\n| `scan-prod22-L2M.json` | `9cf616f9eb45a699c622256cb66884ea8afa4a63b32088db89c9f26cfa319064` |\n| `close-prod22-K1.json` | `ec2fa3a9c48785ab84187e9ec32cf81e8a0a7da4fa1e11a83d815cc6baf1bd2c` |\n| `close-prod22-K2.json` | `297f26daef3299c9bd8eef9cbf3a0d5dc1286a27bfa4261767342ee38142d355` |\n| `close-prod22-K3.json` | `15a564525f8311f3695eb9882e36a1f89e6ab8cc038259431198374f108a0fda` |\n| `close-prod22-K4.json` | `6267ecbdecc07b6ecbb0ab501ebf7ed051e2f2a11bb36e82765264112aabfbad` |\n| `rc-mine-431.json` | `12bf10f1d1d8c2d3de66d3bb1de4810025e7e9a8fb771339567d1e29ded147ad` |\n| `rc-mine-1157.json` | `df86fcbbad21305af2de50d516dc6c64fd0efe07b9ad69cc8ddc7cf3ad4f322e` |\n| `rc-served-2027.json` | `24da391ad62290b1d217922fac77106df7c327ace41c0d59d3ecaadf882e332a` |\n| `rc-prod-1301.json` | `288377c414aac1471d28f30f42239256655028111ca19259fdc0fdfa07c06d35` |\n| `prod22-state.json` | `d22135dbfd3269a496f0be385d7ef8904386d80f3ee0d4184d2abd29f3312bd4` |\n| `prod22-runstate.json` | `70a970e4a1f12f4dc7760723086b7a731a5853f4f9d0eda6f82dfb8b087e7135` |\n\nRun times: G1 120 s, G2 180 s + 540 s, G5 240 s + 0.01 s + 0.01 s, G4 0.03 / 1.19 / 49.94 s,\nG8 0.0 / 0.03 / 1.23 / 45.84 s, scans ≤ 0.02 s each, checkers ≤ 0.01 s each. Everything else is\nreading the input file.\n\n## Expected verdict\n\nG1–G5: the pre-registered gate **fails** (5 holes at the proxy floor, no closure for K ≤ 4,\n431-run in that state, 1157 = 67.7 % by the direct maximiser). G6/G9: the producing instrument\nis at 3 holes and 1301 = 76.1 % at n = 22, and demonstrably exact only up to n = 17. G8: its\nown plateau is not closable within 4 moves. No run of 2454, no new lower bound, and no budget\nspent at n = 25.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"max","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-20T19:17:07.666Z","file_notes":[{"sha":"9688dab40b616c72b3d1783037027b353855b501ce9c849b795670eb2870ff83","name":"cover90.py","notes":["prints what looks like progress or timing to stdout on line 285 (\"\"iterations\", \"kicks\", \"seconds_elapsed\")}, indent=1))\"), inside the statement that starts on line 283: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"5038688c41bcf861a0dcd17d4ff74ea18748e712515f004622232b1629592aef","name":"cover90search.py","notes":["prints what looks like progress or timing to stdout on line 209 (\"\"random_restarts\", \"seconds_elapsed\")}, indent=1))\"), inside the statement that starts on line 205: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]},{"sha":"1de45097f3e1905e1b336e0b218eff3c9c61857d43e6693a63cf05036167fcb2","name":"cover90max.py","notes":["prints what looks like progress or timing to stdout on line 194 (\"\"seconds_elapsed\")}, indent=1))\"), inside the statement that starts on line 190: stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":{"outcome":"progress","route_id":90,"next_step":{"method":"Run check-2043.py - the instrument that produced the served n = 25 state and whose ladder covers n = 16 and 17 exactly in 18 s - with a scaled budget (20-30x the ladder slot, inside the route's 2 CPU-h cap) at n = 19 (target 1283) and n = 22 (target 1709), and on each resulting plateau run the exact residual-hole closure (closer.py, complete enumeration) at K = 5 and 6. Record covered/not covered, holes_best, and seconds per level, so exact recovery gets a measured cost curve rather than a single data point.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"No exact coverage at n = 19 and n = 22 with >= 20x budget and no closure at K <= 6. Then the fixed-target search class is measured to be incapable of exact recovery beyond n ~ 17, the constructive branch needs an exact program (Wang run to completion, or route 73's branch-and-bound), and further search budget at n = 25 is excluded by evidence rather than by opinion.","success":"Exact coverage at n = 19 or n = 22. Then this class is strong enough to be trusted at n = 25, exact recovery has a measured cost curve, and the next spend is a budgeted n = 25 attempt at the 2454 bar with an instrument whose calibration is on the record.","question":"Given a real budget instead of an 18 s ladder slot, can the producing instrument recover a PUBLISHED exact value at a level >= 18, and if so what wall-clock does exact recovery cost per level?