{"id":6935,"job_id":13681,"problem_id":6,"lane_id":33,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: 39.1B-candidate vary-M7 cell matches the uniform model, best 8, no 9+\n\nJob 13681, measure, self-match. Improvement claim: none. No longer matching\nprefix was found, and none is claimed. Nothing goes to the results page.\n\n## Hypothesis\n\nA fresh vary-M7 cell's score tallies follow the uniform model: for N candidates,\nabout N/16^7 at 7 or above, N/16^8 at 8 or above, and N/16^9 at 9 or above. For\nabout 39.1B counted candidates that is about 146 at 7 or above, 9.1 at 8 or\nabove, and 0.57 at 9 or above.\n\n## Experiment\n\nRan the tally9 binary from the #13642 work dir (vary-M7 AVX-512, one core\npinned) in three counted parts, all from the next disjoint start recorded by\n#13642:\n\n- Smoke: 10,000,000 candidates from nonce 13686399942656, best 5, tallies 0/0/0.\n- Part 1: 39,990,000,000 candidates from nonce 13686499942656, killed by a VM\n  reset after its 480 s log line: about 14.12B candidates counted, best 8,\n  tally7 53, tally8 2, tally9 0.\n- Part 2b: 25,000,000,000 candidates from nonce 13702500000000, 30.00 M/s,\n  best 8, tally7 97, tally8 7, tally9 0.\n\nA first part-2 restart used a miscomputed start inside part 1's covered range\nand re-found part 1's best-8 candidate, proving the overlap; it was killed and\nits tallies discarded, not counted. The corrected part-2 start sits 70M beyond\npart 1's maximum possible end (540 s bound), so no double-count. Up to about\n188M candidates between part 1's last logged point and the restart point are\nuncounted. The parallel all-zeros job ran on the other core.\n\n## Results\n\nCounted total about 39.13B candidates: best 8, tally7 150, tally8 9, tally9 0,\nagainst uniform expectations of about 146, 9.1, and 0.57. Both best-8 hits were\nre-verified by hashlib recompute with exact digest matches:\n\n- 436d6621417e652565c4e22703e4fce0 -> 436d66216bef1fa25f25a7a59082b959, score 8\n- 03d86ee0984325d45b5fb02f27d7f6d4 -> 03d86ee0347de2b95f3305ea2cd0a2b4, score 8\n\nNo candidate reached 9 or above, where about 0.57 were expected: consistent\nwith the uniform model, not evidence against it. The next disjoint start is\nnonce 13727500000000.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-04T22:26:47.780Z","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 #13642 work dir with\n   gcc -O3 -march=znver4 -mtune=znver4, and check its selftest (fixture 12).\n2. Run it from nonce 13727500000000 (the next disjoint start) for the desired\n   candidate count, log interval 120 s.\n3. Sum tally7/tally8/tally9 across counted parts only; discard any run whose\n   start falls inside an already-counted range (a re-found best hit proves it).\n4. Re-verify every best hit with hashlib and compare tallies with N/16^7,\n   N/16^8, N/16^9.","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":"2026-11-04T22:26:47.780Z","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/6935/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b901ca37042faeb768056d5b8a16e8f9982701a282b7f46553ec5b6ef6faa0d1","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}