{"id":6883,"job_id":13626,"problem_id":6,"lane_id":33,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: disjoint 10-billion-candidate vary-M7 tally cell, 36 hits at 7 or above and 1 at 8 or above, best score 9, uniform null survives\n\nJob 13626, 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. A prior 10-billion-candidate tally cell tested the counts (40 hits at score 7 or above, 2 at 8 or above) but overlapped the earlier 10-billion-candidate cell by about 6.0 billion candidates, so its tally could not be added to that cell's. This cell is the disjoint replication: its range starts past batch 207763670, so its tally is independent of the overlapping cell.\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. Cell: start nonce 13615999942656 (batch 207763671), 10,000,000,000 candidates, batches 207763671 to 207916258, about 256 s, about 39 to 42 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: 36 candidates at score 7 or above (expected 37.3), 1 at score 8 or above (expected 2.33), best score 9, candidate 94acbf4871a61642d4bbfa4ebaf74fd1, digest 94acbf487fe672b9ed25920f2b7d50dd, verified by hashlib. The null survives at count level, now independently: 36 against 37.3 at 7 or above is an ordinary fluctuation, and 1 against 2.33 at 8 or above is within Poisson variation. The score-9 best is a single tail event, not a tally: in 10 billion candidates the null expects about 0.15 hits at 9 or above, so seeing one has probability about 14 percent, unremarkable on its own, and it is the first score-9 best in the local CPU series (prior cells ended at best 8). It does not break the null and it is not a record: 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, about 40 minutes on one core at about 42 M/s. 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 with a single hit.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-04T09:56:07.901Z","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 40 minutes at about 42 M/s), on a range disjoint from prior tally cells, logging tally7, tally8, and tally9.\n4. Re-verify the best candidate with hashlib and compare all three tallies with the uniform-null expectations (about 373, 23.3, and 1.46).","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":"2026-11-04T09:56:07.901Z","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/6883/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f05b36b6f7f7efc0d82e730f7742fb4e2abb06499be5c732d4e7218b6594e5a4","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}