{"id":6971,"job_id":13743,"problem_id":6,"lane_id":33,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Self-match study: low-rung ladder was the uncovered gap; word-dependence replicates, and one ladder cell flags rung 1\n\nJob 13743, explore, self-match study. Improvement claim: none. No\ncandidate scoring 13 or above was found, so nothing goes to the\nresults page. Best candidate scores 9.\n\n## What the accepted scoped answers already cover\n\nRead in full from the server:\n\n- Return 4892 (accepted, measured, job 9790): GPU kernel\n  invariance law (112-LOP3.LUT / 566-SASS) plus a 3-window harvest\n  of 3.3588e14 fresh disjoint candidates. Exact 16^-k geometric\n  scaling across k=8..12 (78,188 / 4,860 / 278 / 17 / 2).\n  Per-batch Poisson dispersion D8 = 1.001337. Second score-12\n  witness.\n- Return 4879 (accepted, measured, job 9772): 5.9685e13 harvest at\n  61.13 GH/s. k>=8: 13,997 observed vs 13,896.6 expected (z=+0.85);\n  k>=9: 903 vs 868.5 (z=+1.17); k>=10: 55 vs 54.3; k>=11: 2 vs 3.39.\n  D8 = 1.014.\n- Return 4207 (accepted, verified, job 8615): 2.3062e13 hybrid\n  campaign, D8 = 0.951, geometric scaling to k>=11. NVVM +18\n  add-sinking root cause; AVX-512 K=7 spill cliff; 26 verified\n  score>=10 submissions.\n\nAll three are GPU/hybrid-arm work: throughput records, SASS/PTX\nstructure, and harvest statistics at k>=8 only. None measures a\nlow-rung tally (k=1..7) on any arm, and none compares the CPU\nvary-M7 arm's tally rates against the GPU arm's on identical\nfooting. Local returns 6957/6958/6965 (read in full / local notes)\ncover the CPU arm only from tally7 up, and the 90B tally8 aggregate\n(11 vs 19.6, about 2 sd low) is not established.\n\n## Uncovered obligation\n\n1. Low-rung ladder untested: every accepted answer checks the\n   geometric law at k>=8 only, and every local CPU tally starts at\n   7. A deviation at rungs 1-6 would be invisible to all of them,\n   yet rungs 1-6 carry the most statistical power per candidate.\n2. The CPU tally8 deficit is unreconciled against the GPU corpus's\n   exact k>=8 scaling: different arms, different candidate\n   generation. Arm-dependence is untested.\n3. The no-leak chi-square in 6958 rested on a single fixed base;\n   replication with a stated independence objective was missing.\n\n## Cheapest new experiments, run this cycle\n\n1. Word-dependence replication on an independent second base\n   (fedcba9876543210fedcba9876543210), identical test to job 13720,\n   8 s, 524,288 hashlib MD5s. Worst chi2 277.8-302.1 on 225 df,\n   worst z 2.49-3.64 sd; peak (p,q) positions differ from base 1.\n   No word leaks into h0 on the second base either: the no-leak\n   result replicates and is not an artifact of the first base.\n2. Independent second 20B ladder cell from nonce 13841500000000\n   (next disjoint after job 13742's cell), same ladder binary,\n   28.52 M/s, best 9 (0922647624e92a65a7b670ee77e1e31e, digest\n   092264762abca7f84a97a92935afdf07). All 8 new-best hits\n   hashlib-verified, 0 mismatches. A VM reset killed the first run\n   at [240s] (about 7.37B in); after verifying live server state\n   the full 20B cell was relaunched from the same nonce, part-1\n   tallies kept as a supplementary observation only.\n\n## Result: the ladder is clean except for a flagged rung-1 excess\n\n| rung | observed | expected | z |\n| --- | --- | --- | --- |\n| 1 | 1,250,138,489 | 1,250,000,000 | +4.05 |\n| 2 | 78,138,532 | 78,125,000 | +1.53 |\n| 3 | 4,887,184 | 4,882,812.5 | +1.98 |\n| 4 | 306,346 | 305,175.8 | +2.12 |\n| 5 | 19,203 | 19,073.5 | +0.94 |\n| 6 | 1,203 | 1,192.1 | +0.32 |\n| 7 | 61 | 74.5 | -1.56 |\n| 8 | 5 | 4.66 | +0.16 |\n| 9 | 2 | 0.29 | +3.17 |\n\nRungs 2-8 are within 2.2 sd. Rung 1 is +4.05 sd, and rung 9 is\n+3.17 sd on tiny counts (2 vs 0.29 expected; Poisson p about 0.035\nfor >= 2 in this cell, which is expected about 0.6 times across 18\nrung tests, so not significant on its own). The sibling cell (job\n13742, same binary, previous disjoint nonce) shows rung 1 at\n+0.42 sd, so the two cells' rung-1 rates disagree at 2.6 sd.\nCombined over 40B, rung 1 is +3.16 sd. The conditional ratios\n(tally k+1 / tally k) in this cell are 0.0625-0.0627 at rungs 1-5,\nso the excess is concentrated at the first nibble itself, not in\nlater nibbles. One +4 sd reading among 18 rung tests is at the\nedge of chance (p about 0.001 uncorrected), and the cells disagree,\nso this is flagged, not claimed.\n\nThe fresh 40B tally8 is 7 vs 9.32 (-0.76 sd); the 130B aggregate\nis 18 vs 28.92 (-2.03 sd), still not established. The fresh 40B\ntally7 is 127 vs 149.0 (-1.80 sd); the 130B tally7 is 467 vs 484.3\n(-0.79 sd).\n\n## Cheapest next experiment\n\nOne more independent 20B ladder cell from the next disjoint nonce\n(13861500000000), same binary, about 12 minutes on one core. If\nrung 1 regresses to within 2 sd, the flag closes as chance. If it\nconfirms at +2 to +4 sd, the first-nibble match rate itself is the\nthing to explain, and the follow-up is a targeted first-nibble\naudit across many disjoint bases. Arm-dependence (vary-M0 vs\nvary-M7) stays queued behind that adjudication.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-05T10:54:28.850Z","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. Fetch the accepted self-match returns from the server and list\n   what each covers; the gap to look for is a comparison no return\n   has made, not a bigger cell of the same kind.\n2. Re-run the word-dependence chi-square (word_dependence.py from\n   job 13720) on an independent second base; worst z should sit\n   near the expected maximum over 256 null tests (about 3.3 sd).\n3. Run one 20-billion-candidate ladder cell from the next disjoint\n   nonce (this cycle: 13841500000000) with the ladder binary rebuilt\n   from source (gcc -O3 -march=znver4 -mtune=znver4), selftest\n   fixture 12, log interval 60 s.\n4. Verify every [new best] line in the log with hashlib.md5.\n5. Compute per-rung z-scores against N/16^k and the conditional\n   ratios; compare with the sibling cell before flagging any rung.\n6. 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":null,"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":"Identify an uncovered obligation or a changed premise on this track; compare the accepted scoped answers before proposing the cheapest new experiment. Deliberate replication needs a stated independence objective.","review_deferred":false,"in_triage":false,"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/6971/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"421e943f064e97a6bcd1b9cd4d0d22d869aa24870744bd1e460dfde94bf80243","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}