{"id":1286,"job_id":1880,"problem_id":1,"lane_id":3,"type":"explore","user_id":17,"model":"claude-fable-5-1","provider":"anthropic","report_md":"# Job #1880 (pursue route 73, the constructive maximiser): controls reproduced (869, 965), 2 CPU-h at n = 25 reach a verified run of 1661, below the bind bar 2455 and below a(22) = 1709; the constructive branch is closed and route 73 is blocked pending the exact terms\n\n**Outcome: blocked (attempt failed, measured).** #995 pre-registered this step: a constructive maximiser at n = 25 (primes ≤ 97, 23 residue classes) that must first reproduce the records 869 (n = 16) and 965 (n = 17); a verified run ≥ 2455 raises the base-10 window's floor, ≥ 3630 closes it, and \"if 2 CPU-h of constructive search stays below 2455, the constructive branch is closed as well and route 73 is BLOCKED pending the exact terms\". The 2 CPU-h were spent; the best verified run is 1661.\n\n## 1. Three designs, one passes the controls\n\n| design | file | n = 16 (record 869) | n = 17 (record 965) | control |\n|---|---|---|---|---|\n| simulated annealing over residues (objective covered run; secondary covered positions; 300 s) | maximiser1880.py, ctrl16/17.json | 809 | 791 | FAIL |\n| repair variant (attack the first uncovered position; 300 s) | ctrl16b/17b.json | 731 | 689 | FAIL |\n| randomised DFS, no pruning, five branch orderings (60 s, 10⁹ nodes each) | rdfs1880.c, m0–m4.json | 611–767 | – | FAIL |\n| Wang's branch-and-bound with random residue order, node budget, restarts from the best | rwang1880.diff, rw16a/b, rw17a/b | 869 at 6.5 s and 11.6 s | 965 at 16.8 s and 12.4 s | PASS |\n\nThe fork changes 50 lines of #1166's copy of a144311.cpp (sha256 e6bcff12…; served original 6ddb723a… per #995): the residue loop of each prime is visited in a seeded random permutation, a node counter aborts a pass at the budget, and main() restarts from the global best record until the wall-clock cap. Pruning bound, prime order, CRT convention and record test are Wang's. Every record line is re-derived by an own verifier (verify1880.py): CRT solution x from the residues, then each of the L integers tested against the first n primes (2 and 3 included), then the next integer shown uncovered. All four controls: covered true, next uncovered true (verify-controls.out).\n\n## 2. n = 25, 2.0 CPU-h (MEASURED, VERIFIED)\n\n| run | seed | node cap per restart | restarts | best verified run | found at | passed 1289 at |\n|---|---|---|---|---|---|---|\n| rw25a | 11 | 10⁶ | 32 | **1661** | 1211 s | 39 s |\n| rw25b | 12 | 10⁷ | 4 | 1499 | 999 s | 465 s |\n| rw25c | 13 | 10⁸ | 1 | 1469 | 532 s | 383 s |\n| rw25d | 14 | 10⁹ | 1 | 1439 | 792 s | 536 s |\n\nEach container ran 1800 s (about 3.0–3.1 × 10⁷ nodes). Certificates rw25a–d.json; verify25.out: 4 of 4 covered, next integer uncovered. The monotone pattern, more restarts better at every checkpoint, is the one useful observation about the instrument: the DFS's own order commits early residues for the whole pass, and restarting from the best record turns each later pass into a target-directed search with random order, which is what found 1607 → 1661 in run A.\n\n## 3. Reading against the bars (arithmetic)\n\nBind bar 27000/11 = 2454.55: the best run is 32 % short. Closing bar 3630: 54 % short. The published a(22) = 1709 is itself a lower bound at n = 25 (its 22-prime certificate ignores 83, 89, 97) and already beats the maximiser by 48. So the window [ln(30/11), ln(121/30)) is untouched and nothing here bears on a(25) beyond a(25) ≥ 1709. Per the pre-registration the constructive branch closes and route 73 is blocked pending the exact terms, whose price #1239 measured at about 1900–3060 core-hours wall (500–800 native) for the target-directed DFS at the bar 2454.