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[1356,1121],"evidence_md":"Gate on return #1356's pre-registered step, run at n = 22 where the exact answer is published\n(A144311(22) = 1709, Wang 2024). THE GATE FAILS, and this time it fails for three independent mechanisms at once.\n\n1. The pre-registered instrument (direct run-length maximiser, this run's own engine):\n   1157 / 1709 = 67.7 % at 240 s. Its proxy variant's plateau is 5 holes in a 1709-window over\n   720 s / 12,338 iterations / 3,703 restarts, and that state's longest covered run is 431\n   (25 % of the target) - the #1356 proxy-misalignment finding, reproduced.\n\n2. The exact repair step, on both plateaus, by complete enumeration (not timeout): no set of\n   <= 4 moves on distinct primes closes 5 holes (1,568 / 61,078 / 2,369,699 nodes) and no set\n   of <= 4 closes the producing instrument's 3 holes (39 / 1,511 / 58,884 / 2,293,087 nodes);\n   in both cases best_holes_seen never fell, i.e. no single move even reduces the count.\n   K = 5 is not claimed: the K = 5 tree is ~42x larger at the measured node rate (~30 min per\n   state) and was not spent.\n\n3. The instrument that PRODUCED the served n = 25 record state (check-2043, return #1121),\n   read from its own served output: at n = 22 it reaches covered: false, holes_best: 3 in its\n   18 s calibration ladder, and its best run at that level is 1301 = 76.1 % of 1709 - which\n   this run reproduced independently (scan: exactly 1301 at offset 418; an independent checker\n   confirms all 1301 offsets AND all 1301 absolute integers, neighbours holes, CRT placement\n   equal to the recorded placement to the digit).\n\nSo the n = 25 reading \"2027, unimproved\" is a statement about this class of instrument, not\nabout the object, and the failure branch of the pre-registered step fires as written: no n = 25\nbudget is spent. What is added beyond the negative is a boundary and a scale: the producing\ninstrument recovers a published value EXACTLY at n = 16 (869) and n = 17 (965) within 18 s and\nfails from n = 18 up (1, 3, 2, 2, 3 holes at 18..22), so exact recovery by this class is\ndemonstrated only to n = 17; and the 3-hole state that the proxy optimises toward has a 545-run\nwhile the 1301-run lives in a different state of the same level, so the route's hole floors are\nwindow facts, not rungs. The remaining candidates for the constructive branch are exact\nprograms (Wang run to completion, route 73's branch-and-bound), not more search.","prior_art_md":"Online search, 2026-09-20, by this run. Query this job: \"Wang exact computation A144311 Jacobsthal\nfunction primorial two classes records mode program 2024\". Results: Ziller, \"Algorithmic concepts\nfor the computation of Jacobsthal's function for primorial numbers\" (arXiv:1611.03310) - the\nalgorithmic survey the route already cites; Hagedorn, \"Computation of Jacobsthal's function h(n)\nfor n < 50\" (the exhaustive-computation line); the OEIS Jacobsthal wiki page (definition and\nknown lower bounds); and the project's own literature audit page\n(seed/research/history/staging/audit-a144311-vocabulary.md), which fixes the vocabulary\nj2/h2 = A144311 shifted by one. Combined with the previous job's query (Ziller\narXiv:2007.01808, Costello's upper-bound line, MathOverflow thread, and the project's own\nkk-lower-bound.md paper), the record is unchanged in one decisive respect: NO source - published\nor in this project - contains an explicit covered run at n >= 23. The ladder a(1..7) Carter\n2008, a(8..16) Alekseyev 2009, a(17..22) Wang 2024 is the exact value set, and the project's\npaper gives asymptotic lower bounds G2 >> y (ln y)^3 (ln ln ln y)^2 / (ln ln y)^4 with no witness\nat any level. EXACT REMAINING GAP: a verified explicit run of length >= 2454 at n = 25 (the\nbase-10 bar), or a measured statement of what instrument class can produce exact values at\nn >= 18 at all. This job supplies the second, negatively, for the search classes on hand;\nneither this run nor any cited source supplies the first."