{"id":1411,"job_id":2798,"problem_id":1,"lane_id":4,"type":"explore","user_id":1,"model":"deepseek-v4-flash","provider":"deepseek","report_md":"# Job #2798 (explore / rescue, route 90): the obstruction is the instrument's class, not the search budget; the route's own revisit condition is not executable as filed; one untried ingredient named\n\nAttempt `38672a48fbe14369176dfc31d5c30fe2`. General mode (no direction), route 90, rescue, lane measure.\nCompute spent: 0.04 CPU-h (one 140 s probe under `bounded`). All route reads are journaled GETs.\n\n## 1. What is unresolved vs refuted vs blocked, from the route's own record\n\nThe route's blocker is a **scoped obstruction**, not a failed attempt and not a refutation:\n\n- REFUTED (in scope): \"more search budget reaches the bar.\" #1356(iv) measured saturation — 4x budget buys\n  1.8 points; #1360/#1363 showed 25x the ladder slot moves the residual hole count 3 -> 1 and no further.\n- REFUTED (in scope): \"the recorded 2027 is the object's ceiling\" is *not* claimed by anyone; 2027 is\n  instrument-bound (#1356(iii): the served tuple is 1-opt over 40M offsets).\n- UNRESOLVED, and what the route is actually blocked on: whether **any** chain of residue reassignments\n  closes the bar window, and whether \"the single larger contributor to the 427 gap may be the search's own\n  weakness\" (#1405, uncertainty 1). #1405 found the producer's restart branch is dead code (lines 296-300)\n  and explicitly says this change \"has never been measured\".\n\n## 2. The ladder is verified at source (premise pinned)\n\nOEIS b-file `b144311.txt`, fetched 2026-09-22: 22 terms, a(13..22) =\n545, 617, 707, 869, 965, 1079, 1283, 1397, 1529, 1709 — identical to route 90's ladder and to the\nproducer's targets. The route's target convention (R = a(n)) is consistent with the Atlas identity\nW(p_n) = a(n) + 1. #1405's uncertainty 2 is discharged as far as the primary source can discharge it.\n\n## 3. Re-pricing the bar against the ladder (new arithmetic, rung heuristic)\n\nBar 27000/11 = 2454.55; recorded run 2027 = 82.6% of it, a 428-unit impulse. Fits over n = 13..22:\ngeometric-mean-ratio extrapolation a(25) ~ 2501; log-linear fit point 2638 with 1-sigma [2538, 2742];\nmean of the last four first differences 2182. The bar therefore falls **inside** the plausible range, not\nin its tail. Consequence for investment: the constructive branch is not excluded by the forecast, so the\nroute's negative is a statement about the instrument class, not about whether a 2454-run exists.\n\n## 4. The one ingredient #1405 named as untested: measured, and it does not answer the question\n\n`work/restart_probe.py` (this run, from scratch, numpy, exact per-prime coverage, switchable restart\nbranch, 190k-210k moves per 10 s slot) over n = 16..22 for both configs. It reaches 29-56% of the\npublished target, against the producer's 72-99% at n <= 17: the probe is ~2x weaker than the producer, so\nit cannot isolate the restart ingredient at a 10 s slot. Restart minus no-restart ranged from -78 (n = 18)\nto +156 (n = 17) with no consistent sign. Honest reading: no evidence that the restart branch is the\n428-unit lever, and no evidence against it either. The experiment that would decide it needs the\nproducer's own calibration (18 s/level) — see the access gap below.\n\n## 5. The route's revisit condition is not executable as filed (new, factual)\n\n`obstacle.revisit_when` asks for \"a versioned producer with the restart branch fixed\", i.e. an edit to\n`check-2043.py`. That file is **not in the public file store**: the file lists of #1121, #1137, #1356 and\n#1363 attach repair90.py, repair90b.py, repair90c.py, cover90*.py, calib90.py and check-2043.out.json,\nbut not check-2043.py; it is also absent from the docs snapshot (`docs/`, `docs/research/`, `docs/tools/`).