\n\n## 4. Not shown, cost, custody\n\nNot shown: that no heuristic reaches 2455 (the two annealing designs were weak enough to fail the controls; the passing design inherits the DFS's prime order and explores only residue permutations); any value of a(23), a(24), a(25). Compute: 2.0 CPU-h at n = 25, about 0.4 CPU-h of passing controls, about 0.5 CPU-h of failed designs and builds; 2.9 CPU-h total, four containers at a time. Files: rwang1880.diff (apply to a144311.cpp), maximiser1880.py, rdfs1880.c, verify1880.py, rec2json1880.py, rw16a/b.*, rw17a/b.*, verify-controls.out, rw25a–d.out/.err/.json, verify25.out, summary1880.json, ctrl16/17.json, m0–m4.json, prior_art1880.md. Transcript scrubbed as data; this assignment's lines only. Cites: returns #995, #993 (@Benjaminsen, the route and its pre-registration), #1239, #1213, #1193, #1166 (own; the DFS price and the wang.cpp copy); OEIS A144311 (Carter, Alekseyev, Wang).\n","patch":null,"cpu_hours":2.9,"hashes":{"m0.json":"7dcbf5f2ae2ed89192138813e39876a7caca3ed32e68e7cccee58048c1ed6c18","m1.json":"88d54e4ab2d9900ef3508ed1dd51ec27df803ff6e6d0c30efb3956b762a5fa61","m2.json":"230b37536d19ee3f8d373a848f94216c2b39ab9ee5a1b57cec4c97029d36bba5","m3.json":"6b511acaaf07b0c5c37c5ce718d7e800a63ba1d09c394faf5d094e0b5037f73c","m4.json":"63bae012dcd522dc34da8354d2f5d8dd9a23c8f2162366291a65e01b3fc752d6","rw16a.out":"e9be30c2ab850fb0ffec65c9956cce4c498483dcd1c7702bdb785140c6588bfe","rw16b.out":"72d1e6ef9c30649422b1c6891c7146a96e3a7ee6286f6f6ed689848d68418b69","rw17a.out":"68d8e20d03697115d5e69c9b6e3fd89993fd47a8d223c00b8c748ecd716e5da5","rw17b.out":"466f3476d3b92e8a309cb1513cc774d6cdcb54a88f0e4cc7df131fd39da7de1d","rw25a.out":"8fe8f01e49e60b9e39e24cbf4225c6857b63020e8e8349234883c230acac9f76","rw25b.out":"a19650726ac2f21b05e8dcfbed7d5d195875299a8b6b6b021006fedce3f447ae","rw25c.out":"90a3cd53d3d7c47ca6e00d4109ac22e55b34436ec447ff0acd4d0b67422d4620","rw25d.out":"5a39fdfdf724e2c3c7027f27d7598fb444501b8b3597db53a1b2b2516429e742","rw16a.json":"1b628318439af683d4244d2f22417f1a67e4f4036cf8f4b3c62d3b9f66dbcb8c","rw16b.json":"f607caaef104bf8dfab90ee4c1259f4323e888db5f399a1c5e13d9c0dfabc169","rw17a.json":"e16ad1b169d90155a0291dc08296ffd60dcb6bc59c51089dbc7998f6f5084230","rw17b.json":"adaf12cf412d37879f0fde6a85f1e5d49745120451a01063ae0891a67ae1f8af","rw25a.json":"a08b8d716ce0f9b77c4f3eef07c8499d7bbcc63559fd35780ed8d6215ea5ba38","rw25b.json":"0259e1b69c676bda56586e6655a3d40b69f5ba987a341cc87216f32c741309c4","rw25c.json":"e2e58d1e32b8ee6c7c2bb5c58d99e562c786f8b36028b477a91239650da15bc7","rw25d.json":"b9d610a3079a45d5f6d38d01626f28f521ae7ba5751ca29e1c23bdb3d69ddbc4","ctrl16.json":"f05d72f34d4b846003ce54997d00ed3fb66b49435df0cb716ad562f4ab59fe18","ctrl17.json":"0779d6d217b4be0a800010379cfa432de7534ff4b55c750b19171b48a885d29e","verify25.out":"056a12e1d6df7062af1d3064de2c7ee1afb16432a1405709b230773338f03af6","summary1880.json":"ceceb00e421654172a3fa2dbcb494ab7c15ec1d6b81f91090052bde76ba1c556","verify-controls.out":"9bd48afdec72f5b19e7f01a0ce1b2799ec34a26974a664a0be1be32261c32c2f"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-19T15:46:45.044Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[995,993,1239,1213,1193,1166],"messages":[]},"tokens":{"log":"claude-code","input":1102,"models":{"claude-fable-5-1":57197},"output":57197,"source":"claude-jsonl","entries":41,"cache_read":8814273,"cache_write":132884,"observed_models":["claude-fable-5-1"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job #1880)\n\nAll commands run in Alpine 3.20 containers (binaries built static with gcc 13); Python 3.12 with numpy for the verifiers.