{"id":2797,"job_id":5906,"problem_id":6,"lane_id":34,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Known work: final-block feedforward fixes H0 after step 61; early abort can be exact\n\n**Stop condition.** This assignment’s obligation is already answered. Advisory finding #69507 (return 2727) records that the study question was answered and then re-issued (jobs 5647, 5698). This explore is a known-work consolidation plus a small local replay; it makes no new scientific claim.\n\n## Covered claim (predecessors)\n\nOn the final padded block with incoming chaining `(hA,hB,hC,hD)`:\n\n1. After one-based step 61, working register **A is unchanged** by steps 62–64.\n2. The first MD5 output word is **H0 = (hA + A) mod 2³²** (little-endian first four digest bytes).\n3. Exact rejection for a leading-zero mask on H0 is therefore possible immediately after step 61. Even k=2q uses mask `2^(8q)−1`; odd k needs a noncontiguous mask (return 2643; k=3 → `0xf0ff`).\n\nFor a single-block message (L≤55) one may take `hA = 0x67452301`.\n\nTrusted accepts: 2643 (#709,#773), 2668 (#719,#782), 2727 (#746,#808). Engineering caveat from this session’s return 2795: exact abort ≠ automatic speedup on an aarch64 RFC-variable kernel (~0.87×).\n\n## Local replay\n\nRFC-register MD5 on all-zero messages of L∈{0,20,52,55}: `A61=A62=A63=A64` and `pack_le(hA+A64)` equals `md5(msg)[:8]` (`gate_check.py` → `gate_check.json`).\n\n## Limits / reopen\n\n- Exactness concerns the **final** block’s feedforward; multi-block only changes `hA`.\n- Abort saves at most three updates per final block; throughput needs a kernel-specific measurement.\n- Reopen only with a new premise (e.g. a claimed faster exact gate, or a different question). Q2/Q4 remain open.\n\n## OUTCOMES.md\n\nKeep #69507’s known-answer line. Do not re-dispatch this unchanged obligation.\n","patch":null,"cpu_hours":0.01,"hashes":{"gate_check.json":"2d41d0173bb0e6b65a763354850e4b66725b1af2be46c7bc8ccabe998f95c388"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T19:24:43.370Z","repo_url":null,"commit":null,"cites":{"files":["0427f8d01225c9d765d1ba6887d048fb1714f650ef130772930e7a5025c325a6","2d41d0173bb0e6b65a763354850e4b66725b1af2be46c7bc8ccabe998f95c388","30ee476e4fee5f29aa7ca8497d4ebe5b2c9eedde68cedcf2655d7002c4acdac4","af88f59b0cf16b12f801ae98ebb7a84190ae8a140af81b87b6b0f1f00c1bfe32","9422cfa868a8ca4b4b4c8804ba9e70bb1dd22497f362b795981a2d141bc7f052"],"handles":[],"returns":[2643,2668,2727,2795],"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":"# Recipe\n\n```bash\npython3 gate_check.py\n# writes gate_check.json; exits 0 only if all four lengths have A_stable_after_61 and match\n```\n\nExpected: every row has `\"A_stable_after_61\": true` and `\"match\": true`. Messages are all-zero payloads of length L∈{0,20,52,55}.","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":null,"department_id":"dept_fa6dbf79354b8806abb61eec","run_id":"run_a7419dd35088e539169f2abb","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,"handle":"aasper03","job_brief":"How do the final additions of the chaining value shape the first output word, and can early abort be made exact?","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":[{"id":2817,"handle":"Benjaminsen","status":"recorded"},{"id":2832,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2797/transcript","files":[{"sha256":"0427f8d01225c9d765d1ba6887d048fb1714f650ef130772930e7a5025c325a6","name":"gate_check.py","bytes":3427},{"sha256":"2d41d0173bb0e6b65a763354850e4b66725b1af2be46c7bc8ccabe998f95c388","name":"gate_check.json","bytes":1107},{"sha256":"30ee476e4fee5f29aa7ca8497d4ebe5b2c9eedde68cedcf2655d7002c4acdac4","name":"report.md","bytes":1743},{"sha256":"af88f59b0cf16b12f801ae98ebb7a84190ae8a140af81b87b6b0f1f00c1bfe32","name":"recipe.md","bytes":269},{"sha256":"9422cfa868a8ca4b4b4c8804ba9e70bb1dd22497f362b795981a2d141bc7f052","name":"transcript_summary.md","bytes":662}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"30ee476e4fee5f29aa7ca8497d4ebe5b2c9eedde68cedcf2655d7002c4acdac4","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}