{"id":6808,"job_id":13538,"problem_id":6,"lane_id":33,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match measure: a fresh 2e10 vary-M7 cell matches the uniform null\n\nJob 13538, measure, self-match lane. Improvement claim: none. No\ncandidate scoring 13 or above exists, so nothing goes to the\nresults page. The best hit in this cycle scored 9 and is recorded\nhere and in the tally only.\n\n## Hypothesis\n\nFor the vary-M7 family, hit counts follow the uniform model: a\ncandidate's digest behaves as random hex, so the count of\ncandidates whose first 8 digest characters match their own first\n8 characters should be about n / 16^8, and full scores of 9 or\nabove should arrive at about n / 16^9. A large deviation would\nrefute the random-map picture for this structured family, where\ncandidates in a batch share their first 28 characters and differ\nonly in the last 4; agreement confirms that sharing a prefix does\nnot bias the hit distribution, and leaves throughput as the only\nlever.\n\n## Experiment\n\nA counting variant of the local AVX-512 vary-M7 searcher, built\nfrom the same source with counters added for every candidate\nwhose first-8 digest prefix matches and for every full score of\n9 or above. The variant's selftest passed before the run. One\nsingle-core cell: 20,000,000,000 candidates from nonce\n600,000,000,000, a range disjoint from the explore cell and the\nsizing probe running in parallel this cycle. Rate 42.22 M/s\nsustained.\n\n## Results\n\n- First-8 prefix hits: 5 observed vs 4.66 expected.\n- Full score 9 or above: 1 observed vs 0.29 expected.\n- Full score 10 or above: 0 observed vs 0.018 expected.\n- Best score 9, candidate e10d4f87036ad8b5062bd71de991e182,\n  digest e10d4f870a64fcb52912d4a3c8012810, verified with md5sum:\n  the first 9 hex characters match, the 10th does not.\n- The previous best in the cell, score 8, was also recomputed\n  with md5sum and agrees.\n\nThe counts are consistent with the uniform model: 5 vs 4.66 is\nwell within Poisson noise, and 1 vs 0.29 has probability about\n25% of occurring at all in a cell this size, so it is unremarkable\nrather than a hint of structure. The hypothesis survives: no\ndeviation from the null is visible at this scale, and the\nstructured vary-M7 family shows no bias in its hit distribution.\n\n## Cheapest next experiment\n\nA cell ten times larger (2e11 candidates, about 80 minutes at\nthis rate on one core, or split across two cores in a later\ncycle) would bring the expected score-9 count to about 2.9 and\nthe score-10 expectation to about 0.18, tightening the null check\nat the next rung without changing the method. No larger cell fits\nthis cycle's remaining window, so it is proposed, not run.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-02T20:09:07.833Z","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":"To repeat: build the counting variant from the run dir's\nsm_count.c with gcc -O3 -march=znver4 -mtune=znver4, run its\nselftest, then run sm_count 600000000000 20000000000 60 and save\nthe output as cell.log. Expect about 42.2 M/s and a final line\nreporting best 9, h0_8=5, ge9=1, ge10=0. Verify with\nprintf '%s' 'e10d4f87036ad8b5062bd71de991e182' | md5sum, which\nshould give e10d4f870a64fcb52912d4a3c8012810. Compare h0_8\nagainst 20000000000 / 16^8 = 4.66 and ge9 against 0.29.","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":"2026-11-02T20:09:07.833Z","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/6808/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c96e46730deac665dc35b72d8dc8b9b59cff503123dafd40187bb758fe58dea8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}