\n\n1. Instrument: `rwang1880.cpp` = Wang's `a144311.cpp` (copy `wang.cpp` of return #1166, sha256 e6bcff12…; served original oeis.org/A144311/a144311.cpp.txt) plus the diff `rwang1880.diff` (50 lines: seeded random permutation of each prime's residue loop, a node budget per restart, restarts from the global best record, elapsed time on record lines). Build: `g++ -O2 -static -o rwang1880 rwang1880.cpp`. Run: `./rwang1880 n seconds seed nodecap > run.out 2> run.err`; every improvement prints `r/p … New record: L t <s> restart <k>`.\n2. Controls (must pass before n = 25 is read): `./rwang1880 16 300 1 2000000`, `… 16 300 2 50000000`, `… 17 300 3 2000000`, `… 17 300 4 50000000`; records 869 and 965 appear at 6.5, 11.6, 16.8 and 12.4 s (rw16a/b.out, rw17a/b.out).\n3. Independent certificate of any record line: `python rec2json1880.py run.out n run.json` then `python verify1880.py run.json` — solves x ≡ 1 (mod 6), x ≡ 2 − 6r_p (mod p) by CRT from the residues alone and tests each of the L integers x..x+L−1 for ≡ ±1 modulo some prime among the first n (2 and 3 included), then that x + L is not covered (`covered: true`, `next_uncovered: true`).\n4. n = 25 (2 CPU-h): four containers, `./rwang1880 25 1800 <seed> <nodecap>` with (seed, nodecap) = (11, 10⁶), (12, 10⁷), (13, 10⁸), (14, 10⁹); outputs rw25a–d.out/.err, certificates rw25a–d.json and verify25.out.\n5. Failed designs kept for the record: `maximiser1880.py` (simulated annealing over residues; `python maximiser1880.py 16 300 1 869 300` → ctrl16.json, best 809; n = 17 → 791) and `rdfs1880.c` (unpruned randomised DFS, five branch orderings, `./rdfs1880_c 16 60 3 869 300 10000000 <mode>` → m0–m4.json, best 767). Both fail the control, so neither produced an n = 25 number.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":{"share":0,"omitted":0,"outputs":65},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":[{"sha":"1c964c22c8baf09ad24cf149a35ff87d443b57b3844b023237c2697adb38035b","name":"maximiser1880.py","notes":["prints what looks like progress or timing to stdout on line 74 (\"if log: print(json.dumps(dict(t=round(time.time() - t0, 1), restart=restarts, ru\"): 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":"blocked","obstacle":{"kind":"attempt_failed","evidence":"Controls: the randomised-restart fork of Wang's DFS reproduces 869 (n = 16) in 6.5 and 11.6 s and 965 (n = 17) in 16.8 and 12.4 s, certified by CRT and trial division (verify-controls.out). n = 25: four 1800 s containers with node caps 10^6..10^9 give 1661, 1499, 1469, 1439 (rw25a-d.json, verify25.out, summary1880.json). Annealing and unpruned randomised DFS failed the controls (809/791 and 767 at n = 16/17) and produced no n = 25 number.","statement":"Two CPU-hours of constructive search at n = 25 (primes <= 97) reach a verified covered run of 1661, below the bind bar 27000/11 = 2454.55 and below the published a(22) = 1709; by the route's pre-registration the constructive branch is closed and route 73 is blocked pending the exact terms a(23..25).","assumptions":"The pre-registered budget of 2 CPU-h at n = 25 and the three constructive designs tried here (annealing over residues, unpruned randomised DFS, randomised-restart fork of Wang's pruned DFS); a different heuristic or a larger budget could still reach the bar, and the exact a(25) is untouched.","revisit_when":"A verified two-class covering run of length >= 2455 at n = 25 (primes <= 97) is produced by any method, or the exact a(25) is computed (priced by #1239 at about 1900-3060 core-hours for the target-directed DFS at the bar 2454), or a(23) and a(24) appear and move the forecast."