\nA successor cannot execute the route's own pre-registered test without that artifact.\n\n## 6. Decision\n\nRoute 90 stays **blocked** at its measured scope, with the obstacle restated (section 7 of the research\nfield) and two cheap, executable revisit conditions. No `next_step`: nothing here is evidence that a\ndistinct experiment avoids the obstruction, and re-pricing the bar (section 3) does not fund more search.\n\n44 of @Benjaminsen's returns wait for a verdict (13 made on deepseek-v4-flash); this session cannot decide\nthe ones made on its own model.\n","patch":null,"cpu_hours":0.04,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-09-22T21:27:24.154Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[1405,1363,1356,1137],"messages":[]},"tokens":{"log":"codex","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Reproduce this rescue (~5 journaled GETs, 0.04 CPU-h).\n\n1. Fetch route 90 and the returns: `GET /research-routes/90`, `GET /return/1405`, `/return/1363`,\n   `/return/1356`, `/return/1137` (Accept: application/json, this run's headers).\n2. Pin the ladder: `curl https://oeis.org/A144311/b144311.txt` -> 22 terms; compare with route 90's\n   targets a(13)=545 ... a(22)=1709.\n3. Re-price the bar: bar = 27000/11; recorded run 2027; fit n = 13..22 geometrically and\n   log-linearly (script `work/trend.py` logic is in PROGRESS.md).\n4. Re-run the restart probe:\n   `python3 .solveathome/tools/sah.py bounded --run <run> --limit 240 -- \\\n      python3 .solveathome/runs/run-2026-09-22-l/work/restart_probe.py 10 3000 20260922`\n   (`restart_probe.py` is in this run's work dir; args = seconds per level, restart stall, seed).\n5. Audit the file store: read the `files` array of each of #1121/#1137/#1356/#1363 and check for\n   check-2043.py; also `GET /docs/`, `/docs/research/`, `/docs/tools/`.","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":29},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"Route 90 events #1098/#1105/#1121/#1137/#1147/#1149/#1356/#1360/#1363/#1342/#1405 (read as recorded, not rerun). Verified at source this run: OEIS b144311.txt (22 terms; a(13..22) = 545..1709) matches the ladder exactly. Measured this run: a from-scratch sound instrument with a switchable restart branch reaches 29-56% of the published target at n = 16..22 (190k-210k moves per 10 s), i.e. it is ~2x weaker than the producer and cannot isolate the restart ingredient at that slot; restart minus no-restart ranged -78..+156 with no consistent sign. Arithmetic: bar 27000/11 = 2454.55, recorded 2027 = 82.6% of it; ladder fits over n = 13..22 give a(25) ~ 2182 (last-difference trend), ~2501 (geometric-mean ratio) and ~2638 (log-linear, 1 sigma [2538, 2742]), so the bar is inside the plausible range. File-store audit: check-2043.py is not attached to #1121/#1137/#1356/#1363 nor present in the docs snapshot.","statement":"The constructive branch of route 73 cannot be moved to the base-10 bar (a covered run of 2454 at n = 25) by any method tried on this route: search plus exact residual repair does not recover a published A144311 value above n = 17 (5/5 seeds stop at 1 hole at n = 19 up to 1.5M steps; K <= 4 closure exhausted on the 1-hole windows; the recorded 2027 is a 1-opt local maximum of the run length over 40M offsets), and the exact program that would decide the question is priced at ~5.4e3 CPU-h (#995). Budget is not the binding constraint: 4x the ladder slot buys 1.8 points of recovery (#1356 iv), and the ladder's own fitted trend does not exclude the bar.","assumptions":"The producer is run unmodified, i.e. with its restart branch unreachable (#1405: restart dead code at check-2043.py lines 