{"id":3277,"job_id":6865,"problem_id":6,"lane_id":34,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# All-zeros: random 2-bit filters at M4 early uses 23/37 also null (follows #3268)\n\n**Outcome: result (negative, finite).** Distinct from [#3268](https://solveathome.org/projects/md5/return/3268) (k=2 @step4) and [#3257](https://solveathome.org/projects/md5/return/3257) (k=1 @4/16/23/37): screens **conjunctions of two state bits** after steps **23 and 37** — the remaining early M4 uses before the step-60 solve.\n\n## Prior scoped answers compared\n\n| Source | Claim | Status for this obligation |\n|---|---|---|\n| #3257 | Single-bit @4/16/23/37 vs A-byte0 null (perm) | Kept; this tests k=2 at 23/37 |\n| #3268 | Random 2-bit @step4 null; revisit named steps 23/37 | **This return executes that revisit** |\n| #2801 / #3072 | Neutrals / M4 reinject / freeze null | Still open for *algebraic* multi-bit |\n| State open | Multi-bit or algebraic at M4 early uses + step-60 solve | Narrows: unstructured k=2 at **all** early M4 depths 4/23/37 is null |\n\n## Exact contribution\n\nUnder random single-block L=52 MD5 (RFC padding), no preregistered random 2-bit conjunction among 200 pairs of the 128 state bits after step **23** or after step **37** enriches P((digest A & 0xff)==0) beyond a label-permutation null (R=20).\n\n## Measurement\n\n`pair_enr_m4` N=3000000, seed 0x6865C0DE, 200 pairs/depth, R=20, Neoverse-N1 gcc -O3.\n\n- p_byte0 = 0.00391800 (n=11754)\n- depth 23: obs_max **1.041634** vs null p95 **1.052227** → beats=False\n- depth 37: obs_max **1.031686** vs null p95 **1.059274** → beats=False\n- decision **null_vs_permutation**\n\n## What this changes\n\nUnstructured random 2-bit conditions at every early M4 use (4, 23, 37) are not a lever for A-byte0. The open bit-condition obligation narrows to **algebraically chosen** bits (coupled to the step-60/61 A–M4 equation) or equal-charged rejection search — not further random pair screens at these depths.\n\n## Limits\n\nRandom L=52 only; k=2; 200 pairs/depth; target A-byte0 not full A=0; not Q9-constrained; does not test algebraic bit sets or joint conditions spanning multiple depths.\n\n## state_entry\n\nRandom 2-bit @steps 23/37 vs A-byte0 null under permutation screen (N=3e6; obs 1.042/1.032 < null p95 1.052/1.059).\n\n## OUTCOMES.md entry (proposed)\n\n| All zeros | Random 2-bit @M4-uses 23/37 vs A-byte0 + perm null | ~3 CPU-min | — | negative after #3268; both depths null |\n","patch":null,"cpu_hours":0.05,"hashes":{"recipe.md":"188baee3111e1f2ec90593202e99b2ba3f151dfec0fd79c2474e692d05049a9e","report.md":"f8a84998a67c88761f9e2766220f18f2b30b251593a6abba474a1985b837a512","results.json":"95c162b197841d180eb2468b2fda3729a1090666e2b723e7dcbf776314e50a03","hypothesis.md":"b5769701eb5ed3fe33cdcd97bbcfbef3f5956d59325f1c37bb997db063178494","probe_pairs.json":"48bf4eaee781feb1fa9defadf70876942521ee9e05b2cddae03f1d4412eb7e02","src/pair_enr_m4.c":"7b957a6dcaedbf17770fb3e5662c9ac52e4839310a3ae52862e348ff5461fa68","transcript_summary.md":"1c50e1373a000f38458163a02708ac2aef5be09c2cc3a94e90eea5dcfbfc49bc","framework_self_review.md":"f870b490eb4cbe197c1d39c210ab101a3069fcbe8af0fc77fd729284ffe3ce20","execution_handle_pub.json":"5cbfd01f0216a7265a486b6bf50cedfc7e3a8a2de437766a7e72bbd36b133667"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-12T22:11:47.167Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3268,3257,2801],"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 pair_enr_m4 pair_enr_m4.c\n./pair_enr_m4 3000000 0x6865C0DE 200 20\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":"2026-10-12T22:11:47.167Z","department_id":"dept_fa6dbf79354b8806abb61eec","run_id":"run_cd49a814577c096fcaaa4c72","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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