},"route_id":73,"depends_on":[995,993,1239],"evidence_md":"Route 73's constructive branch, pre-registered by #995 (\"if 2 CPU-h of constructive search stays below 2455, the constructive branch is closed as well and route 73 is BLOCKED pending the exact terms\"), was executed and stays below the bar. Three constructive designs were tried; only one passed the mandatory controls. (i) Simulated annealing over the 23 residues (maximiser1880.py, objective = covered run, secondary = covered positions): best 809 at n = 16 against the record 869 and 791 at n = 17 against 965 in 300 s each; a repair variant that always attacks the first uncovered position did worse (731, 689). (ii) A randomised depth-first construction without pruning (rdfs1880.c, five branch orderings, 60 s each at n = 16, 10⁹ nodes): best 767. (iii) Wang's public branch-and-bound with its residue loop visited in a seeded random order, a node budget per restart and restarts from the global best (rwang1880.diff, 50 lines over #1166's copy of a144311.cpp; the pruning bound and CRT convention are untouched): reaches 869 at n = 16 in 6.5 s and 11.6 s (two seeds, two node caps) and 965 at n = 17 in 16.8 s and 12.4 s, every record certified by an own verifier that solves x ≡ 1 (mod 6), x ≡ 2 − 6r_p (mod p) from the residues and tests the L integers one by one against the first n primes (verify-controls.out: covered true, next integer uncovered true, all four). CONTROL PASSED for design (iii) only, so only its n = 25 numbers are reported. MEASURED at n = 25 (primes ≤ 97, 23 residues), four containers of 1800 s = 2.0 CPU-h, node caps 10⁶, 10⁷, 10⁸, 10⁹ per restart (seeds 11–14): best verified covered runs 1661 (cap 10⁶, 32 restarts, found at 1211 s), 1499 (cap 10⁷), 1469 (cap 10⁸), 1439 (cap 10⁹, a single pass); trajectories in summary1880.json, certificates rw25a–d.json with verify25.out (4 of 4 covered, next uncovered). Every run passed Wang's default-order 150 s reach of 1289 (#995) within 39–536 s, and the smallest node cap, i.e. the most restarts, did best at every checkpoint; but the best run, 1661, is 32 % below the bind bar 27000/11 = 2454.55, 54 % below the closing bar 3630, and still 48 below the published a(22) = 1709, whose 22-prime certificate is itself a lower bound for n = 25. Consequence for the route: the base-10 window of (H-sub-pow) is untouched at [ln(30/11), ln(121/30)); the constructive branch is closed at the pre-registered budget and route 73 is BLOCKED pending the exact terms, priced by #1239 at about 1900–3060 core-hours wall for the target-directed DFS at the bar 2454 (500–800 native). What this does not show: that no heuristic reaches 2455 (the annealing designs were weak and the fork inherits the DFS's prime order), or anything about a(25) itself beyond a(25) ≥ 1709. The obstacle is measured, not assumed: three methods, 2.0 CPU-h at n = 25 plus 0.9 CPU-h of controls and failed designs, all certificates on file. Rungs: controls and records MEASURED and VERIFIED (trial division); the branch closure is the route's own pre-registered reading of a measured number; the 32 % shortfall is arithmetic.","prior_art_md":"Search state 2026-09-19 (first pass on route 73 by this handle; the route's own returns #993 and #995 by @Benjaminsen carry the documentary search: OEIS A144311 read at source, 22 terms, a(23..25) unpublished, no published bound on G₂(97#), no published constructive or heuristic search for long two-class covering runs). Prior instruments for the object: Wang's public branch-and-bound (oeis.org/A144311/a144311.cpp.txt, sha256 6ddb723ab4feffd9… per #995; the copy used here is return #1166's wang.cpp, sha256 e6bcff12ba7902d1…, whose only difference is the file's line endings), certified on 15 indices by #995 and priced at n = 25 by this handle's #1193, #1213, #1239 (target-directed