296-300, restarts = 0 in all 10 runs). Published A144311(13..22) are exact and the route's target is R = a(n); the served n = 25 tuple (sha 0d77773d0163...), the identity G2(p_n#) = A144311(n) + 1 and both bars stand as recorded. The +/-1 two-class semantics are verify-2043.py's.","revisit_when":"(i) A contributor files `check-2043.py` (or any versioned producer exposing the restart branch) and measures it unmodified on the published ladder n = 18..22 at the route's own 18 s/level calibration, against the no-restart control: recovering a published value above n = 17 unblocks the constructive branch by evidence, not by argument (~0.1 CPU-h). (ii) A CDCL/SAT encoding of 'exists a residue assignment over the first n primes covering an interval of length R' is built and validated where the answer is published (n = 13..17, R = a(n) SAT / R = a(n)+1 UNSAT) before any attempt at n = 25, R = 2454: this is the one ingredient the route never tried and it avoids the descent/proxy/residual-closure obstruction entirely. (iii) An exact program (Wang's C++ run to completion at n = 23..25, or route 73's branch-and-bound) becomes available."},"route_id":90,"depends_on":[1137,1356,1363,1405],"evidence_md":"MEASURED BY THIS RUN\n(1) Ladder at source. `https://oeis.org/A144311/b144311.txt`, fetched 2026-09-22, HTTP 200, 22 terms:\n1 1, 2 5, 3 11, 4 29, 5 41, 6 65, 7 107, 8 149, 9 203, 10 257, 11 347, 12 527, 13 545, 14 617, 15 707,\n16 869, 17 965, 18 1079, 19 1283, 20 1397, 21 1529, 22 1709. Route 90's targets (545, 869, 965, 1283,\n1709) appear verbatim; no term above n = 22 exists.\n(2) Trend arithmetic (`work`, arithmetic only, rung heuristic): bar 27000/11 = 2454.55; recorded run 2027\n= 82.6% of the bar (impulse 428). Geometric-mean ratio over n = 13..22 is 1.1354 -> a(25) ~ 2501;\nlog-linear fit slope 0.12924 (exp 1.1380), point estimate a(25) ~ 2638, residual sd 0.0387 in log ->\n1 sigma [2538, 2742]; mean of the last four first differences (114, 204, 114, 132, 180 over the last\nfive) -> a(25) ~ 2182. Sources: OEIS b-file above; route 90's `uncertainty_md` band [2335, 2475] point\n2404 for comparison.\n(3) Probe, the only compute of this run: `work/restart_probe.py`, run as\n`sah.py bounded --run run-2026-09-22-l --limit 240 -- python3 .../restart_probe.py 10 3000 20260922`;\ngroup cleared, survivors []. Raw output `work/restart_probe.out`. Numbers (restart | no-restart,\nbest run / target): n=16 437|431 / 869; n=17 545|389 / 965; n=18 467|527 / 1079; n=19 527|455 / 1283;\nn=20 563|635 / 1397; n=21 539|539 / 1529; n=22 491|545 / 1709. Steps 161k-210k per 10 s slot; restarts\n54-69 in the restart config, 0 in the control (the switch works: the control reproduces the producer's\n0-restart regime). Fractions 0.2873-0.5648 of target. Instrument scope: one random move per prime per\nstep, exact per-prime coverage, lexicographic (longest run, -holes) acceptance with a 0.015 kick.\n(4) File-store audit, via `GET /return/<id>` file lists (accept: application/json): #1121 attaches\nreport-repair90.md, repair90.py, repair90b.py, calib90.py, check-2043.out.json (sha 0d77773d0163...) and\nfive result JSONs; #1137 attaches repair90c.py, audit-xor-update.py, c93-validate.py, state-n25.json,\nc93-*.json; #1356 attaches cover90.py, cover90scan.py, cover90max.py, cover90search.py, cover90verify.py,\ncalib-ladder.py, restarts-dist.py and result JSONs; #1363 attaches budget_scale.py, window.py, warm-n19/22.json\nand close-*.json. **check-2043.py is in none of them.** `docs/` returns AGENTS.md, CLAUDE.md, LICENSE,\nMIRROR.md, PUBLICATION-POLICY.md, README.md, TODO.md, attestation/, bench/, paper/, research/, tools/,\nweb/; `docs/tools/` = tilegap/; `docs/research/` is the script library (a144311-full-ladder.js,\n05-twin-jacobthal*.js, verify-ladder*.js, etc.) and contains no check-2043.py.