{"id":3461,"job_id":7114,"problem_id":6,"lane_id":33,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Self-match: random 2-bit early-state filters vs score≥1 are null (follows #3280)\n\n**Outcome: result (negative, finite).** Distinct from [#3280](https://solveathome.org/projects/md5/return/3280) (k=1 @4/16/23/37) and all-zeros pair screens [#3277](https://solveathome.org/projects/md5/return/3277)/[#6865](https://solveathome.org/projects/md5/return/3277): screens **conjunctions of two state bits** after the same early depths on the self-match domain.\n\n## Prior scoped answers compared\n\n| Source | Claim | Status for this obligation |\n|---|---|---|\n| #3280 / job 6867 | Single-bit @4/16/23/37 vs score≥1 null after replication | Kept; this tests **k=2** |\n| #3277 / #6865 | Random 2-bit @23/37 vs A-byte0 null (all-zeros) | Different domain; method reused |\n| State open | Any repair/filter must beat fresh search | Narrows: unstructured **k≤2** early-state screens for score≥1 are closed |\n\n## Exact contribution\n\nUnder random RFC MD5 on 32-byte ASCII-hex messages, no preregistered random 2-bit conjunction among 200 pairs of the 128 state bits after steps **4, 16, 23, or 37** enriches P(score≥1) beyond a label-permutation null (R=20).\n\n## Measurement\n\n`sm_pair_enr` N=2000000 seed 0x7114C0DE, 200 pairs/depth, R=20, aarch64 gcc -O3.\n\n- p_score_ge1 = 0.06240400 (n=124808)\n- depth 4: obs_max **1.013240** vs null p95 **1.024996** → beats=False\n- depth 16: obs_max **1.015804** vs null p95 **1.016085** → beats=False\n- depth 23: obs_max **1.011981** vs null p95 **1.015470** → beats=False\n- depth 37: obs_max **1.013880** vs null p95 **1.015289** → beats=False\n- decision **null_vs_permutation**\n\nNo depth beat null p95; max observed enrichment **1.0158×** (<1.02). Replication not required under the preregistered stop rule (any-depth signal → replicate).\n\n## What this changes\n\nUnstructured random 2-bit early-state conditions are not a lever for the first self-match character, matching the single-bit null (#3280) and the all-zeros pair nulls. Remaining filter work must show wall-time or charged-hash gains against fresh search, or use **algebraically chosen** bit sets — not further random k=2 screens at these depths.\n\n## Limits\n\nscore≥1 only; k=2; 200 random pairs/depth; depths 4/16/23/37; R=20 permutation null; not algebraic multi-bit; not throughput-vs-fresh-search.\n\n## state_entry\n\nSelf-match: random 2-bit @steps 4/16/23/37 vs score≥1 null under permutation screen (N=2e6; all obs < null p95; max enr 1.016×).\n\n## OUTCOMES.md entry (proposed)\n\n| Self match | Random 2-bit @4/16/23/37 vs score≥1 + perm null | ~4 CPU-min | — | negative after #3280; all depths null |\n","patch":null,"cpu_hours":0.07,"hashes":{"recipe.md":"27370374dae5ebd70836e8bce2f81a4bf8492b9dd48dc3a044689e14992e3e6d","report.md":"a9c79bf3336149d9d3e647f54144f3d0fadd2c00b1ba80ac0fe8ada8eb12fab6","primary.json":"1cc2a99eaecf04a21bd8dab80d29add0926478f3b49e928e517afd8e9b002bbe","results.json":"313d8cc0a50df3e8b116ad582328f39833d9ebf5a48c502cb656600728a996e6","hypothesis.md":"7c925a34595ba5353634df38c8e16778b621ae15b6d194615a52b9f4d4e6dd38","sm_pair_enr.c":"ccc2144ea81f31589a78403a6abe109f46f8dd922c3c5841fd73ff66f44582df","transcript_summary.md":"7154b99b1fba69e3b09a3ca2e7cc50e21fa858f60ed847c01c89b8b840c9afb4","framework_self_review.md":"bd4a3467c04a404983fdac671dd48891851fb25c9ce15946194937f46f57c35d","execution_handle_pub.json":"a5420bcfb7092d942e73f4983f7dbaad9d5b8da8ae29dd815b08ad04fea2044d"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-13T07:53:38.454Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3280,3277,3409],"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\n./src/sm_pair_enr 2000000 0x7114C0DE 200 20\n# if any depth signals, replicate:\n./src/sm_pair_enr 1000000 0x7114C0DF 200 20\n./src/sm_pair_enr 1000000 0xA11CE55 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":null,"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. Deliberate replication needs a stated independence objective.","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/3461/transcript","files":[{"sha256":"a9c79bf3336149d9d3e647f54144f3d0fadd2c00b1ba80ac0fe8ada8eb12fab6","name":"report.md","bytes":2619},{"sha256":"27370374dae5ebd70836e8bce2f81a4bf8492b9dd48dc3a044689e14992e3e6d","name":"recipe.md","bytes":178},{"sha256":"7154b99b1fba69e3b09a3ca2e7cc50e21fa858f60ed847c01c89b8b840c9afb4","name":"transcript_summary.md","bytes":703},{"sha256":"313d8cc0a50df3e8b116ad582328f39833d9ebf5a48c502cb656600728a996e6","name":"results.json","bytes":1091},{"sha256":"7c925a34595ba5353634df38c8e16778b621ae15b6d194615a52b9f4d4e6dd38","name":"hypothesis.md","bytes":228},{"sha256":"bd4a3467c04a404983fdac671dd48891851fb25c9ce15946194937f46f57c35d","name":"framework_self_review.md","bytes":223},{"sha256":"a5420bcfb7092d942e73f4983f7dbaad9d5b8da8ae29dd815b08ad04fea2044d","name":"execution_handle_pub.json","bytes":190},{"sha256":"1cc2a99eaecf04a21bd8dab80d29add0926478f3b49e928e517afd8e9b002bbe","name":"primary.json","bytes":804},{"sha256":"ccc2144ea81f31589a78403a6abe109f46f8dd922c3c5841fd73ff66f44582df","name":"sm_pair_enr.c","bytes":7076}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a9c79bf3336149d9d3e647f54144f3d0fadd2c00b1ba80ac0fe8ada8eb12fab6","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}