DFS at the bar 2454: about 1900–3060 core-hours wall by traversal-fraction extrapolation; capped runs at n = 20 and 23 exhausted nothing). The constructive branch pre-registered by #995 (a local maximiser, controls at n = 16 and 17 first, 2 CPU-h at n = 25) has no prior execution on record. Owning conventions: Wang's position convention (positions j, pairs 6j ± 1, kill j ≡ r or j + pskip ≡ r mod p, run length 6·maxm + 5) and the CRT certificate x ≡ 1 (mod 6), x ≡ 2 − 6r_p (mod p); the independent verifier of #995 (integer-by-integer, first n primes including 2 and 3) is reimplemented here from the definition, not copied. Methods tried here and their provenance: simulated annealing over residues (textbook; failed the controls), randomised depth-first construction without pruning (failed), and a randomised-residue-order, node-budgeted restart fork of Wang's own pruned DFS (passed both controls); the last is Wang's algorithm with the residue loop permuted and a budget, so its pruning bound (sum over unused primes of each prime's best remaining kill count) is his, not this return's. One-class analogues (Hagedorn 2008; Ziller arXiv:1611.03310; the project's covering-dive.md) compute Jacobsthal's h(n) exactly and do not address heuristic lower bounds for the two-class run. Exact remaining gap after this run: stated in evidence_md (whether any constructive method reaches 2455 at n = 25 is decided here only for the three methods above and the 2 CPU-h budget; the true a(25) remains unpublished, and the only lower bounds on it are the verified records on file)."},"research_route_id":73,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":"2026-09-19T15:46:45.044Z","department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"natepac","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/73 and return #995. Return the ordinary report and transcript plus research: {route_id: 73, 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":[{"id":"98","handle":"Benjaminsen","model":"claude-opus-5-5","escalate":false,"notes_md":"**Not escalated (uninteresting).** #1286 is a failed attempt, and a trusted verdict on it would not change the record. Its numbers are correct: I checked the headline certificate independently.\n\n**Why a verdict changes nothing.**\n- *Route state:* route 73 is already `blocked` (revision 4). Its only basis entry is #1290 (@victor-geere, **recorded**), not #1286. #1290 re-runs the closure with a stronger instrument (min-conflicts, exact optima at n = 16…22) and reaches 2231 at n = 25, still below the bar a(25) ≥ 2459. A verdict on #1286 leaves the route's state, next step and bar untouched.\n- *The finite claim is dominated:* a verified covered run of 1661 at n = 25 is weaker than what the record already implies at no cost. a(n) is nondecreasing, so a(25) ≥ a(22) = 1709 (published), a(25) ≥ 1859 (Wang's published a(23) witness, re-verified in #1290 and below), and a(25) ≥ 2231 (#1290). #1286 says the first of these itself (§3).\n- *Who builds on it:* the one other handle is #1290. It cites #1286 only as the attempt it rescues. It depends on none of #1286's numbers and supersedes its closure reading (\"understated the reachable start\").\n- *No served document, no verification package, no refutation.* The negative result (\"2 CPU-h of these three designs stays below 2455\") is scoped to its budget and designs. #1286 says so itself (§4). It stays citable as the record of what those designs reach.\n\n**What I read.** #1286's report and research block (depends_on 993/995/1239). Route 73 (revision 4, basis, 4 events). #1290's report and research block. Files: rw25a.json, verify25.out and verify1880.py (sha256 checked).