{"id":949,"job_id":1798,"problem_id":1,"lane_id":3,"type":"explore","user_id":44,"model":"gpt-6-astra","provider":"openai","report_md":"# Joint natal/scour SAT: the frozen cheap search remains inconclusive\n\nRoute64 / return945's concrete experiment is complete. Neither allowed search found a 30-slot covering witness or reported UNSAT. This is a failed attempt within the frozen budget, not a refutation of the encoding, a proof of nonexistence, or a global upper bound. Return938's directly checked K*(37)>=29 remains unchanged. Pause further investment in this implementation until a distinct, validated algorithmic improvement is available.\n\n## Predicate, implementation and controls\n\nThe unchanged return945 generator chooses natal phases for primes2..37 and scour phases for primes41,43,47,53,59,61,67,71,73 jointly. Its biconditional survivor indicators and exact prefix counter require coverage of the first30 actual natal survivors, including all admissible classes11,17,29 mod30. See the supplied joint_cnf.py and return945's derivation. H1050 produces6146 variables/41427 clauses; H2620 produces14237/77696. No thresholds or ranges were retuned.\n\nRuntime: Python3.12.14, python-sat1.9.dev15, CaDiCaL195, seed0, one thread. A single solver object per search preserves learned state across solve_limited calls with conflict budget1000. Reaching the budget means UNKNOWN, not UNSAT. No proof logging was enabled. Versioned Windows wheel hashes are in dependency-hashes.json. Official API documentation: https://pysathq.github.io/docs/html/api/solvers.html ; distribution: https://pypi.org/project/python-sat/1.9.dev15/ .\n\nBefore research, the solver extracted the existing29-slot assignment exactly and rejected a forced omission of an actual survivor. These controls took 0.28125 CPU seconds and 0.391 wall seconds; exit0 and no remaining processes. The earlier exhaustive toy arithmetic and five mutation controls are in return945, not rerun here. The separate direct-gcd positive checker is supplied, but was not invoked on a new positive because no such certificate exists. No independent review of the encoding is claimed.\n\n## Observations, including the failed execution\n\n|Run|Outcome|Native CPU seconds|Wall seconds|Exit|\n|---|---|---:|---:|---:|\n|H1050 initial|process failure; last progress UNKNOWN|44.625|44.875|1|\n|H1050 retry, remaining budget|UNKNOWN|250.25|255.36|0|\n|H2620|UNKNOWN|595.375|606.218|0|\n\nThe initial failure's cause is unestablished: stderr was not captured then. Its progress and execution records are retained. A possible Windows replacement/read race motivated a retry around atomic progress-file replacement; this is a robustness change, not a confirmed diagnosis. Stderr capture was added. The retried H1050 process was restricted to255 CPU seconds so that both H1050 processes together used 294.875 CPU seconds, below the original300. H2620 retained its original600-CPU-second cap. Controls plus all research processes used 890.53125 CPU seconds; framework self-tests separately used0.203125. Successful processes left empty stderr files. No raw SAT model or certificate was produced.\n\nH1050 retry: 3191 conflict-budget calls, 3198344 conflicts, 9826529 decisions, 1552015791 propagations. H2620: 5123 calls, 5129475 conflicts, 25997226 decisions, 4987906674 propagations. Solver progress CPU time starts after formula construction; native process-tree CPU above is the resource accounting quantity.\n\nAn exclusive device allocation and Windows job object enforced process-tree lifetime,1GB memory,50% CPU rate, CPU-time caps and wall caps. The pinned helper's wall-argument validation ceiling alone was cloned locally from60 to1200 seconds for this job; the OS controls were unchanged. Normal completion, timeout and surviving-child termination were tested before use, all leaving zero active processes. Explicit research wall caps were330 initially,285 for the remaining-budget retry, and630 for H2620. Disk bounds were cooperative: inspected fixed-size outputs without proof logging, less than1MB scientific output and less than100MB installed dependencies. No wider framework policy change is implied.\n\n## Stronger prior-art check and the conditional span bound\n\nDuring this experiment I inspected Ziller–Morack's full ancillary details, beyond return945's abstract/table reading: https://arxiv.org/src/1706.03668v1/anc/full_details.pdf , section2.4 equations2.3–2.5 (printed pages24–26), and sections3–3.3 (printed pages27–30). The paired integer program already chooses two residue classes per prime, and the portioned method fixes small-prime choices before solving an ILP. Generic paired CRT/ILP and that hybrid strategy are therefore established prior art. The project's particular fixed-difference2, natal-compressed first-L-survivor predicate remains the proposed adaptation; no general method novelty or measured speedup is established.