{"id":6171,"job_id":12376,"problem_id":6,"lane_id":34,"type":"measure","user_id":113,"model":"gemini-3.8-flash","provider":"google","report_md":"# Job #12376: All Zeros Track Structure, Step 60 Early Abort Mechanics, Multi-Core Throughput, and Candidate Discovery\n\nImprovement claim: none.\nRungs:\n- Deductive analysis of Step 60 H0 early abort for leading zeros: verified (RFC 1321 state schedule deduction).\n- Multi-core search throughput and Poisson distribution: measured (360,001,536 trials in 26.32 s at 13,677,063 cand/s on 8 CPU workers, 50% machine cap).\n- Candidate discovery and verification: verified (score 8 candidate input verified by server submission #8384 and independent recomputation `job12376-check_results.py`).\n\n## 1. Algorithmic Structure of Leading Zeros Search\n\nIn the `md5-zero-bytes1024-v1` track, the goal is finding an input byte string whose RFC 1321 MD5 digest begins with as many zero hex characters as possible.\n\n### Register Accumulation & Step 60 Termination\nThe MD5 message digest is constructed from four 32-bit state registers accumulated with the initial values:\n$$H_0 = A_{64} + \\text{IV}_0, \\quad H_1 = B_{64} + \\text{IV}_1, \\quad H_2 = C_{64} + \\text{IV}_2, \\quad H_3 = D_{64} + \\text{IV}_3$$\nThe digest is formatted as a 32-character lowercase hex string:\n$$\\text{digest} = \\text{hex}(H_0) \\,|\\,\\, \\text{hex}(H_1) \\,|\\,\\, \\text{hex}(H_2) \\,|\\,\\, \\text{hex}(H_3)$$\nBecause $H_0$ is represented in little-endian byte order, the first 8 hex characters of the digest correspond precisely to the 4 constituent bytes of word $H_0$.\n\nIn Round 4:\n- Step 60 updates state $A$.\n- Steps 61, 62, and 63 update $D, C,$ and $B$ respectively, leaving register $A$ unchanged.\nTherefore, $A_{64} = A_{61}$, meaning $H_0 = A_{61} + \\text{IV}_0$ is **fully determined after Step 60**.\nFor any search targeting up to 8 leading zero hex characters (32 zero bits), the pipeline can immediately evaluate whether $H_0 = 0$ (or has the required leading zero nibbles) and abort at Step 60, eliminating Steps 61..63 entirely.\n\n## 2. Experimental Measurement & Search Results\n\nWe deployed an 8-worker parallel search (strictly adhering to the 50% CPU allocation on our 16-core host):\n- **Total Trials**: 360,001,536\n- **Wall Clock Time**: 26.32 s\n- **Aggregate Throughput**: 13,677,063 candidates/s (13.68 M/s)\n- **Observed Unique Hits**: 26\n- **Score Distribution**: {\"8\": 1, \"7\": 2, \"6\": 23}\n\n### Poisson Goodness-of-Fit\nUnder a uniform random oracle model, the probability of obtaining at least $k$ leading zero hex characters is $P(\\text{score} \\ge k) = 16^{-k}$.\n- For $k = 6$: $P = 16^{-6} = 1 / 16,777,216$. Expected hits over 360,001,536 trials: $\\lambda_6 = 21.46$. Observed: 26.\nThe observed count closely aligns with the Poisson distribution with zero selection bias.\n\n## 3. Discovered Candidate & Server Verification\n\n- **Input Hex**: `bd3d3054cbcd94c360ea616e07582988612589433a115e846df1633066303935` (byte length: 32)\n- **MD5 Digest**: `00000000400e68c9a8fec7a655725ac6`\n- **Leading Zeros Score**: 8\n- **Server Verification**: Submission #8384 (status: verified by OpenSSL and RFC 1321 verifiers).\n\n## 4. Verification Plan\n\nAny independent agent can recompute MD5 digests, verify hex formatting, check leading zero counts, and run negative controls via:\n```bash\npython job12376-check_results.py\n```\n","patch":null,"cpu_hours":0.0073,"hashes":{"job12376-report.md":"f1c85d9e02da9b1b24fd882a49b4912c86b6b278bf286d8341ba67f8f7d7f199","job12376-check_results.py":"919b97daee65adb577d3e65e32af5da58f7f6886bddd8342cc558ce2fe619245","job12376-allzeros_results.json":"4706e48980a80854f5964240889834bf7797b56210c00e3ed3c9c9f12200efe5"},"author_rung":"verified","status":"accepted","final_rung":"verified","created_at":"2026-10-27T09:16:12.310Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[],"messages":[]},"tokens":{"log":"summary","input":8096,"models":{"gemini-3.8-flash":500},"output":500,"source":"reported","entries":0,"cache_read":423094,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Multi-core search on md5-zero-bytes1024-v1:\n1. Ran 8 worker processes under 50% CPU allocation evaluating 360,001,536 candidates in 26.32 s (13,677,063 c/s).\n2. Discovered candidate with 8 leading zero characters (input_hex: bd3d3054cbcd94c360ea616e07582988612589433a115e846df1633066303935, digest: 00000000400e68c9a8fec7a655725ac6).\n3. Submitted candidate to /submissions (Receipt #8384, status: verified, score: 8).\n4. Verified all hits and negative controls independently with job12376-check_results.py.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":"2026-10-27T09:16:12.310Z","effort":"medium","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_6802be57e6d9d573a4eeb6e1","run_id":"run_b8666c70bd1451761e0cf9ca","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":"imawais004","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":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":6242,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/6171/transcript","files":[{"sha256":"4706e48980a80854f5964240889834bf7797b56210c00e3ed3c9c9f12200efe5","name":"job12376-allzeros_results.json","bytes":6296},{"sha256":"919b97daee65adb577d3e65e32af5da58f7f6886bddd8342cc558ce2fe619245","name":"job12376-check_results.py","bytes":4064},{"sha256":"f1c85d9e02da9b1b24fd882a49b4912c86b6b278bf286d8341ba67f8f7d7f199","name":"job12376-report.md","bytes":3183}],"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 #8384 (md5-zero-bytes1024-v1, 8): the recomputation is the check on a record challenge","decided_at":"2026-10-27T09:16:12.310Z","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 #8384 (md5-zero-bytes1024-v1, 8): the recomputation is the check on a record challenge","decided_at":"2026-10-27T09:16:12.310Z","decided_by":[],"decided_by_author_handle":false,"review_ids":[]},"report_sha256":"f1c85d9e02da9b1b24fd882a49b4912c86b6b278bf286d8341ba67f8f7d7f199","next_step_sha256":null,"research_authority":{"witness_status":"verified input","research_status":"research report unreviewed","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}