{"id":959,"job_id":1801,"problem_id":1,"lane_id":3,"type":"explore","user_id":42,"model":"deepseek-v4-pro","provider":"deepseek","report_md":"# Route 64 rescue: separate discovery (validated C engine) from certification (arithmetic check)\n\nCalibration: **heuristic** (the alternate method is evidence-backed; its positive-branch cost is unmeasured).\n\n## Result\n\nThe obstruction is **solver-specific**, not mathematical: the pinned single-thread CaDiCaL 1.9.5 run on the H1050,L30 and H2620,L30 joint formulas ended UNKNOWN within 900 CPU s (return #949). The encoding itself is correct (return #945; toy-validated). The rescue preserves route 64's distinct value — the **independently checkable positive certificate** — while replacing the discovery step that timed out.\n\n**Alternate method: separate discovery from certification.**\n1. *Discovery*: run the validated route-23 C engine (`kstar_rework.c`, block+phase collapse + reflection quotient `T(x)=-x-2`, established in #594/#918/#936) on its **positive branch** to search for a 30-slot covering witness at s=37.\n2. *Certification*: on the first hit, reconstruct the natal/scour phases `(a_p, b_q)` and emit route 64's arithmetic certificate (direct gcd/divisibility check over the L=30 span).\n\nThis removes the SAT solver from discovery, so the CaDiCaL timeout cannot recur; the independent certificate is preserved.\n\n## Honest scope\n\nThe positive-branch cost is unmeasured — a 30-window, if it exists, could sit deep in the 108.9e9 reflection representatives (the full negative scan is #938's 12 CPU h). This does not guarantee a speedup over the SAT; it guarantees a **deterministic** decision path with a preserved certificate. Secondary SAT-only improvements (reflection symmetry-breaking clauses, 29-witness seeding) are noted but unproven.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-09-17T22:22:21.378Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[936,938,945,949],"messages":[]},"tokens":{"log":"custom","input":7322,"models":{"deepseek-v4-pro":24567},"output":24567,"source":"custom-jsonl","entries":11,"cache_read":4237184,"cache_write":0,"observed_models":["deepseek-v4-pro"]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"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":0},"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":null,"file_notes":null,"research":{"outcome":"progress","route_id":64,"next_step":{"method":"Run kstar_rework.c's positive branch (reflection-quotiented windows in order) searching for a 30-cover at s=37; on the first hit reconstruct (a_p,b_q) from the window and emit the route-64 arithmetic certificate (direct gcd check over the 30-span); report the search cost and the certificate.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The positive branch completes negative (K*(37) = 29) at a measured cost, or reaches the 12 CPUh negative price without a witness — record the measured cost honestly.","success":"A 30-slot witness with an independent arithmetic certificate, i.e. K*(37) >= 30 certified without trusting the engine.","question":"Does the validated route-23 C engine find a 30-slot covering witness at s=37 on its positive branch, and can that witness be certified by route 64's independent arithmetic check?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[936,938,945,949],"evidence_md":"Obstruction #949 is solver-specific (CaDiCaL UNKNOWN in 900s), not mathematical. Encoding #945 is correct (toy-validated; known-29 passes). Route 64's value is the independent certificate. The distinct alternate method separates discovery (validated C engine, block+phase collapse + reflection quotient, #594/#918/#936) from certification (route 64's arithmetic check). This avoids the CaDiCaL timeout by construction (deterministic scan) and keeps the certificate. Positive-branch cost unmeasured (up to #938's 12 CPUh negative).","prior_art_md":"2026-09-17 update for the changed ingredient (an alternate discovery method to the SAT timeout). Searched: 'SAT solver solved Erdos discrepancy Boolean Pythagorean triples Keller conjecture'. Inspected: Heule SAT4Math tutorial; Cruz-Filipe-Schneider-Kamp LPAR-21 (formally proving Boolean Pythagorean triples). The SAT/proof-complexity home of route 64 is real but already charted (route 64 itself). The exact uncovered step is a deterministic discovery path that preserves the independent certificate; the C engine is that path, validated in route 23."},"research_route_id":64,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_f60e0aa013ff494788a759be","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"handle":"victor-geere","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/64 and return #949. 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":"936","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"938","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"945","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"949","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/64","transcript_url":"/projects/twin-primes/return/959/transcript","files":[{"sha256":"f262575ee8857024de397df94fd9479e941f3dd048c85832119be1208f266aba","name":"qa.md","bytes":29495}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}