{"id":6885,"job_id":13629,"problem_id":6,"lane_id":33,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: disjoint 60-billion-candidate vary-M7 tally cell, 198 at 7 or above and 9 at 8 or above, best score 8, uniform null survives\n\nJob 13629, measure, self-match. Improvement claim: none. No fixed point and no score above 12 was found, and none is claimed. Nothing goes to the results page.\n\n## Hypothesis\n\nThe self-match score distribution follows the uniform null, each digest hex char matching with probability 1/16 independently. The prior disjoint tally cell (10 billion candidates) gave 36 at 7 or above and 1 at 8 or above with a single score-9 best. This cell is the larger disjoint replication: it starts exactly where that cell ended, so its tally is independent of it, and at 60 billion candidates the null expectations are large enough to test at count level (about 224 at 7 or above, about 14 at 8 or above).\n\n## Experiment\n\nBinary work/selfmatch_tally.c (the vary-M7 searcher with counters for first-word scores of 7 or above and exactly 8), built with gcc -O3 -march=znver4 -mtune=znver4. Selftest passed, fixture recomputed at score 12. One core (taskset -c 0), AMD EPYC 9D25 VM, run in parallel with a second job on the other core. Cell: start nonce 13625999942656 (the exact end nonce of the prior tally cell, so the two cells are contiguous with no overlap and no gap), 60,000,000,000 candidates, about 1902 s, about 31.55 M/s under dual-core load (single-core rate for this binary was about 39 to 42 M/s in the prior cell).\n\n## Results\n\nTally: 198 candidates at score 7 or above (expected 223.5), 9 at score 8 or above (expected 14.0). Both are ordinary Poisson fluctuations (about 1.7 and 1.3 standard deviations low). Best full score 8, candidate c2f817f6324ffa32b5f40517fcfe9944, digest c2f817f61e4eff95e75a6ba3ede6c6ba, verified by hashlib. None of the 9 candidates at first-word score 8 extended to score 9; under the null about 0.56 of 9 would, so zero is unremarkable. The null survives at count level, now on a second independent cell and a combined 70 billion disjoint candidates. The fixture still stands at 12.\n\n## Next step\n\nA score-9-capable tally: extend the tally searcher to count score 9 or above (first nibble of the second output word for candidates already at score 8) and run a 100-billion-candidate cell on a range disjoint from this one. Expected tallies under the null: about 373 at 7 or above, about 23.3 at 8 or above, about 1.46 at 9 or above. That cell would test the tail this cell only glimpsed through its 9 first-word-8 candidates.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-04T12:23:02.915Z","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 (next step)\n\n1. Copy the tally searcher and add a score-9 counter: for candidates already at first-word score 8, check the first nibble of the second output word.\n2. Build with gcc -O3 -march=znver4 -mtune=znver4, run the binary selftest, and re-verify the fixture at score 12.\n3. Run a 100-billion-candidate vary-M7 cell on one core (about 50 minutes at about 31 to 42 M/s depending on load), on a range disjoint from this cell, starting past nonce 13685999942656.\n4. Report tallies at 7, 8, and 9 or above against the null expectations (about 373, 23.3, and 1.46), plus the best candidate verified by hashlib.","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":"2026-11-04T12:23:02.915Z","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":"Study how a candidate's 32 ASCII bytes flow through the 64 steps into the first digest characters, and use what you learn to reach a longer matching prefix. Ideas to test: which message words the first output word depends on most, fixing a prefix and solving for the rest, early-exit tests on the first output word, meet-in-the-middle on the step function. Start from the algorithm, not the search. Read the track's state of the art in this brief (the fastest known way per machine, what worked, the dead ends) and research/QUESTIONS.md, then state one hypothesis about MD5's structure that would make this track cheaper than generic search, and why you expect it. Test it with the smallest experiment that could refute it, against a measured baseline on the same machine. Submit the best candidates the experiment produced. The report is a finding: the hypothesis, the experiment, what it showed about MD5 (positive or negative, with numbers), and what the next run should try. Send what you learned as a state_entry with your return (the method, the exact hardware, the measured throughput, the best reached), so the track's state of the art carries it. If the run used only a known tool or plain search, report it as a baseline measurement.","review_deferred":false,"in_triage":true,"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/6885/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"0d5a3c28df144159b17ca8d94a1e09fbbe592679004c37a3ea7d17faed94371a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}