{"id":6898,"job_id":13642,"problem_id":6,"lane_id":33,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: score-9 tally extension built and verified; the 9+ tail is now countable\n\nJob 13642, explore, self-match lane. Improvement claim: none. No candidate\nscoring 13 or above is claimed, so nothing goes to the results page. This\nreturn is a survey plus a small tool build and verification; it is not a\nreplication of a prior return, so it states no independence objective.\n\n## Accepted scoped answers compared\n\n- Record: 12, from the known fixture candidate. The best local candidate\n  scores 9, found in the 13626 cell.\n- Score distribution: two disjoint tally cells both fit the uniform model,\n  where a candidate scores s or better with probability 16^-s: 10 billion\n  candidates gave 36 at 7 or above and 1 at 8 or above, and 60 billion gave\n  198 at 7 or above and 9 at 8 or above.\n- The gap both of those returns named, but neither closed, is the 9+\n  tail: the tally searcher counted first-word scores of 7 and 8 only, and\n  computed a full score only for new-best candidates, so once the best\n  reached 8, later score-8 candidates were never fully scored and a 9+\n  hit could pass uncounted. The tally code for 9+ was never built.\n\n## The build\n\nThe tally searcher was extended in work/selfmatch_tally9.c: every score-8\nsurvivor now gets a full scalar MD5 score, and tally9 counts those reaching\n9 or above. Score-8 hits are about 1 per 4.3 billion candidates, so the\nextra scalar cost is negligible. Verification, all on one pinned core:\n\n- Build with gcc -O3 -march=znver4 -mtune=znver4; selftest passes\n  (fixture recomputed at score 12, vector and scalar first-word paths agree).\n- A first patch attempt broke best tracking for scores below 8, because\n  the survivor branch only ran at score 8. The smoke run caught it\n  (best stayed at -1 over 200 million candidates). The branch condition\n  was fixed to run for any new best or any score-8 survivor, and the\n  binary was rebuilt and re-verified.\n- Two 200-million-candidate smoke runs, contiguous from nonce\n  13685999942656, the exact end of the 60-billion cell: the first run's\n  7+ and 8+ tallies were unaffected by the bug and were both 0, so no\n  high candidate was missed there; the fixed binary ran at 46.85 M/s\n  solo, best 6, tally7, tally8 and tally9 all 0, as expected for 200\n  million candidates. The next disjoint range therefore starts at nonce\n  13686399942656.\n\n## Cheapest new experiment\n\nRun a 100-billion-candidate cell with the tally9 binary from nonce\n13686399942656, about 40 minutes on one core at about 42 to 47 M/s.\nExpected tallies under the uniform model: about 373 at 7 or above, about\n23.3 at 8 or above, and about 1.46 at 9 or above. That cell tests the tail\nthe earlier cells only glimpsed, and this return is what makes its 9+\ncount a real count instead of a side effect of best tracking.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-04T17:55:58.926Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"summary","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":"# Recipe\n\nTo repeat the build and verification, on a machine with gcc and AVX-512:\n\n1. Copy the tally searcher from the 60-billion cell and add a tally9\n   counter: in the survivor branch, compute the full scalar score for\n   every score-8 candidate, not only new-best ones, and increment tally9\n   when it reaches 9 or above. Keep the branch running for any new best\n   as before.\n2. Build with gcc -O3 -march=znver4 -mtune=znver4 and run the selftest.\n   Expected result: fixture 12, vector and scalar paths agree, selftest\n   passes.\n3. Run a short smoke cell on one pinned core and check the done line\n   shows a best above -1 and tally9 printed. Expected result on 200\n   million candidates: best around 6, all tallies 0.\n4. For the proposed cell, run 100 billion candidates from nonce\n   13686399942656 and read tally9 from the done line.","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":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"sundayweaver","job_brief":"Identify an uncovered obligation or a changed premise on this track; compare the accepted scoped answers before proposing the cheapest new experiment. Deliberate replication needs a stated independence objective.","review_deferred":false,"in_triage":false,"triage":[],"lean_statement_binding":null,"lean_execution_binding":null,"lean_scientific_identity":null,"lean_execution_identity":null,"verification_runs":[],"verification_state":null,"verification_summary":null,"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/6898/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0d813b0c5d4051793f28f70dcbebb049f1f3243e971de77b8271eb784aae4385","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}