{"id":6970,"job_id":13742,"problem_id":6,"lane_id":33,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match: full tally ladder over a fresh 20B vary-M7 cell matches uniform at every rung; best 8\n\nJob 13742, measure, self-match. Improvement claim: none. No candidate\nscoring 13 or above was found, so nothing goes to the results page.\nBest candidate scores 8.\n\n## Hypothesis\n\nThe vary-M7 arm's digest nibbles follow the uniform geometric law at\nevery rung: P(score >= k+1 | score >= k) = 1/16 for k = 0..7.\nMotivation: the five-cell aggregate over 90B has tally8 11 against\n19.6 expected (about 2 sd low, not established), while the accepted\nGPU corpus (return 4892: 3.36e14 candidates) shows exact geometric\nscaling at k >= 8 only. No accepted return measures the low rungs\n(1-6) on any arm, and no local cell ever counted them. The full\nladder localizes any deviation: low rungs carry the most power\n(tally1 about 1.25B per 20B cell), so a rung-1..6 deviation would be\nglaring, and a clean ladder would leave only the weak high-rung\ncounts to explain the tally8 deficit as chance.\n\n## Experiment\n\nselfmatch_ladder.c, derived from selfmatch_tally9.c with the kernel\nand scoring unchanged, counts tally1..tally9 (the h0-prefix score s\nis already computed per candidate; only >= 7 was counted before).\nRebuilt from source (gcc -O3 -march=znver4 -mtune=znver4), selftest\nPASS (fixture 12, h0 path OK, vector vs scalar OK). Fresh disjoint\n20B cell from nonce 13821500000000 (next disjoint after job 13731's\ncell), log interval 60 s, one core (a parallel job ran on the other\ncore). A VM reset killed the first run at its [300s] line, about\n10.22B in; after verifying live server state (job still held) the\nfull 20B cell was relaunched from the same start nonce. Part-1\ntallies are a supplementary observation only and are not added to\nthe relaunched cell's counts (same nonces re-covered).\n\n## Result: the ladder matches uniform at every rung in this cell\n\n20,000,000,000 candidates, 28.70 M/s, best 8. All 8 new-best hits\nhashlib-verified from the log, 0 mismatches. Best:\n3881d4f4c2bd89cc9987e435d3f8583e, digest\n3881d4f40d1ac5c4102fc6a429d829e6.\n\n| rung | observed | expected | z |\n| --- | --- | --- | --- |\n| 1 | 1,250,014,331 | 1,250,000,000 | +0.42 |\n| 2 | 78,121,551 | 78,125,000 | -0.39 |\n| 3 | 4,881,614 | 4,882,812.5 | -0.54 |\n| 4 | 305,453 | 305,175.8 | +0.50 |\n| 5 | 19,058 | 19,073.5 | -0.11 |\n| 6 | 1,242 | 1,192.1 | +1.45 |\n| 7 | 66 | 74.5 | -0.99 |\n| 8 | 2 | 4.66 | -1.23 |\n| 9 | 0 | 0.29 | -0.54 |\n\nEvery rung is within 1.5 sd of uniform in this cell. The hypothesis\nis not refuted at any rung here.\n\n## Cross-cell observation (sibling cell, job 13743)\n\nThe parallel job ran an identical second 20B ladder cell from the\nnext disjoint nonce (13841500000000) with the same binary. Its\nrung-1 count is 1,250,138,489 against 1,250,000,000 expected\n(+4.05 sd), while this cell shows +0.42 sd; the two cells' rung-1\nrates disagree at 2.6 sd. Combined over 40B, rung 1 is +3.16 sd.\nIts other rungs are within 2.2 sd, and its conditional ratios\n(tally k+1 / tally k) are 0.0625-0.0627 at rungs 1-5, so any excess\nis concentrated at the first nibble itself, not in later nibbles.\nOne +4 sd reading among 18 rung tests (9 rungs x 2 cells) is at the\nedge of chance (p about 0.001 uncorrected), and the two cells\ndisagree with each other, so this is flagged, not claimed: the\ncheapest adjudication is one more independent 20B ladder cell. If\nthe excess is real, a third cell should show +2 to +4 sd again; if\nchance, it regresses.\n\nThe fresh 40B tally8 is 7 against 9.32 expected (-0.76 sd). Added\nto the prior 90B aggregate, the 130B tally8 is 18 against 28.92\n(-2.03 sd): the deficit persists near 2 sd but is still not\nestablished, and the fresh cells on their own are consistent with\nuniform. The fresh 40B tally7 is 127 against 149.0 (-1.80 sd);\nthe 130B tally7 is 467 against 484.3 (-0.79 sd).\n\n## What the next run should try\n\nOne more independent 20B ladder cell from the next disjoint nonce\n(13861500000000) to adjudicate the rung-1 flag. If it regresses,\nthe flag closes as chance and the open question becomes\narm-dependence (vary-M0 vs vary-M7 on the CPU), which needs a new\nsearcher variant. If it confirms, the first-nibble match rate\nitself is the thing to explain.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-05T10:54:20.973Z","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 selfmatch_tally9.c to selfmatch_ladder.c and add tally1..6\n   counters on the per-candidate h0-prefix score s (tally7..9 as\n   before); rebuild with gcc -O3 -march=znver4 -mtune=znver4 and run\n   the selftest; the fixture must score 12.\n2. Run one 20-billion-candidate cell from the next disjoint nonce\n   (this cycle: 13821500000000), log interval 60 s.\n3. Verify every [new best] line in the log with hashlib.md5\n   (digest and true prefix score must match the printed values).\n4. Compute per-rung z-scores against N/16^k expectations and the\n   conditional ratios tally(k+1)/tally(k).\n5. If a VM reset kills the run, verify live server state before\n   relaunching, restart the full cell from the same nonce, and keep\n   the partial tallies as a supplementary observation only.","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":"2026-11-05T10:54:20.973Z","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/6970/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"f019399e201d9de14aca83b9ed26e62a4ebde8efd515a639ac18c854c65b5d64","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}