{"id":5235,"job_id":10346,"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; m15 is shared by both members.\n- #10332 / return 5229 (recorded): sub-128B route structurally open for\n  L in [24,55] (2L<=110<128); residual obstruction = completing a\n  characteristic under padding.\n- #10339 / return 5231 (recorded): independent re-verification of the above;\n  obligation on the question as asked is answered; obstruction is\n  characteristic completion under padding.\n- #10338 / return 5230 (measure, pending triage): m15 top-byte padding screen\n  over the 163-path #4307 corpus: 46/163 admit top byte 0x00 (L=62 route),\n  56/163 admit top byte 0x80 (L=63 route).\n\n## Uncovered obligation / changed premise\n#10338's L=62 number used the NECESSARY top-byte condition only. Exact MD5\npadding at L=62 fixes two bytes of m15: byte 62 = 0x80 (first padding byte),\nbyte 63 = 0x00 (zero fill; the 8-byte length lives in block 1), i.e.\n(m15>>16)&0xFF == 0x80 AND (m15>>24)&0xFF == 0x00. At L=63 the top-byte\ncondition is already exact (byte 63 = 0x80; byte 62 is a free message byte).\nSo the true L=62 candidate pool was never measured -- 46/163 was an\noverestimate, and the L=62 vs L=63 asymmetry reported in #10338 is sharper\nthan stated.\n\n## Cheapest decisive check\nruns/job-10345/m15_exact.py: the identical #10338 completion scan (same\n163-path corpus, seed 10338, 2^18 cap, same step-15 m15 formula), now also\ntesting the two-byte condition. ~35 s on one CPU core.\n- L=63 exact: 56/163 (replicates #10338 exactly; scan consistent)\n- L=62 necessary (top byte): 46/163 (replicates #10338)\n- L=62 EXACT (two bytes): 2/163 (corpus paths 80, 82)\n- 44 necessary-but-not-exact dropouts resampled at 2^20 (seed 10346): 0 flips\n- Direct verification: a path-80 admitting completion has m15 = 0x00804813\n  (top byte 0x00, byte2 0x80), byte-exact.\n\nThe L=62 route's padding-feasible pool is 2 paths, not 46. The remaining\nobstruction is unchanged in kind (completing a characteristic under padding)\nbut its search space just shrank ~23x: any L=62 connect/completion effort\nshould target paths 80 and 82 first.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-21T11:02:00.191Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"cron worker harness (Muse Spark scheduled run) keeps no per-job token usage record","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"python3 runs/job-10345/m15_exact.py (needs numpy). Replays the #10338\ncompletion scan over tools/r301/paths_C13q.jsonl (Q12..Q16 free-bit\ncompletions, seed 10338, 2^18 cap), computes m15 per completion via the\nstep-15 inversion m15 = RR(Q16-Q15,22) - F(Q15,Q14,Q13) - Q12 - K15, and\ntests the L=63 exact (top byte 0x80), L=62 necessary (top byte 0x00) and\nL=62 exact (top byte 0x00 AND byte2 0x80) conditions. Resamples dropouts at\n2^20 (seed 10346). Writes m15_exact_result.json. Deterministic; ~35 s on\none EPYC 9D64 core. Full script text is in return #10345's recipe_md\n(same experiment, filed this cycle).","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/5235/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b791b39957699b8fd3db92974d505a874e872bb7a4edd5ce484e056f925a8154","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}