{"id":951,"job_id":1799,"problem_id":1,"lane_id":5,"type":"explore","user_id":42,"model":"deepseek-v4-pro","provider":"deepseek","report_md":"# Route 23 rescue: #933's block-boundary translation is the ~35x reduction #938 priced without using\n\nCalibration: **heuristic** (identification + arithmetic; the reduction's correctness rests on #933's pending two-sided proof, and my quick small-case gloss of the survivor-count objective did not yet match).\n\n## Result\n\nThe decisive obstruction (#938) is that the full low canonical domain of the 37# base is unsearched: native linear prices 12.3 CPU h (L30) and 117.8 CPU h (L34) against a 4 CPU h assignment budget, so K*(37) is unresolved.\n\nThe revisit_when asks for \"a distinct exact reduction ... establishes sufficient speedup (roughly 30-fold)\". That reduction is already on the record, and #938's pricing did not use it:\n\n- **#933's block-boundary translation**: promote 37 and add 73; filter old slots by a 37-phase and translate. The 37# base is exactly **35 copies** of the 31# base: N_37 = 217,929,355,875 = 35 × N_31 = 35 × 6,226,553,025. Reflected start counts are 108,964,677,938 vs 3,113,276,513 — ratio exactly 35. #933 states a two-sided proof: **K*(37) = max survivor count (slots not hit by 37) in an old 31#-base window fully covered by {37,…,73}**.\n\nIf that reduction is used, the search runs over the 31# base (35× fewer windows), and the priced costs drop to ≈ 12.3/35 ≈ 0.35 CPU h (L30) and ≈ 117.8/35 ≈ 3.4 CPU h (L34) — both within budget, making the full exact K*(37) feasible.\n\n## What I checked\n\n- The 35× domain ratio is exact arithmetic (N_37/N_31 = 35), independent of any proof status.\n- #938's own summary prices \"New base P37 …, Q41..73, N217929355875\" directly — it searched the 37# base, not the reduced 31# base.\n- I attempted a small-case validation of the survivor-count formula (s=7, 5#→7#, promote 7/add 13). My naive per-slot gloss did NOT match the direct K*(7) (direct 2 vs gloss 1): the objective is over the interleaved phase-lifts (e.g. slot 29's lift 209 is killed by 11 and is cyclic-adjacent to slot 11's lift 11), not a per-slot count. So the precise objective must be implemented from #933's proof, not from a paraphrase. The 35× domain arithmetic is unaffected.\n\n## Conclusion\n\nThe rescue identifies the concrete path that satisfies the revisit_when: implement #933's boundary translation exactly and benchmark it on the native engine. If the 35× holds (as the domain arithmetic guarantees for slot count), the full K*(37) scan fits the budget and the obstruction is removed. The remaining work is the precise implementation of the survivor-count objective, which my small-case attempt shows is subtle (interleaved lifts) and must follow #933's proof.\n","patch":null,"cpu_hours":0.02,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-09-17T20:48:51.750Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[933,938,936,918],"messages":[]},"tokens":{"log":"custom","input":9503,"models":{"deepseek-v4-pro":32744},"output":32744,"source":"custom-jsonl","entries":10,"cache_read":3609216,"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":23,"next_step":{"method":"Implement the old 31#-base survivor-count objective from #933's two-sided proof (not a paraphrase); benchmark on the native incremental engine; compare a full reduced run's wall/CPU time and the resulting K*(37) against #938's 29-slot lower bound and 17 L34 negatives.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0},"failure":"The survivor-count objective over interleaved lifts is no cheaper than the direct 37# scan (no 35x), or the reduction's correctness fails a small-case check; then record the precise reason and preserve #938's finite certificates.","success":"A full reduced-domain scan that yields exact K*(37) within the 4 CPU h budget, with a checkable certificate.","question":"Does #933's boundary translation, implemented exactly on the native engine, give the 35x speedup (K*(37) in <= 4 CPU h), and does the survivor-count objective over interleaved phase-lifts reproduce the direct search?","budget_hours":2,"required_tools":[],"required_sources":[]},"depends_on":[933,938],"evidence_md":"N_37 = 217,929,355,875 = 35 * N_31 = 35 * 6,226,553,025; reflected starts 108,964,677,938 vs 3,113,276,513 (ratio 35). #933's boundary translation (promote 37, add 73, filter by 37-phase) reduces K*(37) to a search over the 31# base with a survivor-count objective. #938 priced the 37# base directly (12.3/117.8 CPUh), not this reduction; 12.3/35 ~ 0.35 and 117.8/35 ~ 3.4 CPUh fit the 4 CPUh budget. Small-case gloss of the survivor-count formula did not match (interleaved phase-lifts), so the objective needs #933's proof, not a paraphrase.","prior_art_md":"2026-09-17. #933 (pending) supplies the boundary translation and a two-sided proof; #938 (pending) supplies the 37#-base native benchmark (12.3/117.8 CPUh) and the 29-slot certificate plus 17 high-component L34 negatives; #936 supplies the complete-domain repair of the 31# scans. The exact remaining gap is unchanged: exact K*(37) requires a full next-length noncovering scan, now reduced to the 31# base (35x smaller). No new external literature needed for this reduction."},"research_route_id":23,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_23424801c73890cd6fd3264c","run_id":"run_fb22a1982ed97962998ff647","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/23 and return #938. Return the ordinary report and transcript plus research: {route_id: 23, 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":"933","status":"accepted","final_rung":"proven","canonical_return_id":null},{"id":"938","status":"accepted","final_rung":"verified","canonical_return_id":null}],"research_url":"/projects/twin-primes/research-routes/23","transcript_url":"/projects/twin-primes/return/951/transcript","files":[{"sha256":"6aeeeac7204b1b088b176aef7cf4390485b03501ac98cf4370c2cb738fa08bbc","name":"validate_boundary_reduction.py","bytes":3368},{"sha256":"4313c68ad630417947cab880cd7dd0be2ced1ac2e0b31e2fc356e3909ee100b5","name":"qa.md","bytes":13452}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"duplicates":[],"cited_messages":[]}