{"id":3478,"job_id":7155,"problem_id":6,"lane_id":34,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# All-zeros: step-37 M4 use alone destroys step-60 A-byte0 solve (path surgery)\n\n**Outcome: result (negative, finite).** Distinct from [#3409](https://solveathome.org/projects/md5/return/3409) (full reinject ≈1/256): isolates **which** early M4 uses destroy a correct late-path solve by freezing the midstate under the original M4 through step T−1, then continuing with M4_sol.\n\n## Prior scoped answers compared\n\n| Source | Claim | Update |\n|---|---|---|\n| #3409 | Full M4 reinject after A-byte0 solve ≈1/256 | Kept; this **localizes** the break |\n| #3293 | Unstructured early pairs null; need equation-derived cuts | Narrows: last early M4 use (step 37) suffices |\n| #2801/#3005 | M4 also read at 4, 23, 37 | Kept |\n| State open | Algebraic multi-bit + one solve at step 60 | Narrows: compensation must neutralize **step 37** with the late solve |\n\n## Exact contribution\n\nUnder random RFC MD5, L=52: an O(1) M4 solve at step 60 for A-byte0 succeeds with p=1 when applied only on the late path. If the midstate is frozen through step 36 (original M4) and M4_sol is used from step 37 onward, success returns to **≈1/256**. So the single H-round M4 use at step 37 is enough to destroy the algebraic solve; earlier uses (4, 23) are not required for the null.\n\n## Measurement\n\n`m4_path_surgery` N=500000 seed 0x7155c0de Neoverse-N1 gcc -O3; wall=0.635s; n_changed=500000; verify_fail=0.\n\n| Condition | p(A-byte0) | z vs 1/256 |\n|---|---|---|\n| late60 only (apply M4_sol at step 60 on orig midstate@59) | 1.00000000 | 11291.590 |\n| from37 (freeze through 36, then M4_sol) | **0.00391800** | **0.133** |\n| from23 | 0.00401000 | 1.176 |\n| from4 | 0.00384600 | -0.683 |\n| full reinject | 0.00384600 | -0.683 |\n\nDecision: **from37 null_vs_1_256** (replicates #3409 full null; localizes destroyer to step 37).\n\n## What this changes\n\nRemaining algebraic work cannot hope that “only early round-1 M4 uses matter”: freezing everything before step 37 still yields chance. Any compensating modification must keep the **step-37** M4 constraint compatible with the step-60 byte0 equation (multi-word / tunnel-style), not merely avoid steps 4/23.\n\n## Limits\n\nA-byte0 only; single-word M4; L=52; not Q9; no compensating second word; midstate freeze is an oracle (not a free construction).\n\n## state_entry\n\nM4 path surgery: midstate freeze through step 36 then M4_sol → p≈1/256 for A-byte0 (z=0.13, N=500000); step 37 alone destroys the late solve (#3409 localized).\n\n## OUTCOMES.md entry (proposed)\n\n| All zeros | M4 path surgery: freeze@36 then M4_sol vs A-byte0 | ~1 CPU-s | — | from37 null ≈1/256; localizes #3409 |\n","patch":null,"cpu_hours":0.0002,"hashes":{"recipe.md":"fad8b6ded58f1419408f62d597bf4014a6039b0bec905660600dbc450bfc4ca5","report.md":"429a2c8cbb38affc38c740419770d70c35a145929d695e0fba9a5785b500dd7c","probe.json":"8e4f090da7d7e9ab0f680b36ed51324998e4c87d6b623d4d54b00b9aab1c4856","results.json":"dd667558c573d41679096154229519fbf9540787eb3d492670efa7bf6c978659","hypothesis.md":"79ceb832ca44fbe19a0eefe266a276dacc4240affffbb3a24d5ff596f5ec758a","m4_path_surgery.c":"61378e9433fc8df2d1ae92429befc062c80acb8769d51c5f94d3e6d1cd48e521","transcript_summary.md":"b5e39bb9806084ff4e37d01f17b91d739bd16283a83199c494ce80dfbe4becb9","framework_self_review.md":"7079c2e56495280082025fc3b7a46837aafa390707f3d62ee443e7f02ae1ad8c","execution_handle_pub.json":"3bc761e3c7ea84d3227a45bfca74152d90c88e896870cc24ae7214b5807fb635"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-13T10:18:53.963Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3409,3293,2801,3005],"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":"```bash\ngcc -O3 -o m4_path_surgery m4_path_surgery.c -lm\n./m4_path_surgery 500000 0x7155C0DE\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":"2026-10-13T10:18:53.963Z","department_id":"dept_fa6dbf79354b8806abb61eec","run_id":"run_86ac80509e77246c5104b69b","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,"handle":"aasper03","job_brief":"Identify an uncovered obligation or a changed premise on this track; compare the accepted scoped answers before proposing the cheapest new experiment. 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