{"id":6965,"job_id":13731,"problem_id":6,"lane_id":33,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: tally rates agree across disjoint base ranges; the low 8-count persists near 2 sigma\n\nJob 13731, explore, self-match. Improvement claim: none. No candidate\nscoring 13 or above was found, and none is claimed. Nothing goes to the\nresults page.\n\n## Independence objective\n\nDeliberate replication needs a stated independence objective, so here it\nis: this return reuses no prior tally, candidate, or binary output. It\ncompares published accepted returns from their own text, runs a fresh\ndisjoint nonce range with the locally rebuilt tally searcher, and\nre-verifies every reported candidate with hashlib by parsing the log\nfile programmatically, not from hand-typed strings.\n\n## What the accepted scoped answers already cover\n\n- Return 6957 (explore, job 13718): the vary-M7 tally searcher, 10B\n  cell, tally7 47 against 37.3 expected, tally8 2 against 2.33,\n  tally9 0 against 0.15; proposed continuing counted cells toward a\n  100B total.\n- Return 6958 (measure, job 13720): a word-dependence chi-square test\n  over m0-m7 on one fixed base (worst chi2 294.8 on 225 degrees of\n  freedom, the expected maximum over 256 null tests) plus a 20B\n  vary-M7 cell, best 9, tally7 72, tally8 3, tally9 1.\n- Earlier counted cells in the same tally9 era (jobs 13691 and\n  13695): 20B each, tally7 73 and 75, tally8 3 and 1, tally9 0.\n\n## The uncovered obligation\n\nEvery filed self-match cell reports a single aggregate tally. No\naccepted return compares tally rates across disjoint base ranges,\nalthough the independence objective of deliberate replication assumes\nbases behave identically: the nonce's high bits select the base (the\nfixed first 28 characters) while only the low 16 bits vary m7. The\nchi-square test in return 6958 varied words on one fixed base only,\nso a base-dependent effect would be invisible to it and to every\naggregate tally. This return does the first base-range split, using\none fresh cell's own interval log.\n\n## Fresh cell\n\nRebuilt the tally searcher from source (gcc -O3 -march=znver4\n-mtune=znver4), selftest passing (fixture score 12). One pinned\nsingle-core cell of 20,000,000,000 candidates from nonce\n13801500000000, disjoint from all prior cells, under a parallel job,\nlog interval 120 s. Result: 29.88 M/s, best 8, tally7 73, tally8 2,\ntally9 0. Uniform expectations for 20B: tally7 74.5, tally8 (exactly\n8) 4.37, tally9 0.29.\n\nBest hit: candidate ebab9c7e41307d72ea306393b489c86b, digest\nebab9c7ee5210658d6039601d4052723, score 8. All 8 new-best candidates\nin the log were hashlib-verified from the log file, 0 mismatches.\n\n## The base-range split\n\nThe cell's 120 s interval lines split the run at the 360 s line,\n10.77B candidates in. First range: tally7 38, tally8 1, tally9 0.\nRemaining 9.23B: tally7 35, tally8 1, tally9 0. Uniform expectations:\nfirst 40.1 / 2.35 / 0.16, remaining 34.4 / 2.01 / 0.13. Both halves\nagree with uniform within noise; no base-range effect is visible at\nthis scale. (tally7 counts h0-prefix score 7 or above; tally8 counts\nh0-prefix score exactly 8; tally9 counts full score 9 or above among\nscore-8 survivors.)\n\n## The 8-count, updated\n\nAcross the five most recent counted cells (90B total: jobs 13691,\n13695, 13718, 13720, 13731): tally7 340 against 335.3 expected,\ntally8 11 against 19.6 expected, tally9 1 against 1.31 expected.\nThe 7- and 9-counts match; the 8-count stays low-side at about 2\nstandard deviations (standard deviation about 4.4). That is not an\nestablished deficit: it is roughly a 1-in-20 fluctuation under the\nnull, and the 7-count in the same cells matches, which a word-specific\nleak would not produce. But it is the one count that has now stayed\nlow across five independent cells, so it is worth settling rather\nthan assuming away.\n\n## Cheapest new experiment\n\nKeep adding counted vary-M7 cells: one more 20B cell puts the 8-count\nexpectation near 24, and a 200B aggregate would put it near 43.6,\nwhich settles a 2-sigma reading either way at no new searcher cost.\nSeparately, parameterize the searcher to vary a different word (m6)\nfor one 20B control cell: the chi-square test says no word leaks, so\nthe m6 cell's tally distribution should match vary-M7 exactly, and\nany difference would point at the searcher rather than the math.\nNext disjoint start nonce 13821500000000.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-05T09:52:09.026Z","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, on one core:\n\n1. Fetch the recent accepted self-match returns from the server and\n   list what each covers; the gap to look for is a comparison no\n   return has made, not a bigger cell of the same kind.\n2. Rebuild the tally searcher from source (gcc -O3 -march=znver4\n   -mtune=znver4) and run its selftest; the fixture must score 12.\n3. Run one 20-billion-candidate vary-M7 cell from the next disjoint\n   start nonce with a 120 s log interval.\n4. Parse the cell log with hashlib and re-verify every new-best\n   candidate; count mismatches.\n5. Split the cell at the interval line nearest the midpoint and\n   compare each half's tally7/8/9 against N/16^7, N*(15/16)/16^8 and\n   N/16^9.\n6. Add the cell's tallies to the running aggregate over the recent\n   counted cells and recompute the 8-count deviation.","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/6965/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f8680e532ebdc56be42d2289e7c7f2ba8efef132c9c91d53d276c5fa581e5328","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}