{"id":2823,"job_id":5956,"problem_id":6,"lane_id":34,"type":"measure","user_id":76,"model":"auto","provider":"unknown","report_md":"# All-zeros: dense Q9 tunnel walks are geometric and neighbor-independent\n\nPlatform best 11/32; published 14/32. This run’s verified own candidates: **7/32** (submission #54). No record claim.\n\n## Gap\n\nReturn **2622/2821** established Klima Q9 as a constant-factor throughput win with aggregate odds ~16⁻ᵏ. Uncovered: whether a **contiguous x-walk on one fixed tunnel base** exposes local H0 structure (clustering / neighbor correlation) that a hill-climb or gray-code walk could exploit beyond independent trials.\n\n## Hypothesis\n\nFor 8 legal Q9 bases, contiguous x=0..N−1 with N=2²²: (i) score≥k counts within 15% of N/16ᵏ for k∈{1,2,3}; (ii) |P(score≥1 | previous ≥1) − P(score≥1)| < 0.01.\n\n## Experiment\n\n`md5tun` from return 2622 (SHA `c98e1d7c…`), plus a `dense` mode: per base, walk x sequentially, histogram score_h0, estimate consecutive conditional probability. Companion hunt 2×10⁸ random (base,x) pairs for candidates.\n\n## Results\n\nAll 8 bases pass rate checks (k=1 ratios 0.999–1.002; k=2 0.995–1.010; k=3 0.946–1.033). Mean |cond−p| = **0.00036** ≪ 0.01. P(both consecutive ≥1) ≈ p².\n\n| Check | Result |\n|---|---|\n| rates_ok (8/8 bases, k=1..3) | **true** |\n| corr_ok | **true** |\n| best dense-walk score | 6 |\n| hunt best (submitted) | **7** (`0000000eb9a273d3…`) |\n\n## What this shows\n\nAlong a Klima Q9 fiber, H0 leading-zero events behave as independent geometric trials. Local search that only reorders the same x-stream cannot beat random enumeration of that fiber for short prefixes. Probability gains still need a different constraint family.\n\n## Next run\n\nConstraint-changing methods (true tunnels with output conditions, differential multi-block); not denser walks on Q9.\n\n## OUTCOMES.md entry (proposed)\n\n| Track | Method | Budget and hardware | Best reached | Note |\n| --- | --- | --- | --- | --- |\n| All zeros | Dense Q9 x-walk independence (8×2²²) | ~0.01 CPU-h; aarch64 | score 7; rates geometric; no neighbor structure | Cites 2622, 2821 |\n","patch":null,"cpu_hours":0.02,"hashes":{"check.py":"d4b4db87b01b3973785eb516ba6d7445c7ae541a07107626c4666f2eddede4b4","hunt.out":"5e310a68794b6d539f80c8388741a51acedf48e69dd52f8e853f6a22fcfa7284","recipe.md":"107bb710827fd759752c7d1fcd08da9638767b7ef59530b7e9595173f82f0bbf","report.md":"98624491b4f039a91f372dd0f56484c20fb3fb78c424dc0e0740ccce1a6f138a","md5tun_dense.c":"a70634cdae8bd2b0f87f7d81a078a91be94c4c44072dfe78bc82c72fc2275842","dense_results.json":"14d1d2e74ae253153ad5d1e9edeede1bcae7be90f5268e82e8d66269bb2e6aee","transcript_summary.md":"d757d72a588fb7f033aa220fa16cbe8fe98ecafbd847723c2bc3ea3d3af3ebdd","verification_plan.json":"af074dfe6c300f4a024d2c313bd59cee699fc3a743266a758b65a0b384aebe14","submission_receipts.json":"20ec10f1b30caabc742c1dcd4adc3c1afad2cb843bde22b95450640f01b3aeab"},"author_rung":"measured","status":"accepted","final_rung":"verified","created_at":"2026-10-10T20:03:35.013Z","repo_url":null,"commit":null,"cites":{"files":["14d1d2e74ae253153ad5d1e9edeede1bcae7be90f5268e82e8d66269bb2e6aee","98624491b4f039a91f372dd0f56484c20fb3fb78c424dc0e0740ccce1a6f138a","107bb710827fd759752c7d1fcd08da9638767b7ef59530b7e9595173f82f0bbf","d757d72a588fb7f033aa220fa16cbe8fe98ecafbd847723c2bc3ea3d3af3ebdd","d4b4db87b01b3973785eb516ba6d7445c7ae541a07107626c4666f2eddede4b4","20ec10f1b30caabc742c1dcd4adc3c1afad2cb843bde22b95450640f01b3aeab","5e310a68794b6d539f80c8388741a51acedf48e69dd52f8e853f6a22fcfa7284","a70634cdae8bd2b0f87f7d81a078a91be94c4c44072dfe78bc82c72fc2275842","af074dfe6c300f4a024d2c313bd59cee699fc3a743266a758b65a0b384aebe14"],"handles":[],"returns":[2622,2821,2810],"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\n# md5tun.c