{"id":6757,"job_id":13427,"problem_id":6,"lane_id":34,"type":"measure","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Job 13427 — finding: structured families show no first-word bias\n\n## Hypothesis (one)\n\nFixing most message words and varying only a few — the Q9 tunnel structure,\nwhere one 32-bit counter drives message words m8/m9/m12 and the base is fixed\nper 2^32 block — leaves the first MD5 output word effectively uniform, so a\nstructured family loses no leading-zero hit rate versus fully random\nmessages. Expected because MD5's rounds 2-4 diffuse a single-word change\nacross the whole state, and the final first word is a heavily mixed state\nplus the initial word; nothing in the compression function preserves a bias\nfrom \"most words were fixed\" into the top bits of word 0. If true, the\ntunnel's per-candidate savings (steps 24-60 only, base amortised over a\nblock) are a pure win over generic search. If a family had deviated, that\nbias itself would be the next lever to chase.\n\n## Experiment\n\nSame machine, one core each, run sequentially (no contention between parts):\n\n1. Baseline: production binary tools/md5tun_avx512_il4 (interleave-4),\n   pinned to one core, start nonce 0, 30 billion hashes, 125 s wall.\n   Measured 239.61 M/s. Best score 8 (see candidates.md). Expectation under\n   uniformity: score >= 8 about 7 times in 30B hashes, score >= 9 about\n   0.4 times — so best 8 with no 9 is exactly the uniform prediction, not\n   evidence for or against structure either way.\n2. Decisive proxy test: runs/job-13427/family_test.py (hashlib, 300,000\n   52-byte messages per family):\n   - A: fully random messages.\n   - B: tunnel-like — words 8, 9, 12 vary with a counter, rest fixed.\n   - C: one-word only — word 0 varies, rest fixed.\n   Metric: digest byte 0 chi-square (df=255, the byte the track score\n   checks first) and leading-zero-bit counts of digest word 0.\n   Uniform prediction: P(>= k leading zero bits) = 2^-k.\n\n## What it showed (not refuted, at this resolution)\n\n| family | byte-0 chi2 (df=255) | >=8 bits obs/exp | >=10 bits | >=12 bits | >=14 bits |\n|---|---|---|---|---|---|\n| A random | 261.2 | 1206 / 1172 (z +1.00) | 305 / 293 (+0.70) | 91 / 73 (+2.08) | 20 / 18 (+0.39) |\n| B tunnel-like | 264.2 | 1075 / 1172 (z -2.84) | 278 / 293 (-0.87) | 77 / 73 (+0.44) | 18 / 18 (-0.07) |\n| C one-word | 238.4 | 1214 / 1172 (z +1.23) | 308 / 293 (+0.88) | 72 / 73 (-0.15) | 17 / 18 (-0.31) |\n\nAll three byte-0 chi-square values sit within about one standard deviation\nof the mean (255 +- 22.6), and all families reach the same best word-0\nleading-zero count (18 bits). One single bin is soft: family B at >= 8 bits\nis z = -2.84. Across 12 bins plus 3 chi-square tests one ~2.8-sigma bin is\nunremarkable, and B is normal at every higher threshold and on chi-square,\nso there is no consistent bias pattern. Verdict: hypothesis NOT refuted at\nn = 300,000 per family. Structure neither helps nor hurts the first-word\nhit rate at this resolution; the tunnel's advantage remains its step\nsavings, not a distributional edge.\n\n## Next run to try\n\nTwo options, in order:\n1. Scale the same proxy test 10x (3M per family) to settle the family-B\n   >= 8-bit dip: if it persists at z beyond ~4 with higher thresholds\n   still normal, it is a low-bit quirk, not a record lever; if a bias\n   grows with n, chase it.\n2. Test the other brief idea directly: early abort on the final additions.\n   Write a variant searcher that scores candidates from the state after\n   step 60 plus a cheap bound on steps 61-64, and measure candidates/s\n   against il4's 239.61 M/s on the same core. Only adopt it if it beats\n   il4 on measured throughput with an equal hit rate.\n\n## Candidates\n\nBest from the baseline: score 8, digest\n00000000e50c0b99336620006479067a (52-byte input in candidates.md,\nmd5sum recompute verified). Below 13, so it belongs in this return only,\nnever as a results-page claim. Nothing was filed; this payload is staged.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"pending","final_rung":null,"created_at":"2026-11-01T02:05:21.921Z","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 (reproduce this run)\n\nSurvey first (no new searcher code was written):\n- Read the Q9 tunnel report and the il4 source in tools/, plus the prior\n  zeros tallies and recent zeros run notes in runs/, before touching code.\n  Carry forward: quote measured rates on this host, not inherited headlines.\n\nBinary check:\n- `./tools/md5tun_avx512_il4 test` must print SELFTEST PASS.\n- sha256 of the binary used:\n  5ef5e64ac4a39b3ce15a96fef92c68d18dd920492a1a76dc3e669c8f8555d5cf\n\nBaseline (one core, restartable in chunks by nonce range):\n- `taskset -c 0 ./tools/md5tun_avx512_il4 0 30000000000 30`\n- Log to runs/job-13427/baseline.log. Expect ~239 M/s and best 8 in ~125 s.\n\nHypothesis test:\n- `python3 runs/job-13427/family_test.py`\n- 300,000 messages per family, hashlib, a few seconds. Output is saved in\n  runs/job-13427/family_test.log.\n\nCandidate verification:\n- Recompute each logged candidate: md5 of the 52-byte input hex must equal\n  the logged digest. All 9 new-best lines verified; see candidates.md.\n\nIf rebuilding il4 from source: gcc 13.3 -O3 -march=znver4 -mtune=znver4\n(this VM's chip reports Zen 5 via CPUID but gcc 13.3 rejects -march=znver5;\nznver4 is the working target).","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":"2026-11-01T02:05:21.921Z","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":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/6757/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"9598566b96683a9139ad90e727e8ce8bad4f30aaf478731cc4e87a4c48ec6213","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}