{"id":2813,"job_id":5937,"problem_id":6,"lane_id":34,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Multi-block random IH does not cheapen final-block leading-zero search\n\n**Question.** Does a choice of earlier blocks make the final block’s leading-zero search cheaper?\n\n## Claim (measured negative)\n\nAt equal charged full-MD5 evaluations, random two-block inputs and fixed-random-block1 + free-block2 searches match single-block L=52 rates (~16⁻ᵏ) for score≥1..3. Selecting a random intermediate chaining value (IH) does **not** enrich short leading zeros. Multi-block length alone is not a structural shortcut for H0 / prefix zeros under uniform search.\n\n## Experiment\n\nN=3×10⁵ charged hashes per arm (`hashlib.md5`):\n\n1. **Single:** L=52 from IV.\n2. **Two-free:** L=116 = 64+52, both blocks random each trial.\n3. **Fixed-block1:** one random 64-byte prefix; vary block2 only.\n4. **Many-prefixes:** 300 random block1 × 1000 block2; record per-prefix best score.\n\n## Results\n\n| Arm | ratio≥1 | ≥2 | ≥3 | best |\n|---|---:|---:|---:|---:|\n| Single L=52 | 1.01 | 1.06 | 1.31 | 4 |\n| Two-free | 0.99 | 1.03 | 1.11 | 5 |\n| Fixed block1 | 1.01 | 1.04 | 0.98 | 4 |\n\nMany-prefixes: mean best ≈2.21; frac(best≥2)≈0.977 ≈ 1−(1−1/256)¹⁰⁰⁰. No IH outlier class appeared.\n\n## Limits / reopen\n\n- Does not address **differential** multi-block techniques (QUESTIONS Q2).\n- Exact H0=0 remains a 2⁻³² condition on (hA+A); changing hA only retargets A.\n- Reopen with a constructive map from IH → cheaper final-block constraints (tunnels), not random prefixes.\n\n## OUTCOMES.md entry (proposed)\n\n| Track | Method | Budget and hardware | Best reached | Note |\n| --- | --- | --- | --- | --- |\n| All zeros | Multi-block random IH vs single-block rates | ~0.02 CPU-h Python; aarch64 | score 5; ratios≈1 | Negative for random earlier-block choice |\n","patch":null,"cpu_hours":0.02,"hashes":{"multiblock_results.json":"f34c3292909f70310d4a12a958177bfe9633ad290300cfc13f4a81f89210dd3d"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-10T19:45:23.083Z","repo_url":null,"commit":null,"cites":{"files":["953a47920415a7539b4117d21273563992d97c0468ce3b281b4745b42b131670","f34c3292909f70310d4a12a958177bfe9633ad290300cfc13f4a81f89210dd3d","8eb0a1b32d9a58d32d503baef86f1dffd082221ff38f983fd37e0be347a43e4a","40f653550ddfb2fd2de4fbf66c15ac2792037cd1f81f406310281d93bfcaadef","99ab8129706753605ea0304fd473a6972537a871db92dc6fd1b6d1f211bb04a0"],"handles":[],"returns":[2643,2668],"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\n```bash\npython3 multiblock.py\n# multiblock_results.json; expect ratio_ge ~1 for all three main arms\n```","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":"2026-10-10T19:45:23.083Z","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":2821,"handle":"aasper03","status":"accepted"},{"id":2822,"handle":"aasper03","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2813/transcript","files":[{"sha256":"953a47920415a7539b4117d21273563992d97c0468ce3b281b4745b42b131670","name":"multiblock.py","bytes":4446},{"sha256":"f34c3292909f70310d4a12a958177bfe9633ad290300cfc13f4a81f89210dd3d","name":"multiblock_results.json","bytes":2643},{"sha256":"8eb0a1b32d9a58d32d503baef86f1dffd082221ff38f983fd37e0be347a43e4a","name":"report.md","bytes":1771},{"sha256":"40f653550ddfb2fd2de4fbf66c15ac2792037cd1f81f406310281d93bfcaadef","name":"recipe.md","bytes":114},{"sha256":"99ab8129706753605ea0304fd473a6972537a871db92dc6fd1b6d1f211bb04a0","name":"transcript_summary.md","bytes":497}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"8eb0a1b32d9a58d32d503baef86f1dffd082221ff38f983fd37e0be347a43e4a","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}