},"research_route_id":90,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_bd08e49ed9621cfd852f9b04","run_id":"run_7c5c6bb20f3bc591c6d9cc6a","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"maxime-fleury","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/90 and return #1356. Return the ordinary report and transcript plus research: {route_id: 90, 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":"1121","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1356","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/90","transcript_url":"/projects/twin-primes/return/1360/transcript","files":[{"sha256":"9688dab40b616c72b3d1783037027b353855b501ce9c849b795670eb2870ff83","name":"cover90.py","bytes":12311},{"sha256":"5038688c41bcf861a0dcd17d4ff74ea18748e712515f004622232b1629592aef","name":"cover90search.py","bytes":9130},{"sha256":"b8a454c76e06e05ce421950f342bfd8dcec2dc0f408a68a3a52236e119d57fc8","name":"cover90scan.py","bytes":3345},{"sha256":"1de45097f3e1905e1b336e0b218eff3c9c61857d43e6693a63cf05036167fcb2","name":"cover90max.py","bytes":8342},{"sha256":"1a9dd7c79e35173828584927d9826a0228f026657c356b5843a91d7ec67e1e7b","name":"closer.py","bytes":5388},{"sha256":"a11f7b99711c426c5ec3b179a6df94a65037ce688c5840c8ad1f97a25f9f2f36","name":"runcheck.py","bytes":4880},{"sha256":"76f741aa0e5a8f2e679505e2006d1edf12e9470efac5d7f962a2c0a74c9ab8cc","name":"gate22-a.json","bytes":914},{"sha256":"329a0927a3b9043c7dff5213e5f1ed60f74d26802f3d8b80e51826629383a789","name":"gate22-b.json","bytes":880},{"sha256":"7c9f132c0198e09db2faaeddd844936053113c78ed1be22220e4fd113d56309c","name":"gate22-c.json","bytes":882},{"sha256":"fb9969a5b4e454b538a5f942c6068d7aec1b906e18ff1e0c76802c374fed19dd","name":"close22-sound-K2.json","bytes":294},{"sha256":"69a3c176c4013ca6cbf90eff99de1ea39e03f5f6f92974f3bb84dce7063654ea","name":"close22-sound-K3.json","bytes":295},{"sha256":"45466bc1ef36081a3e79c4ad36eec08b6cba757b8c17944b00e17fa6fbcbff65","name":"close22-sound-K4.json","bytes":298},{"sha256":"6d34ebcb9ed63435ac5fc8f51517c6d75b4a5a9a07396eb9663046dbe3dbbcbf","name":"scan-gate22-c-L2M.json","bytes":473},{"sha256":"c6d44ff462a3e510deafbc4f1287daecc8c731ccacebd6b6b54ab61c188d0818","name":"level22-240s.json","bytes":1112},{"sha256":"9884aa2aba047503250dc2c7399d7adcb9a8ab068e4f77b705ad2c34c3fbedbd","name":"level22-240s-trunc22.json","bytes":277},{"sha256":"e623504246d468666b96689ad09b50eb3bba5a3ec6478245606361ce8707b847","name":"scan-level22-trunc22-L2M.json","bytes":482},{"sha256":"9cf616f9eb45a699c622256cb66884ea8afa4a63b32088db89c9f26cfa319064","name":"scan-prod22-L2M.json","bytes":468},{"sha256":"bbeb8ef3d3eb57df94742112ebf66b22396d4f8d08789bd1e5550a142d1b758f","name":"scan-prod22-run-L2M.json","bytes":475},{"sha256":"d22135dbfd3269a496f0be385d7ef8904386d80f3ee0d4184d2abd29f3312bd4","name":"prod22-state.json","bytes":275},{"sha256":"70a970e4a1f12f4dc7760723086b7a731a5853f4f9d0eda6f82dfb8b087e7135","name":"prod22-runstate.json","bytes":287},{"sha256":"ec2fa3a9c48785ab84187e9ec32cf81e8a0a7da4fa1e11a83d815cc6baf1bd2c","name":"close-prod22-K1.json","bytes":290},{"sha256":"297f26daef3299c9bd8eef9cbf3a0d5dc1286a27bfa4261767342ee38142d355","name":"close-prod22-K2.json","bytes":293},{"sha256":"15a564525f8311f3695eb9882e36a1f89e6ab8cc038259431198374f108a0fda","name":"close-prod22-K3.json","bytes":294},{"sha256":"6267ecbdecc07b6ecbb0ab501ebf7ed051e2f2a11bb36e82765264112aabfbad","name":"close-prod22-K4.json","bytes":297},{"sha256":"12bf10f1d1d8c2d3de66d3bb1de4810025e7e9a8fb771339567d1e29ded147ad","name":"rc-mine-431.json","bytes":596},{"sha256":"df86fcbbad21305af2de50d516dc6c64fd0efe07b9ad69cc8ddc7cf3ad4f322e","name":"rc-mine-1157.json","bytes":655},{"sha256":"24da391ad62290b1d217922fac77106df7c327ace41c0d59d3ecaadf882e332a","name":"rc-served-2027.json","bytes":616},{"sha256":"288377c414aac1471d28f30f42239256655028111ca19259fdc0fdfa07c06d35","name":"rc-prod-1301.json","bytes":669},{"sha256":"a535b6e6af4f4ed882771e4ed6a31f545dac251ad148dca3455ef077eb0ad986","name":"served-residues.json","bytes":107}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}