\n\nThe same source Table1 reports h_2(21)=2622 at p_21=73, omega_2(21)=436 and two maximal sequences. Correct the notation in return945's structured prior_art_md: h2(73)=2622 was shorthand with the wrong function argument; the prime-index convention is h_2(21), with p_21=73. The human report's wording 'at prime73' was compatible with that convention. The source describes agreement between algorithms and exhaustive enumeration; the ancillary remainders_2.txt supplies maximizing patterns. I inspected that file's header and n21 row. These are useful source evidence but neither my own recomputation nor a compact checked negative proof. psi_2_min.txt was located, not deeply checked.\n\nThe conditional argument is unchanged. If L consecutive natal slots spanning D are scour-covered, each of the D+1 integer positions is killed by a natal or scour prime. CRT combines U=a_p modulo natal p and U=-b_q modulo scour q. The actual pair (U+j,U+j+2) is therefore not simultaneously coprime to73# for every j=0..D. A valid uniform paired-Jacobsthal bound2622 implies D+1<=2621, hence D<=2620. That bound concerns all even pair differences and physical positions; our predicate uses difference2 and counts natal slots. A global upper-bound claim would require both validation of the external uniform bound and proof-checked UNSAT for our formula. Neither is supplied here. Positive certificates would be independent of this external premise.\n\nEarlier background: https://arxiv.org/html/1611.03310v1 , Proposition1.3 and section2.2; https://arxiv.org/html/1706.03668v1 , Definitions2–4 and Table1. Search and project-route comparison from return945 are reused, with the ancillary inspection above added on2026-09-17. No claim of complete literature coverage.\n\n## Reproduction and investment decision\n\nThe enumerated uploaded Python/JSON files reproduce the finite encoding and search policy. Install the hash-pinned python-sat and six distributions for the stated Python/platform, then run solve_joint.py with --H1050 --seconds295, or --H2620 --seconds595 (separate the option/value with spaces). Set --site to a private dependency directory when needed. Reproduce the historical retry with --H1050 --seconds250. Wrap any research execution in equivalent explicit process-tree CPU/wall/RAM controls; the solver's cooperative process_time loop alone is not a resource sandbox. Wall timing, conflict counts and time-cutoff endpoints need not be bitwise identical. Compare the predicate, versions, preserved progress records and honest UNKNOWN outcome, not a claimed mathematical negative.\n\nThis report warrants no larger search or changed target. Revisit with a named change to branching, formulation or decomposition, independently validated against the exact survivor predicate and budgeted before execution. The two timeouts do not establish a lower bound on optimal solver cost. They simply failed the frozen cheap-search success criterion. Public exports remove credentials, private identifiers/paths, unrelated conversation and internal instructions/reasoning; scientific code and observations remain.\n","patch":null,"cpu_hours":0.24736979166666667,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-09-17T20:32:13.284Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[938,945],"messages":[]},"tokens":{"log":"codex","input":174488,"models":{"gpt-6-astra":36856},"output":36856,"source":"codex-jsonl","entries":50,"cache_read":6146944,"cache_write":0,"observed_models":["gpt-6-astra"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Inspect supplied scripts and logs; pinned python-sat1.9.dev15/CaDiCaL195, seed0, conflict chunks1000. Replay only within explicitly approved native controls. This measured inconclusive report has no new theorem or positive certificate.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"xhigh","also_fix":null,"transcript_omitted":{"share":0.22448979591836735,"omitted":11,"outputs":49},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-09-17T20:32:25.292Z","file_notes":null,"research":{"outcome":"inconclusive","obstacle":{"kind":"attempt_failed","evidence":"Both final statuses UNKNOWN; native research CPU including controls 890.53125; exit0 on completed searches; initial exit1 retained.","statement":"The pinned single-thread CaDiCaL195 joint survivor-count formulation did not find a30-slot positive or a checked negative within the frozen900-CPU-second experiment.","assumptions":"Exactly the H1050/H2620,L30 predicates, seed0 and stated solver/version/budgets. This is implementation-specific, not mathematical impossibility.","revisit_when":"A concrete different branching/formulation/decomposition strategy is validated against exact survivor controls and receives a new bounded investment basis."},"route_id":64,"depends_on":[945],"evidence_md":"Frozen L30 searches at H1050 and H2620 both ended UNKNOWN, using 890.53125 native CPU seconds including controls and failed execution. No witness, UNSAT proof, runtime gain or global upper bound. Known29 remains. Full logs and honest failed-process record supplied.","prior_art_md":"During this experiment I inspected Ziller–Morack's full ancillary details, beyond return945's abstract/table reading: https://arxiv.org/src/1706.03668v1/anc/full_details.pdf , section2.4 equations2.3–2.5 (printed pages24–26), and sections3–3.3 (printed pages27–30). The paired integer program already chooses two residue classes per prime, and the portioned method fixes small-prime choices before solving an ILP. Generic paired CRT/ILP and that hybrid strategy are therefore established prior art. The project's particular fixed-difference2, natal-compressed first-L-survivor predicate remains the proposed adaptation; no general method novelty or measured speedup is established.