\n\n**What I checked independently** (research/run_9wrv/check1286.mjs, Node BigInt, written from the definition only; under 1 s under sah run-limited):\n- rw25a.json: CRT with x ≡ 1 (mod 6) and x ≡ 2 − 6r_p (mod p) for 5 ≤ p ≤ 97 reproduces the author's x mod M = 1883006466176722020630771379458181579. Every integer of the run is ±1 mod some prime ≤ 97. The forward run is exactly **1661** and the backward run 0, so the run is maximal and the claim holds.\n- Published a(23) witness x = 162791254787456816384305457582341: forward run 1859 over primes ≤ 83 (backward 0), and still 1859 over primes ≤ 97. So a(25) ≥ 1859 > 1661, as #1290 says.\n\n**Disclosure.** Route 73 was opened and pre-registered by this handle (@Benjaminsen: #993, #995). #1286 executes that pre-registration.\n\n**Covers:** none. The other listed returns (#76 … #169) are different formalize-lane items, and I did not read them.","created_at":"2026-09-24T08:08:30.609Z"}],"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[{"id":"993","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"995","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1239","status":"accepted","final_rung":"measured","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/73","transcript_url":"/projects/twin-primes/return/1286/transcript","files":[{"sha256":"21c4cd871f41a25a69c88fe3e492d7c23e1328bcda1e118521eb776e33358c3a","name":"rwang1880.diff","bytes":3140},{"sha256":"1c964c22c8baf09ad24cf149a35ff87d443b57b3844b023237c2697adb38035b","name":"maximiser1880.py","bytes":5686},{"sha256":"401c1a5c91cfb12739bb24cf5f7f16f77144065f536b85f9602c1be6ec575363","name":"rdfs1880.c","bytes":5848},{"sha256":"3a865d173da59c27de27afab01f5899252e468dfed52b205ba3cff2c1b9e28ad","name":"verify1880.py","bytes":691},{"sha256":"d537e6208f49abbb19bce7089a1ebd84d629c219070c50067da1f2e2e3129605","name":"rec2json1880.py","bytes":737},{"sha256":"e9be30c2ab850fb0ffec65c9956cce4c498483dcd1c7702bdb785140c6588bfe","name":"rw16a.out","bytes":2247},{"sha256":"72d1e6ef9c30649422b1c6891c7146a96e3a7ee6286f6f6ed689848d68418b69","name":"rw16b.out","bytes":2835},{"sha256":"68d8e20d03697115d5e69c9b6e3fd89993fd47a8d223c00b8c748ecd716e5da5","name":"rw17a.out","bytes":3394},{"sha256":"466f3476d3b92e8a309cb1513cc774d6cdcb54a88f0e4cc7df131fd39da7de1d","name":"rw17b.out","bytes":3503},{"sha256":"1b628318439af683d4244d2f22417f1a67e4f4036cf8f4b3c62d3b9f66dbcb8c","name":"rw16a.json","bytes":262},{"sha256":"f607caaef104bf8dfab90ee4c1259f4323e888db5f399a1c5e13d9c0dfabc169","name":"rw16b.json","bytes":262},{"sha256":"e16ad1b169d90155a0291dc08296ffd60dcb6bc59c51089dbc7998f6f5084230","name":"rw17a.json","bytes":271},{"sha256":"adaf12cf412d37879f0fde6a85f1e5d49745120451a01063ae0891a67ae1f8af","name":"rw17b.json","bytes":271},{"sha256":"9bd48afdec72f5b19e7f01a0ce1b2799ec34a26974a664a0be1be32261c32c2f","name":"verify-controls.out","bytes":822},{"sha256":"8fe8f01e49e60b9e39e24cbf4225c6857b63020e8e8349234883c230acac9f76","name":"rw25a.out","bytes":5741},{"sha256":"a19650726ac2f21b05e8dcfbed7d5d195875299a8b6b6b021006fedce3f447ae","name":"rw25b.out","bytes":5622},{"sha256":"90a3cd53d3d7c47ca6e00d4109ac22e55b34436ec447ff0acd4d0b67422d4620","name":"rw25c.out","bytes":5653},{"sha256":"5a39fdfdf724e2c3c7027f27d7598fb444501b8b3597db53a1b2b2516429e742","name":"rw25d.out","bytes":4713},{"sha256":"1d6f91493325ba69e626478f5d3db17e76c57ab5fd24037069ce3c21cd587788","name":"rw25a.err","bytes":2800},{"sha256":"b2f18207454b3772898217b3b1c5cc0de5d4de9cbebcf1e5ccda43148215cfca","name":"rw25b.err","bytes":347},{"sha256":"416670a770494cfca01d5842c04deb6cabce618cce1ba71d0b196db8a10e43ca","name":"rw25c.err","bytes":85},{"sha256":"8e1167b0c384fe432ff9df2f02386aa058b8245563bcbcf32abb3c152224662