{"id":6791,"job_id":13514,"problem_id":6,"lane_id":34,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Measure: 4.18e11-candidate zeros cell, max score 11, uniform model survives\n\nJob 13514, measure, all-zeros lane. Improvement claim: none. No\ncandidate scoring 13 or above exists, so nothing goes to the results\npage. All finds below are recorded in this return and the tally\nonly.\n\n## Hypothesis\n\nPer-candidate score-s-or-better hits arrive with p = 16^-s\n(uniform model) for the interleave-4 AVX-512 tunnel on this VM, so\na fixed-size cell's max and tail counts follow the binomial model.\nA large deviation would refute the throughput-only sizing premise\nthe record push rests on.\n\nIndependence objective: deliberate replication of the pooled-cell\nuniform-model test on a fresh VM instance after a reset, in a\ndisjoint nonce range (starting at 4.0e13, never used by the earlier\n2^43 and 2^44 cells), with fresh nonces and independent recompute\nof every top hit, rather than copying prior numbers.\n\n## Baseline (same machine)\n\nFrom job 13513 in this same cycle, on this AMD EPYC 9D25 VM at\nabout 1.5 GHz: single-core 241.41 M/s; dual-core aggregate about\n348 M/s in short runs. The cell below ran dual-core at 164.8 to\n164.9 M/s per core at completion (part 2), with part 1 at about\n169 to 170 M/s per core before the reset.\n\n## Measurement\n\nThe cell is complete: 418,000,000,000 unique candidates. Part 1\nran 360 s per segment before a VM reset (A consumed 60,933,600,000,\nB 61,300,800,000, from the last logged cumulative rates). Part 2\nrestarted from those points with a 1e9 overlap per segment and no\ngaps (A 149,066,400,000, B 148,699,200,000, both to [done]).\nUnique total: 122,234,400,000 plus 297,765,600,000 minus 2,000,000,000\noverlap = 418,000,000,000.\n\nObserved, record-breaking hits only (the searcher logs only\nrecord-breaking hits, so tail counts are lower bounds): score 9 in\nsegment A, score 9 then score 11 in segment B, no score 10 record.\nCell max 11, against an expected max of log16(4.18e11) = 9.65.\nExpected counts: score>=9 about 6.08, score>=10 about 0.38,\nscore>=11 about 0.024. Observed score>=9 record-breaking hits: 3\nagainst 6.08 expected (Poisson P(X<=3) about 0.14, and the true\ncount is at least 3, so the true tail probability is higher).\nThe single score 11 is on the lucky side (P of at least one\nscore>=11 in a cell this size is about 2.3%), but across three\nlocal cells (maxes 10, 9 and now 11) it is a tail event, not a\nrefutation, and no odds change is claimed.\n\nTop hits, all verified by independent recompute:\n- score 11: input\n  5248f93a624df93e4d9a2ccb795a108cb25901d1f82b650d6d99bbcdc7dbe08dfd2f177cd26292fe6aabf097932b35eb02a00a63\n  (52 bytes) -> 00000000000e281c444c35f3cd0b8325\n- score 9: input\n  21535347165401be7f00fba185aebcbab2b98ab407dc1eab39d9908c43dcbede028fd700cc98975b8160a4a2166732aaab19e037\n  -> 0000000007059ce4523699a5c64fa6b8\n- score 9: input\n  5ce10c5020a1eb38c7ae43adde1bfd642b5273bf87c49673bb3fe97fa3e14d68b2af9e03be6fdecf2c42a348f9e1d0d79ec3e4c9\n  -> 000000000b699b878a01bf60089ba09\n- part 1 score 8 hits in each segment, also verified by recompute.\n\n## Verdict\n\nNo decisive deviation: the cell yield is consistent with the\nuniform binomial model once the lower-bound caveat is applied.\nThe hypothesis survives; the wait-time premise keeps its measured\nsupport. The next run should try a further disjoint cell rather\nthan a new structural idea, since no structural shortcut has\nsurvived testing on this track.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-02T14:21:19.933Z","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: verify the interleave-4 AVX-512 tunnel binary with its\nselftest, then run two parallel processes, at most 2 cores, on a\nfresh disjoint range (starts 40000000000000 and 40209000000000,\n209000000000 candidates each, log interval 60 s). If a reset kills\na segment, read the last [NNNs] cumulative rate line, consumed =\nNNN times rate, restart at old start plus consumed minus 1e9\noverlap, with the remaining count plus 1e9, and run to [done].\nCollect every [new best] line at score 9 or above, recompute each\nwith an independent hash implementation, and compare counts and\nmax against N/16^s and log16(N).","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":"2026-11-02T14:21:19.933Z","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 what makes the first output word of MD5 small, and use it to reach more leading zeros than generic search would with the same compute. Ideas to test: freedom from extra message blocks, neutral bits and message modification from collision attacks applied to the output instead of a difference, early abort on the final additions. 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":[{"id":6793,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/6791/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"79f22a8610414ec9e8871b0f2371ae5e8fbd6a3d3b611d3e1449a36b0a13f1b8","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}