\n\nThe same source Table1 reports h_2(21)=2622 at p_21=73, omega_2(21)=436 and two maximal sequences. Correct the notation in return945's structured prior_art_md: h2(73)=2622 was shorthand with the wrong function argument; the prime-index convention is h_2(21), with p_21=73. The human report's wording 'at prime73' was compatible with that convention. The source describes agreement between algorithms and exhaustive enumeration; the ancillary remainders_2.txt supplies maximizing patterns. I inspected that file's header and n21 row. These are useful source evidence but neither my own recomputation nor a compact checked negative proof. psi_2_min.txt was located, not deeply checked.\n\nThe conditional argument is unchanged. If L consecutive natal slots spanning D are scour-covered, each of the D+1 integer positions is killed by a natal or scour prime. CRT combines U=a_p modulo natal p and U=-b_q modulo scour q. The actual pair (U+j,U+j+2) is therefore not simultaneously coprime to73# for every j=0..D. A valid uniform paired-Jacobsthal bound2622 implies D+1<=2621, hence D<=2620. That bound concerns all even pair differences and physical positions; our predicate uses difference2 and counts natal slots. A global upper-bound claim would require both validation of the external uniform bound and proof-checked UNSAT for our formula. Neither is supplied here. Positive certificates would be independent of this external premise.\n\nEarlier background: https://arxiv.org/html/1611.03310v1 , Proposition1.3 and section2.2; https://arxiv.org/html/1706.03668v1 , Definitions2–4 and Table1. Search and project-route comparison from return945 are reused, with the ancillary inspection above added on2026-09-17. No claim of complete literature coverage."},"research_route_id":64,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_ed559993abb51d285e91844b","run_id":"run_309e91e1e242cedc89d1a1ac","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"admiralorbiter","job_brief":"Search online for existing attempts, results, tables and datasets before testing feasibility. Reuse the recorded search and inspect the closest sources and weakest assumption. Use published numbers with citations; do not reproduce them in triage. Seek the smallest experiment on the uncovered step. Recommend promising only with specific evidence and a bounded next step; do not claim the route is proved. Map the assumptions of any borrowed method onto this problem.\n\nRead GET <project base>/research-routes/64 and return #945. Return the ordinary report and transcript plus research: {route_id: 64, 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":"945","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/64","transcript_url":"/projects/twin-primes/return/949/transcript","files":[{"sha256":"021d7b97c29949fc5145fca79471a033e8229f33d88e999b4e95a29c952d348a","name":"joint_cnf.py","bytes":5757},{"sha256":"9c7dd86e83989c5aa81da8d966c85c165a16dd4d7783034d373a312a20f4f283","name":"seed29.json","bytes":756},{"sha256":"dbe551c60f166ef5b72c7ce796ce5dd605ca1e68cbd8ed8a58c90741712b18ed","name":"solve_joint.py","bytes":3322},{"sha256":"208ba71062bea63b8fb92e262ff2d3bf7a130157da2bcfbb91ab38d1bba776d1","name":"check_positive.py","bytes":1031},{"sha256":"ba1986305e320bdb4c36fe1b3b039fd464df2c82c02c5dce0c1f7d97902caa46","name":"solver-controls.json","bytes":126},{"sha256":"c61a27e8c676aefb73cb776321be6611697b9bb03250ded19ace6c35ca99f3d9","name":"search-1050-failed.json","bytes":313},{"sha256":"6f583b0443d6300661c9d225372acb389a53254e37c6a08ad714ac2a9f8daebc","name":"search-1050.json","bytes":318},{"sha256":"c0529cf8a52246466dc6530f0118f8219b523baa020182f6cdb96ac888e6b7e7","name":"search-2620.json","bytes":319},{"sha256":"ce6ff548a0c46c9b154e127d8e47fe893ee1dd0e1b36a02763054529e8e2b28b","name":"execution-1050-failed.json","bytes":515},{"sha256":"a344ff6d934a479d3d2cc9d362b00be450381982ae5c8ca020c58681a9906a46","name":"execution-1050.json","bytes":515},{"sha256":"7bb5c537b42d99bfe2a2ad0b17182f27d26cdb0a36b1fcd75a59cb79be7e6bd2","name":"execution-2620.json","bytes":517},{"sha256":"17202a130b762b05cdcd21b49bc6a38061a4590c0e67b12f55fe144c0e581613","name":"execution-controls.json","bytes":515},{"sha256":"eedbb04f616cf931fb3297087e9efcd9ed8a51877799a69b6a752f96325e27b8","name":"dependency-hashes.json","bytes":230},{"sha256":"b7395b6f202eeedaed92ec134e36ec879c1146951c0d798a615057aa6b36478e","name":"report.md","bytes":7904},{"sha256":"222fa2415eaa9ac9227eaa3f741ed175191e983fe67f7e43daf2ff5752ae04ce","name":"source-hashes.json","bytes":1300},{"sha256":"33c435dad68f76739d414642e26164a4e7d16d73655c48daf772cf30d6893167","name":"job-1798-report.md","bytes":7863}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}