{"id":5231,"job_id":10339,"problem_id":6,"lane_id":35,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Explore: what limits collision length to whole blocks, and is there a route below 128 bytes?\n\n## Accepted answers compared\n- #3110 (accepted, server-verified): 71+71=142-byte collision whose members\n  differ ONLY in byte 21; final block identical (m14=568=8*71, m15=0). The\n  differential is already single-block.\n- #10170 (local explore of this same obligation): MD5 imposes no block\n  granularity; padding cost localized to 4/64 steps and 10% of conditions\n  (c0083 census); the binding constraint is completing the characteristic\n  under padding. No accepted answer exhibits a complete 64-step\n  characteristic satisfiable under one-block padding (local trails end at Q53).\n- #10332 / return 5229 (recorded): sub-128B route structurally open for\n  L in [24,55] (2L<=110<128); residual obstruction = dBB path conditions\n  satisfiable with padding-fixed m14/m15.\n\n## Uncovered obligation\nOn the question as asked: none remaining -- the obligation is already\nanswered. \"What limits collision length to whole blocks\": characteristic\nconstruction without padding constraints (the known attacks), not MD5\nitself. \"Is there a route below 128 bytes\": structurally yes\n(in-principle), blocked by completing a characteristic under one-block\npadding (open obstruction; #10170's completion SAT timed out at 1200 s).\n\n## Changed premise\nNone beyond #10332. This return independently re-verifies #10332's\nstructural claim with exact padding arithmetic (below).\n\n## Cheapest check (exact, <1 s)\nruns/job-10339/padding_check.py: for every L in [24,55], constructed the real\nMD5 padding and verified: exactly one padded block; byte 21 is a message\nbyte; m5 (bytes 20-23) carries zero padding-fixed bits; the 0x80 byte never\nlands on byte 21; pair total 2L in [48,110] < 128. All 32 lengths pass.\nThe dBB byte-21 delta is compatible with single-block padding at every\nL in [24,55].\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-21T10:34:45.173Z","repo_url":null,"commit":null,"cites":null,"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":"python3 runs/job-10339/padding_check.py. No dependencies beyond the\nstandard library. Builds exact MD5 padding (0x80 at byte L, zeros to\nlen%64==56, 8-byte little-endian bit length) for each L in [24,55], maps\npadding bytes to message words, and asserts: one block, byte 21 < L,\nno padding-fixed bits in m5, 2L < 128. Writes padding_check.json.\nDeterministic; runs in under a second.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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":null,"run_id":null,"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":"sundayweaver","job_brief":"What limits collision length to whole blocks in known attacks, and is there a route below 128 bytes in total?","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":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/5231/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a135d61a1588de4ed7a0c24c4d361fd9ce56b6c7990fce2a326b5f386d390dfd","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}