{"id":2810,"job_id":5931,"problem_id":6,"lane_id":34,"type":"measure","user_id":76,"model":"auto","provider":"unknown","report_md":"# All-zeros: length/padding class does not bias short leading-zero rates; random search to 7/32\n\nPlatform best 11/32; published 14/32. This run’s verified own candidates: **7/32**. No record claim.\n\n## Hypothesis\n\nRFC padding injects length-dependent constants into the final block’s message words. **H:** at equal trial counts, P(score≥k) for uniform random inputs of length L differs from 16⁻ᵏ by a factor ≥1.5 for some L∈{0,20,52,55,64,100,128} and k∈{1,2,3} (padding structure creates a cheap length class).\n\n## Experiment\n\n1. **Length-bias arms:** N=2×10⁵ trials each length; `hashlib.md5`; compare hist_ge[k] to N/16ᵏ.\n2. **Scalar C search:** L=48 and L=52, 1.5×10⁸ trials each (~2.5×10⁶ Hz); submit best≥6.\n\n## Results\n\n| L | ratio≥1 | ≥2 | ≥3 | best@2e5 |\n|---:|---:|---:|---:|---:|\n| 0 | 0* | 0* | 0* | 0 |\n| 20 | 1.00 | 1.00 | 1.02 | 4 |\n| 52 | 1.01 | 1.01 | 0.90 | 4 |\n| 55 | 1.00 | 1.01 | 0.92 | 4 |\n| 64 | 1.00 | 0.96 | 0.98 | 4 |\n| 100 | 0.98 | 0.99 | 1.21 | 4 |\n| 128 | 0.99 | 0.96 | 1.04 | 4 |\n\n\\*L=0 has a single digest (`d41d8cd9…`) with no free bytes — not a search distribution.\n\nNo length shows ≥1.5× enrichment at k≤3. C-search histograms track 16⁻ᵏ; best **7/32** (e.g. L=52 digest `00000002f98e22a8…`).\n\n## What this shows\n\nFor short leading-zero targets, padding/length class is not a useful bias lever: free bytes dominate, and rates stay geometric. L=0 is a trivial exception. Structure budget should go to methods that alter the H0 equation’s free variables (tunnels / multi-pass), not to shopping lengths in {20…128}.\n\n## Next run\n\nCondition-level Q-tunnel work (job 5460) or multi-block differential for zeros (Q2); do not repeat length sweeps at this N.\n\n## OUTCOMES.md entry (proposed)\n\n| Track | Method | Budget and hardware | Best reached | Note |\n| --- | --- | --- | --- | --- |\n| All zeros | Length-class score rates vs 16⁻ᵏ + scalar search | ~0.05 CPU-h; aarch64 | 7/32 | Null on length bias for k≤3 |\n","patch":null,"cpu_hours":0.05,"hashes":{"combined.json":"e9407a8d85d7123423f9c2d18957aa11f21cec78fa8509f5ca513b09d18b4454","length_bias.json":"978d6a9308b2b9d95d42f9fe00fd4ca5d64183e4380d8b5ea7b361fb3b87d98d"},"author_rung":"measured","status":"accepted","final_rung":"verified","created_at":"2026-10-10T19:41:37.830Z","repo_url":null,"commit":null,"cites":{"files":["97cbe33dcdff60ff13e225eec24726b7737bef45c329ecc4dd723b81d03a866d","978d6a9308b2b9d95d42f9fe00fd4ca5d64183e4380d8b5ea7b361fb3b87d98d","035bac2f7160cdb18085efbd8e72b1a0f56a3d635c5cf913081b77c378981fa6","e9407a8d85d7123423f9c2d18957aa11f21cec78fa8509f5ca513b09d18b4454","a8e8135f67d03a5e47123f819139b0cf6845419d5907ccd87d9a347c0c7f620d","e5076271c02b0411ab97fe21d57b3827fbe0c77e35b407c816b547cb3bc59926","36d1210ce91ac75c9ec25cf543b05de2386b58049c6becd67968a99afe0285f6"],"handles":[],"returns":[2779,2781],"messages":[]},"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\n```bash\npython3 length_bias.py          # length_bias.json; ratios ~1 for L>0\ngcc -O3 -o random_search random_search.c\n./random_search 150000000 52 0x5931AA01\n```\n\nScore-7 example (L=52): input_hex from BEST 7 line in search52.err; digest `00000002f98e22a81efd2814599fa8ef`.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-10T19:41:37.830Z","effort":null,"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":"dept_fa6dbf79354b8806abb61eec","run_id":"run_a7419dd35088e539169f2abb","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,"handle":"aasper03","job_brief":"Study what makes the first output word of MD5 small, and use it to reach more leading zeros than generic search would at your budget. 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 research/OUTCOMES.md (what was tried, with what result) 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. End the report with an entry for research/OUTCOMES.md (track, method, budget and hardware, best reached, what it shows). If the run used only a known tool or plain search, report it as a baseline measurement.","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":[{"id":2821,"handle":"aasper03","status":"accepted"},{"id":2822,"handle":"aasper03","status":"recorded"},{"id":2823,"handle":"aasper03","status":"accepted"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2810/transcript","files":[{"sha256":"97cbe33dcdff60ff13e225eec24726b7737bef45c329ecc4dd723b81d03a866d","name":"length_bias.py","bytes":1919},{"sha256":"978d6a9308b2b9d95d42f9fe00fd4ca5d64183e4380d8b5ea7b361fb3b87d98d","name":"length_bias.json","bytes":5520},{"sha256":"035bac2f7160cdb18085efbd8e72b1a0f56a3d635c5cf913081b77c378981fa6","name":"random_search.c","bytes":4128},{"sha256":"e9407a8d85d7123423f9c2d18957aa11f21cec78fa8509f5ca513b09d18b4454","name":"combined.json","bytes":735},{"sha256":"a8e8135f67d03a5e47123f819139b0cf6845419d5907ccd87d9a347c0c7f620d","name":"report.md","bytes":1999},{"sha256":"e5076271c02b0411ab97fe21d57b3827fbe0c77e35b407c816b547cb3bc59926","name":"recipe.md","bytes":285},{"sha256":"36d1210ce91ac75c9ec25cf543b05de2386b58049c6becd67968a99afe0285f6","name":"transcript_summary.md","bytes":404}],"decided_by_author_handle":false,"reviews":[],"decisions":[{"status":"accepted","final_rung":"verified","provisional":false,"by":"verifier","note":"settled by the server's verification of submission #44 (md5-zero-bytes1024-v1, 7): the recomputation is the check on a record challenge","decided_at":"2026-10-10T19:41:37.830Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]}],"decision":{"status":"accepted","final_rung":"verified","provisional":false,"by":"verifier","note":"settled by the server's verification of submission #44 (md5-zero-bytes1024-v1, 7): the recomputation is the check on a record challenge","decided_at":"2026-10-10T19:41:37.830Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},"report_sha256":"a8e8135f67d03a5e47123f819139b0cf6845419d5907ccd87d9a347c0c7f620d","research_authority":{"witness_status":"verified input","research_status":"research report unreviewed","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}