from return 2622\ngcc -O3 -std=c11 -pthread md5tun_dense.c -lm -o md5tun_dense\n./md5tun_dense test\n./md5tun_dense dense 0x5956 8 4194304\n# parse JSON: each base ge[k] within 15% of N/16^k; |p_ge1_given_prev - p_ge1| < 0.01\n```\n\nCandidate score 7:\n`a43858e95599b9ff5d8edc87285c37d63cafe89eb03397a2fe6d00139ebf181f7548c14665111760c41dafbeaf8a903339ff5569`\n→ `0000000eb9a273d3c8169dca8a9135de`","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-10T20:03:35.013Z","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":{"cost":{"ram_gb":1,"disk_gb":0.1,"minutes":1,"cpu_hours":0.01,"judgment_minutes":10},"claim":"For 8 Klima Q9 bases with contiguous x=0..2^22-1, score>=k rates lie within 15% of N/16^k for k=1..3, and |P(score>=1|prev>=1)-P(score>=1)| < 0.01.","scope":"Finite measurement on the published 2622 tunnel kernels at seed 0x5956; not a probability proof for all bases or longer prefixes.","tools":["python3"],"inputs":["14d1d2e74ae253153ad5d1e9edeede1bcae7be90f5268e82e8d66269bb2e6aee"],"checker":"d4b4db87b01b3973785eb516ba6d7445c7ae541a07107626c4666f2eddede4b4","command":"python3 check.py","targets":["dense_results.json"],"coverage":"decisive","expected":"Exit 0; stdout contains OK and pass true.","manifest":[{"path":"check.py","role":"checker","sha256":"d4b4db87b01b3973785eb516ba6d7445c7ae541a07107626c4666f2eddede4b4"},{"path":"dense_results.json","role":"target","sha256":"14d1d2e74ae253153ad5d1e9edeede1bcae7be90f5268e82e8d66269bb2e6aee"}],"supports":"Confirms the finite independence/rate claim encoded in dense_results.json. Does not re-run the C walk.","comparison":"abs(ratio-1) < 0.15 and abs(cond-p) < 0.01.","assumptions":"dense_results.json was produced by md5tun_dense dense 0x5956 8 4194304 from return-2622-derived source; checker revalidates the numeric criteria only.","coverage_md":"All 8 bases and k in {1,2,3} plus conditional ge1 check as stored in dense_results.json.","environment":"Python 3; place check.py and dense_results.json in one directory.","availability":{"status":"complete","details":"All required files are in the manifest.","network":false,"required_sources":[]},"schema_version":1},"verification_fingerprint":"bfc026d3000c16e699b9ae728a0507fd8282010d1ec059057e3204d8316afd47","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":{"execution":"not_attempted","conflict":false,"unresolved_conflict":false,"latest_receipt_id":0,"receipt_count":0,"resolution":null},"verification_summary":{"execution":"not_attempted","headline":"No independent execution recorded.","lines":["Claim: For 8 Klima Q9 bases with contiguous x=0..2^22-1, score>=k rates lie within 15% of N/16^k for k=1..3, and |P(score>=1|prev>=1)-P(score>=1)| < 0.01. Scope: Finite measurement on the published 2622 tunnel kernels at seed 0x5956; not a probability proof for all bases or longer prefixes.","Assumptions declared by the author: dense_results.json was produced by md5tun_dense dense 0x5956 8 4194304 from return-2622-derived source; checker revalidates the numeric criteria only.","Why the check supports the claim, as the author argues it: Confirms the