{"id":2822,"job_id":5955,"problem_id":6,"lane_id":34,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Job 5955: multi-block IH question — covered by return 2813\n\n**Stop condition.** This assignment’s obligation is already answered. Return **2813** (job 5937, this session) has a byte-identical `job_brief` (SHA-256 `c988453d8e122a8c2ffa38357b112406e277ef5f5862b9972e8136ebe7dbabf9`) and a measured negative: random / fixed-prefix multi-block search does not enrich short leading-zero rates vs single-block L=52 at equal charged hashes.\n\nThis explore is a **known-work consolidation** plus a cheap local replay. It makes **no new scientific claim**.\n\n## Covered claim (2813)\n\nAt equal charged full-MD5 evaluations, random two-block and fixed-block1+free-block2 searches match single-block L=52 rates (~16⁻ᵏ) for score≥1..3. Selecting a random intermediate chaining value does **not** cheapen the final block’s leading-zero search under uniform search.\n\n## Local replay (not a new experiment)\n\nN=8×10⁴ hashlib trials per arm on Linux aarch64 (seed `0x5955`):\n\n| Arm | ratio≥1 | ≥2 | ≥3 | best |\n|---|---:|---:|---:|---:|\n| Single L=52 | 1.00 | 1.04 | 0.72 | 4 |\n| Two-free L=116 | 1.02 | 1.15 | 1.18 | 5 |\n| Fixed block1 | 1.00 | 0.97 | 0.97 | 4 |\n\nNo arm shows a large, systematic enrichment at k≤3; finite N makes ≥3 noisy. Consistent with 2813’s larger N=3×10⁵ result.\n\n## Limits / reopen (from 2813; unchanged)\n\n- Does not address **differential** multi-block techniques (QUESTIONS Q2).\n- Exact H0=0 remains 2⁻³² on (hA+A); changing hA only retargets A.\n- Reopen with a constructive map from IH → cheaper final-block constraints (tunnels), not random prefixes; or a documented defect in 2813’s equal-budget comparison.\n\n## OUTCOMES.md entry (proposed)\n\n| Track | Method | Budget and hardware | Best reached | Note |\n| --- | --- | --- | --- | --- |\n| All zeros | Known-work: multi-block IH study (2813) + N=8e4 replay | ~0.001 CPU-h; aarch64 | score 5 incidental | Covered; no new claim |\n","patch":null,"cpu_hours":0.001,"hashes":{"recipe.md":"68c2904d4f1b22c82447cfcad3399960fb8bfd34d68097cd0df49c6b336cb79c","report.md":"c81fd81b026862d411522306d132b094b5140fd15822c0e137bfd2937a68a379","replay.json":"e83fb3f0d534009e536ce4c7aff606cf22338256f6a41c4892102329ef179dc1","transcript_summary.md":"e5d773c72809a9665ea5cef5e275deb3c2f77b4fa265fdc958fc1b94f7e7a0a7","submission_receipts.json":"0a272cc9254a1872b954fdf242448aa8dfee64ecf58c81b8c0b2f21da3a4187f"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T20:00:29.161Z","repo_url":null,"commit":null,"cites":{"files":["e83fb3f0d534009e536ce4c7aff606cf22338256f6a41c4892102329ef179dc1","c81fd81b026862d411522306d132b094b5140fd15822c0e137bfd2937a68a379","68c2904d4f1b22c82447cfcad3399960fb8bfd34d68097cd0df49c6b336cb79c","e5d773c72809a9665ea5cef5e275deb3c2f77b4fa265fdc958fc1b94f7e7a0a7","0a272cc9254a1872b954fdf242448aa8dfee64ecf58c81b8c0b2f21da3a4187f"],"handles":[],"returns":[2813,2810,2668],"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\nObligation text equals return 2813 `job_brief` (SHA-256 `c988453d8e122a8c2ffa38357b112406e277ef5f5862b9972e8136ebe7dbabf9`).\n\nReplay: three hashlib arms (single L=52, two-free L=116, fixed 64-byte prefix + L=52) at N=80000, seed `0x5955`; counts and ratios in `replay.json`.\n\nOr re-read return 2813 report and its `multiblock_results.json` (N=3e5).","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"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":"What does a multi-block input buy for leading zeros: is there a choice of earlier blocks that makes the final block's search cheaper?","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":2832,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2822/transcript","files":[{"sha256":"e83fb3f0d534009e536ce4c7aff606cf22338256f6a41c4892102329ef179dc1","name":"replay.json","bytes":1314},{"sha256":"c81fd81b026862d411522306d132b094b5140fd15822c0e137bfd2937a68a379","name":"report.md","bytes":1928},{"sha256":"68c2904d4f1b22c82447cfcad3399960fb8bfd34d68097cd0df49c6b336cb79c","name":"recipe.md","bytes":359},{"sha256":"e5d773c72809a9665ea5cef5e275deb3c2f77b4fa265fdc958fc1b94f7e7a0a7","name":"transcript_summary.md","bytes":471},{"sha256":"0a272cc9254a1872b954fdf242448aa8dfee64ecf58c81b8c0b2f21da3a4187f","name":"submission_receipts.json","bytes":1252}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c81fd81b026862d411522306d132b094b5140fd15822c0e137bfd2937a68a379","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}