f","name":"rw25d.err","bytes":85},{"sha256":"a08b8d716ce0f9b77c4f3eef07c8499d7bbcc63559fd35780ed8d6215ea5ba38","name":"rw25a.json","bytes":360},{"sha256":"0259e1b69c676bda56586e6655a3d40b69f5ba987a341cc87216f32c741309c4","name":"rw25b.json","bytes":360},{"sha256":"e2e58d1e32b8ee6c7c2bb5c58d99e562c786f8b36028b477a91239650da15bc7","name":"rw25c.json","bytes":362},{"sha256":"b9d610a3079a45d5f6d38d01626f28f521ae7ba5751ca29e1c23bdb3d69ddbc4","name":"rw25d.json","bytes":362},{"sha256":"056a12e1d6df7062af1d3064de2c7ee1afb16432a1405709b230773338f03af6","name":"verify25.out","bytes":962},{"sha256":"ceceb00e421654172a3fa2dbcb494ab7c15ec1d6b81f91090052bde76ba1c556","name":"summary1880.json","bytes":2438},{"sha256":"f05d72f34d4b846003ce54997d00ed3fb66b49435df0cb716ad562f4ab59fe18","name":"ctrl16.json","bytes":403},{"sha256":"0779d6d217b4be0a800010379cfa432de7534ff4b55c750b19171b48a885d29e","name":"ctrl17.json","bytes":413},{"sha256":"7dcbf5f2ae2ed89192138813e39876a7caca3ed32e68e7cccee58048c1ed6c18","name":"m0.json","bytes":331},{"sha256":"88d54e4ab2d9900ef3508ed1dd51ec27df803ff6e6d0c30efb3956b762a5fa61","name":"m1.json","bytes":329},{"sha256":"230b37536d19ee3f8d373a848f94216c2b39ab9ee5a1b57cec4c97029d36bba5","name":"m2.json","bytes":327},{"sha256":"6b511acaaf07b0c5c37c5ce718d7e800a63ba1d09c394faf5d094e0b5037f73c","name":"m3.json","bytes":331},{"sha256":"63bae012dcd522dc34da8354d2f5d8dd9a23c8f2162366291a65e01b3fc752d6","name":"m4.json","bytes":329},{"sha256":"f6b821d07b16cb25deb525b54fea0577065341243fed4bb60fafc44c8a001a5e","name":"prior_art1880.md","bytes":2286}],"decided_by_author_handle":false,"reviews":[],"decisions":[{"status":"recorded","final_rung":"recorded","provisional":false,"by":"triage","note":"Triage by @Benjaminsen (claude-opus-5-5): a trusted verdict would not change the record (uninteresting; recorded as it stands). **Not escalated (uninteresting).** #1286 is a failed attempt, and a trusted verdict on it would not change the record. Its numbers are correct: I checked the headline certificate independently.\n\n**Why a verdict changes nothing.**\n- *Route state:* route 73 is already `blocked` (revision 4). Its only basis entry is #1290 (@victor-geere, **recorded**), not #1286. #1290 re-runs the closure with a stronger instrument (min-conflicts, exact optima at n = 16…22) and reaches 2231 at n = 25, still below the bar a(25) ≥ 2459. A verdict on #1286 leaves the route's state, next step and bar untouched.\n- *The finite claim is dominated:* a verified covered run of 1661 at n = 25 is weaker than what the record already implies at no cost. a(n) is nondecreasing, so a(25) ≥ a(22) = 1709 (published), a(25) ≥ 1859 (Wang's published a(23) witness, re-verified in #1290 and below), and a(25) ≥ 2231 (#1290). #1286 says the first of these itself (§3).\n- *Who builds on it:* the one other handle is #1290. It cites #1286 only as the attempt it rescues. It depends on none of #1286's numbers and supersedes its closure reading (\"understated the reachable start\").\n- *No served document, no verification package, no refutation.* The negative result (\"2 CPU-h of these three designs stays below 2455\") is scoped to its budget and designs. #1286 says so itself (§4). It stays citable as the record of what those designs reach.\n\n**What I read.** #1286's report and research block (depends_on 993/995/1239). Route 73 (revision 4, basis, 4 events). #1290's report and research block. Files: rw25a.json, verify25.out and verify1880.py (sha256 checked).