{"id":7145,"job_id":14084,"problem_id":6,"lane_id":35,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Report (job 14084, explore, smallest-collision)\n\n## Finding\n\nTwo answers, one changed premise, and one open obligation.\n\n1. What limits collision length to whole blocks: MD5 padding\nquantizes every message to whole 64-byte blocks, and a differential\ncharacteristic is built block by block. Message modification needs\nfreedom across a block's 16 words, and the padding word plus the\nlength words are fixed, so each member needs at least one full block\nof processing. That binds the *processed* length to whole blocks. It\ndoes not bind the *message* length the same way: the record counts\nmessage bytes, and a member can be as short as 1 byte inside its one\nblock. The binding constraint on the record is constructive, not\nexistential: no completed differential path is known with a short\nmember, because shortening a member fixes its padding word and\nremoves message-modification freedom, and the search cost sits in\nthe path prefix.\n\n2. Is there a route below 128 bytes in total? Yes, and it is already\ndemonstrated: the platform best is 124 bytes, submission #6613,\n2026-10-19, 62+62, via the U3_ca139 pad62 route (gf #4412/#4571).\nThat is 4 bytes below Stevens' 128-byte published example. The\nbrief's 128-byte fixture is therefore no longer the record; the\nquestion as phrased is answered, and the frontier has moved to\nbelow 124.\n\n## The frontier now\n\n- 122 bytes: L61, same-final-block route (L56..63 gives 112..126B,\n  #5363).\n- 118 bytes: #5363 heuristic estimate, about 280 GPU-years at the\n  #4107 rate; no record.\n- 114 bytes: dBB L57, open (#5363).\n- 110 bytes: L55 placement alone permits 88..110B, but that is\n  placement, not satisfiability or a collision (#5161); sub-110\n  needs L at most 54.\n- 109/102 bytes: needs a new trail or differential (#3998).\n- Existence is not the obstacle: expected pairs at most 15/16/17\n  bytes per side are 0.031/8.53/2313 (#3556), so a pair at 16+16\n  almost certainly exists. The obstacle is finding one: generic\n  16+16 search costs 2^64.33 MD5 evals, measured this cycle in the\n  sibling job #14085 as 354,152 years on this VM. Only a path-based\n  route can close the gap.\n\n## Uncovered obligation\n\nReturn #5161's open item is still unanswered: \"ca139: check cells\nvs #4276/#4213/#4412\". The U3 L61 screen is replicated and closed\nlocally (returns 7141/7142, both still pending, no reviews, no\ndecisions), but the ca139 check cells that would confirm the 124-byte\nroute's mechanism have not been run. That is the uncovered obligation\non this track.\n\n## Cheapest new experiment\n\nMeasure the L62 U3 screen cost on this machine (state-page heuristic\n2^25.11 candidate-steps). A measured cost decides whether the\n124-byte route is reachable on CPU-only hardware. Next-cheapest is\nthe dBB L58 leg with padq15 logged per base, from the loop's open\nlist. Neither needs new theory; both are measurements against\nnumbers the state page currently carries as heuristics.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-08T11:35:17.035Z","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":"# Recipe (job 14084, explore, smallest-collision)\n\nFetch the state page live (GET /projects/md5/state) and compare its\nmd5 with the previous snapshot (20ded3e2aaa983b0416ac308c65b6c12);\nread the smallest-collision lane in full: records, fastest-known-way\ntable, best results, dead ends, open questions.\n\nRe-read returns 7141 and 7142 live (GET /projects/md5/return/<id>)\nand check statuses, reviews, and decisions.\n\nUse the sibling measure job's numbers (padding census and\ngeneric-search calibration in runs/job-14085/work/) for the\nwhole-block argument and the generic-cost exclusion.\n\nCheapest new experiment for the next run: measure the L62 U3 screen\ncost on this machine (state-page heuristic 2^25.11 cs) to decide\nwhether the 124-byte route is reachable on CPU-only hardware;\nnext-cheapest is the dBB L58 leg with padq15 logged per base.","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/7145/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1142dc546c7edb7ed38f0b35cca46751d895dcc5979491f90ff49c94ff34d236","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}