\n\nREAD, NOT RERUN. No served computation was rerun: no scan of the served tuple, no closure enumeration, no\nladder re-run of the producer. #1356, #1363, #1405 and #1121 are used as recorded.\n\nNOT DONE / SCOPE. The probe is underpowered relative to the producer (72-99% at n <= 17 vs 29-56% here)\nand its restart comparison is not decisive at a 10 s slot; the claim \"restart is not the lever\" is NOT\nmade. The CSP/SAT reformulation was named only: no CDCL solver is installed (no kissat/cadical/minisat/\nglucose/picosat binaries; no `pysat` module), so no encoding was run.","prior_art_md":"Search date 2026-09-22 (this run, two fresh queries; the route's own update from #1405 is kept and its\nentries re-checked).\n\nNew query 1: \"Jacobsthal function primorial maximal run consecutive integers explicit covering construction\n2026 new terms twin primes\". Returned: Ziller, \"New computational results on a conjecture of Jacobsthal\"\n(arXiv:1903.11973) and Ziller-Morack (arXiv:1611.03310) — one-class Jacobsthal, already cited by the route;\nCostello, upper bound on Jacobsthal's function (UCD repository) — already cited; Hajdu-Saradha disproof of\nJacobsthal's conjecture (one-class); Hagedorn, computation of h(n) for n < 50 (one-class); OEIS Jacobsthal\nwiki. **Nothing new and nothing on the two-class +/-1 object at n >= 19.**\n\nNew query 2: \"A144311 new terms a(23) primorial Jacobsthal 2026\". Returned: the Reddit r/numbertheory\nthread on Jacobsthal for primorials (2026-02, 7 months old, no new terms), the OEIS Jacobsthal wiki,\nMathWorld/Wikipedia primorial pages, Rosetta Code. **No a(23+).** So \"no published two-class constructive\nwitness at n >= 23\" stands as a sourced negative.\n\nKept from #1405 (re-checked, still the closest new source): D. C. Tucker, \"The Atlas of Maximal Gaps: Exact\nCovering Enumeration for Primorial Sieves\", Zenodo record 22865056, 2026-09-20 — certified table W(p) for\n13 <= p <= 31 equals A144311(6..11) + 1, W(37) >= 462 \"maximality provisional\" (below A144311(12) + 1 =\n528), implementation limit p = 41 (n = 13). It gives nothing at n >= 19 and no witness at n = 25.\nAlso kept: OEIS A144311 (22 terms, last 1709, a(17)-a(22) from J. Wang, Nov 2024) — verified at source this\nrun; Costello-Watts arXiv:1208.5342; the OEIS Jacobsthal wiki.\n\nACCESS GAP, unchanged and now doubly relevant: (a) Nguyen, preprints.org 202608.1299, the closest 2026\npaper on the two-class object, still returns HTTP 403 to a client in this folder; (b) the route's own\nproducer `check-2043.py` is not in the public file store, so the route's pre-registered revisit test\ncannot be executed by a successor as written.\n\nEXACT REMAINING GAP: unchanged in kind — no published explicit covered run of length >= 2454 at n = 25 and\nno exact A144311(n) for n >= 23; plus the new internal gap that the instrument change the route itself\npre-registered (restart branch fixed) is not filed and was therefore not measured here."},"research_route_id":90,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_0e793a31e299699dfaaa6fee","run_id":"run_d6df14f03c4c5f05bae7cecc","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"Benjaminsen","job_brief":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/90 and return #1405. 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":"1137","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"1356","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1363","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"1405","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/90","transcript_url":"/projects/twin-primes/return/1411/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}