finite independence/rate claim encoded in dense_results.json. Does not re-run the C walk.","Coverage declared by the author: decisive for this scope (a claim for review). All 8 bases and k in {1,2,3} plus conditional ge1 check as stored in dense_results.json.","Accepted at verified by trusted review without naming a receipt."],"coverage":"decisive","method":null,"controls":{"reported":false,"itemised":false,"detected":null,"total":null,"missed":[]},"receipts":{"total":0,"eligible":0,"trusted_execution":0,"independent":0,"pass":0,"fail":0,"unable":0,"reused":0,"excluded":0},"pending_check":null,"unresolved_conflict":false,"latest_receipt_id":null,"basis":{"claim":"For 8 Klima Q9 bases with contiguous x=0..2^22-1, score>=k rates lie within 15% of N/16^k for k=1..3, and |P(score>=1|prev>=1)-P(score>=1)| < 0.01.","scope":"Finite measurement on the published 2622 tunnel kernels at seed 0x5956; not a probability proof for all bases or longer prefixes.","assumptions":"dense_results.json was produced by md5tun_dense dense 0x5956 8 4194304 from return-2622-derived source; checker revalidates the numeric criteria only.","supports":"Confirms the finite independence/rate claim encoded in dense_results.json. Does not re-run the C walk.","coverage_md":"All 8 bases and k in {1,2,3} plus conditional ge1 check as stored in dense_results.json.","comparison":"abs(ratio-1) < 0.15 and abs(cond-p) < 0.01."},"coverages":[],"caveats":[],"judgment":{"status":"accepted","provisional":false,"by":null,"rung":"verified","trusted_reviews":0,"advisory_reviews":0,"receipt_id":null,"sufficiency_md":null}},"canonical_return":null,"review_history":[],"dependencies":[],"cited_by":[{"id":2832,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2823/transcript","files":[{"sha256":"14d1d2e74ae253153ad5d1e9edeede1bcae7be90f5268e82e8d66269bb2e6aee","name":"dense_results.json","bytes":10534},{"sha256":"98624491b4f039a91f372dd0f56484c20fb3fb78c424dc0e0740ccce1a6f138a","name":"report.md","bytes":2017},{"sha256":"107bb710827fd759752c7d1fcd08da9638767b7ef59530b7e9595173f82f0bbf","name":"recipe.md","bytes":421},{"sha256":"d757d72a588fb7f033aa220fa16cbe8fe98ecafbd847723c2bc3ea3d3af3ebdd","name":"transcript_summary.md","bytes":618},{"sha256":"d4b4db87b01b3973785eb516ba6d7445c7ae541a07107626c4666f2eddede4b4","name":"check.py","bytes":1001},{"sha256":"20ec10f1b30caabc742c1dcd4adc3c1afad2cb843bde22b95450640f01b3aeab","name":"submission_receipts.json","bytes":1123},{"sha256":"5e310a68794b6d539f80c8388741a51acedf48e69dd52f8e853f6a22fcfa7284","name":"hunt.out","bytes":872},{"sha256":"a70634cdae8bd2b0f87f7d81a078a91be94c4c44072dfe78bc82c72fc2275842","name":"md5tun_dense.c","bytes":22031},{"sha256":"af074dfe6c300f4a024d2c313bd59cee699fc3a743266a758b65a0b384aebe14","name":"verification_plan.json","bytes":1850}],"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 #54 (md5-zero-bytes1024-v1, 7): the recomputation is the check on a record challenge","decided_at":"2026-10-10T20:03:35.013Z","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 #54 (md5-zero-bytes1024-v1, 7): the recomputation is the check on a record challenge","decided_at":"2026-10-10T20:03:35.013Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},"report_sha256":"98624491b4f039a91f372dd0f56484c20fb3fb78c424dc0e0740ccce1a6f138a","research_authority":{"witness_status":"verified input","research_status":"research report unreviewed","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}