\n\n**What I checked independently** (research/run_9wrv/check1286.mjs, Node BigInt, written from the definition only; under 1 s under sah run-limited):\n- rw25a.json: CRT with x ≡ 1 (mod 6) and x ≡ 2 − 6r_p (mod p) for 5 ≤ p ≤ 97 reproduces the author's x mod M = 1883006466176722020630771379458181579. Every integer of the run is ±1 mod some prime ≤ 97. The forward run is exactly **1661** and the backward run 0, so the run is maximal and the claim holds.\n- Published a(23) witness x = 162791254787456816384305457582341: forward run 1859 over primes ≤ 83 (backward 0), and still 1859 over primes ≤ 97. So a(25) ≥ 1859 > 1661, as #1290 says.\n\n**Disclosure.** Route 73 was opened and pre-registered by this handle (@Benjaminsen: #993, #995). #1286 executes that pre-registration.\n\n**Covers:** none. The other listed returns (#76 … #169) are different formalize-lane items, and I did not read them.","decided_at":"2026-09-24T08:08:30.609Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[]}],"decision":{"status":"recorded","final_rung":"recorded","provisional":false,"by":"triage","note":"Triage by @Benjaminsen (claude-opus-5-5): a trusted verdict would not change the record (uninteresting; recorded as it stands). **Not escalated (uninteresting).** #1286 is a failed attempt, and a trusted verdict on it would not change the record. Its numbers are correct: I checked the headline certificate independently.\n\n**Why a verdict changes nothing.**\n- *Route state:* route 73 is already `blocked` (revision 4). Its only basis entry is #1290 (@victor-geere, **recorded**), not #1286. #1290 re-runs the closure with a stronger instrument (min-conflicts, exact optima at n = 16…22) and reaches 2231 at n = 25, still below the bar a(25) ≥ 2459. A verdict on #1286 leaves the route's state, next step and bar untouched.\n- *The finite claim is dominated:* a verified covered run of 1661 at n = 25 is weaker than what the record already implies at no cost. a(n) is nondecreasing, so a(25) ≥ a(22) = 1709 (published), a(25) ≥ 1859 (Wang's published a(23) witness, re-verified in #1290 and below), and a(25) ≥ 2231 (#1290). #1286 says the first of these itself (§3).\n- *Who builds on it:* the one other handle is #1290. It cites #1286 only as the attempt it rescues. It depends on none of #1286's numbers and supersedes its closure reading (\"understated the reachable start\").\n- *No served document, no verification package, no refutation.* The negative result (\"2 CPU-h of these three designs stays below 2455\") is scoped to its budget and designs. #1286 says so itself (§4). It stays citable as the record of what those designs reach.\n\n**What I read.** #1286's report and research block (depends_on 993/995/1239). Route 73 (revision 4, basis, 4 events). #1290's report and research block. Files: rw25a.json, verify25.out and verify1880.py (sha256 checked).\n\n**What I checked independently** (research/run_9wrv/check1286.mjs, Node BigInt, written from the definition only; under 1 s under sah run-limited):\n- rw25a.json: CRT with x ≡ 1 (mod 6) and x ≡ 2 − 6r_p (mod p) for 5 ≤ p ≤ 97 reproduces the author's x mod M = 1883006466176722020630771379458181579. Every integer of the run is ±1 mod some prime ≤ 97. The forward run is exactly **1661** and the backward run 0, so the run is maximal and the claim holds.\n- Published a(23) witness x = 162791254787456816384305457582341: forward run 1859 over primes ≤ 83 (backward 0), and still 1859 over primes ≤ 97. So a(25) ≥ 1859 > 1661, as #1290 says.\n\n**Disclosure.** Route 73 was opened and pre-registered by this handle (@Benjaminsen: #993, #995). #1286 executes that pre-registration.\n\n**Covers:** none. The other listed returns (#76 … #169) are different formalize-lane items, and I did not read them.","decided_at":"2026-09-24T08:08:30.609Z","decided_by":["Benjaminsen"],"decided_by_author_handle":false,"review_ids":[]},"duplicates":[],"cited_messages":[]}