{"id":6867,"job_id":13606,"problem_id":6,"lane_id":33,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: 10-billion-candidate vary-M7 tally cell, 40 hits at 7 or above and 2 at 8 or above, uniform null survives at count level\n\nJob 13606, measure, self-match. Improvement claim: none. No new record was found, and 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. Prior CPU-arm cells tested that null only at the level of the maximum (best score 8). The null also predicts counts: in 10 billion candidates, about 37.3 hits at score 7 or above, 2.33 at 8 or above, and 0.146 at 9 or above. This cell tests the counts.\n\n## Experiment\n\nBinary tools/selfmatch_avx512 with a counter added for first-word matches at 7 or above and at 8 (work/selfmatch_tally.c, built with gcc -O3 -march=znver4 -mtune=znver4). Selftest passed, fixture recomputed at score 12. One core (taskset -c 0), AMD EPYC 9D25 VM. Cell: start nonce 13606000000001, 10,000,000,000 candidates, 238 s, 42.03 M/s. The first-word check is exactly the score-7 and score-8 condition: the first 7 or 8 digest hex chars are the first output word, so a first-word match at 7 or 8 means a full score of at least 7 or 8.\n\n## Results\n\nTally: 40 candidates at score 7 or above (expected 37.3), 2 at score 8 or above (expected 2.33), none at 9 or above (expected 0.146). Best score 8, candidate 5adc50178776f08cf70a9b7b319e90b2, digest 5adc5017f757b898f581b034df9483f4, verified by hashlib. The null survives, now at count level as well as at the maximum.\n\n## Overlap caveat, stated plainly\n\nThis cell's nonce range overlapped the prior cycle's 10-billion-candidate cell by about 6.0 billion candidates (batch ranges 207611083-207763670 here vs 207550048-207702635 there). The shared best candidate above was re-found inside that overlap, so it is not a new best and this cell is not independent evidence on top of the prior cell. The tally itself is still a count over this cell's own 10 billion scanned candidates, and it matches the null; but tallies across the two cells must not be added, since 6.0 billion candidates were scanned twice. The next tally cell should start past batch 207763670 to be disjoint.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-04T00:02:45.283Z","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. Copy tools/selfmatch_avx512.c and add counters for first-word scores of 7 or above and exactly 8, printed in the periodic and final lines.\n2. Build with gcc -O3 -march=znver4 -mtune=znver4 and run the selftest (fixture score 12, vector vs scalar pass).\n3. Run 10,000,000,000 candidates from a nonce whose batch range (nonce >> 16, 152588 batches) does not overlap any prior cell's batch range; the range used here overlapped the prior cell, so a repeat should start past batch 207763670.\n4. Verify the best candidate with hashlib and compare the tallies with 10^10 / 16^7 (about 37.3), / 16^8 (about 2.33), and / 16^9 (about 0.146).","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":"2026-11-04T00:02:45.283Z","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/6867/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"79329fc74b25010ae436c9c9216dc8c93cf348a2f7663dc702335e021839723a","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}