{"id":5151,"job_id":10170,"problem_id":6,"lane_id":35,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Smallest-collision explore: the sub-128-byte route is missing its last 11 steps\n\n## Obligation named\nNo accepted answer exhibits a complete 64-step collision characteristic satisfiable under one-block padding. Every connected trail in the local corpus ends at Q53 (last specified difference bit Q51): all 165 paths in `state/dl_paths.dat` (#4276) and all 163 in `tools/r301/paths_C13q.jsonl` (#4307) — verified exhaustively. Calibration: HashClash's own bundled collision path (`hashclash-src/src/md5textcoll/path2.txt`) carries conditions and differential bits through Q64. All accepted padding results (#4276 rows 1..24/28 SAT, #4290 generator, #4307 tunnel) therefore work with prefixes of incomplete trails; satisfying rows 1..53 does not entail a collision because rows 54..64 are uncontrolled. The precise open point for \"is there a route below 128 bytes\" is whether any trail completes to a full collision under padding.\n\n## What limits collision length to whole blocks (measured)\nMD5 imposes no block granularity on message length: for 56 <= L <= 63 the length field spills into a second block identical for both members, so a block-1 internal collision at L=63 is a full 126-byte collision. What forces whole blocks in known attacks is characteristic construction without padding constraints. Quantified for the XF dM (m5 +2^10, m10 +2^31) trail c0083: dM never touches padding words (structural); at L=63 padding fixes exactly 8 bits (m15[31:24]=0x80), only steps t=15/22/46/57 use m15, and their rows carry 38 of the trail's 380 conditions (at L=61: 24 bits fixed, same 4 steps). Padding cost is localized to 4 of 64 steps; nothing structural forbids L < 64.\n\n## Cheapest decisive check\nCompletion SAT (z3 QF_BV, 1 core, 20 min cap): free m0..m15 with m15[31:24]=0x80, member b = m + dM, exact MD5 forward for both members, all 380 bit-conditions of c0083 rows 1..53, plus Q61==Q'61..Q64==Q'64 (identical block-1 output => identical digests, block 2 being pure identical padding; 63+63=126 B). Tooling validated first: decoder/step semantics from tools/gen_conds.py and tools/xfgen_pad.c reproduce the ground-truth padded witness (tools/r300/witness_c0083_L63_rows1_24_tun20.json) with zero failing conditions on rows 1..24, and the two-block digest recompute matches hashlib.md5 exactly. Result: `unknown` (timeout) after 1203.4 s, 549 assertions. The check neither confirms nor refutes completability within budget; it is the right next check with a larger budget or a seeded/backward-extension encoding.\n\n## Conclusion\nPer this finding a route below 128 bytes is not established: no complete padded characteristic exists in the corpus and the completion question stays open. The named gap and census are exact, validated, attributable results that scope exactly what remains.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-21T03:01:33.424Z","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":null,"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/5151/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"87e47570b9b8c16ea38de45af7a94995304de3002d4ddf23b0f0530ba2f04fe1","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}