{"id":7006,"job_id":13803,"problem_id":6,"lane_id":33,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: 20-billion-candidate vary-M7 cell at 38.37 M/s, best 9, tally9 1; uniform model holds\n\nJob 13803, measure, self-match. Improvement claim: none. The best candidate\nreached score 9, below the 13 floor, so nothing goes to the results page.\n\n## Hypothesis\n\nA fresh vary-M7 cell's score tallies follow the uniform model: for N\ncandidates, about N/16^7 at 7 or above, N/16^8 at 8 or above, and N/16^9 at\n9 or above. For 20,000,000,000 candidates that is about 74.5 at 7 or above,\n4.66 at 8 or above, and 0.29 at 9 or above. The brief asks for a hypothesis\nabout MD5's structure that would make this track cheaper than generic\nsearch, tested by the smallest refuting experiment: if tallies deviate from\nuniform, structure is leaking; if they match, the vary-M7 route is generic\nsearch with a known rate, and no structural shortcut is visible at this\nscale.\n\n## Experiment\n\nRan the tally9 binary (vary-M7 AVX-512, one core) from the next disjoint\nstart recorded by the prior cell, nonce 13793500000000, in a single counted\nrun, log interval 120 s, while a parallel explore job ran on the other core.\nThe binary was verified against its selftest (fixture 12) before the run.\n\n- [120s] 35.26 M/s, best 9, tally7 12, tally8 1, tally9 1\n- [240s] 35.07 M/s, best 9, tally7 35, tally8 2, tally9 1\n- [360s] 37.13 M/s, best 9, tally7 52, tally8 3, tally9 1\n- [480s] 38.14 M/s, best 9, tally7 67, tally8 3, tally9 1\n- [done] 38.37 M/s, total 20,000,000,000, best 9, tally7 72, tally8 3, tally9 1\n\n## Results\n\nCounted total 20,000,000,000 candidates: best 9, tally7 72, tally8 3,\ntally9 1, against uniform expectations of about 74.5, 4.66, and 0.29.\nTally7 at 72 is within about one standard deviation of expectation, tally8\nat 3 is a small-number fluctuation, and tally9 at 1 against 0.29 expected\nis the first 9-or-above hit in the tally9 era: about a 25% chance of at\nleast one under Poisson, consistent with the uniform model, not evidence\nfor a leak. The best-9 candidate was re-verified by hashlib recompute from\nthe log, with an exact digest match:\n\n- a2e4626ea8125fcd55966c83ba5fbe8d -> a2e4626ea46b4cb5bad89ad121fba3f0, score 9\n\nEvery new-best candidate in the run log (scores 0 through 9) was likewise\nverified by hashlib from the log, all matching exactly. Combined with the\nprior 105.13 billion and the parallel explore cell's corrected 2 billion\nfrom the next disjoint start, the tally9-era counted total is now about\n127.13 billion, with tally9 at 1 against about 1.86 expected: still\nconsistent with uniform. The next disjoint start is nonce 13813520000000.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-06T02:43:30.166Z","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. Build the tally9 binary from the self-match tally9 source with\n   gcc -O3 -march=znver4 -mtune=znver4, and check its selftest (fixture 12).\n2. Run it from nonce 13793500000000 for 20,000,000,000 candidates, log\n   interval 120 s. Expected result: about 38.37 M/s, best 9, tally7 72,\n   tally8 3, tally9 1.\n3. Parse the log programmatically and verify every new-best candidate with\n   hashlib; do not hand-type candidates.\n4. For the next cell, run it from nonce 13813520000000.","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":"2026-11-06T02:43:30.166Z","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/7006/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"22608e56cfb90c7f20dd1392ce0d1095d5f0e714fac2c3e0393102ddee134bb9","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}