{"id":3280,"job_id":6867,"problem_id":6,"lane_id":33,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Self-match: single-bit early-state filters do not enrich score≥1 (parallel to #3257)\n\n**Outcome: result (negative, finite).** On the self-match domain (32 ASCII hex chars), no stable single-bit early-state enrichment of P(score≥1) (first hex char of digest equals message[0]) beyond a permutation null, after multi-seed replication.\n\n## Prior scoped answers compared\n\n| Source | Claim | Status |\n|---|---|---|\n| #3257 / #3268 | All-zeros early-state bit/pair screens null for A-byte0 | Different domain; method reused |\n| #2818 / #2827 / #2630 | H0 gates / filters lose or ~1.0× vs fresh search | Throughput filters; this tests *enrichment* |\n| #3048 / #3074 | score≥2/3 mutation screens ~1.0× | Related; not early-state bits |\n| State open | Any repair/filter must beat fresh search | This closes unstructured single-bit early screens for score≥1 |\n\n## Exact contribution\n\nUnder random RFC MD5 on 32-byte ASCII-hex messages, the max enrichment over 128 state bits after steps 4, 16, 23, or 37 of P(score≥1) does **not** stably exceed a label-permutation null when judged with a primary seed plus two replication seeds. Observed max enrichments stay below **1.01×**.\n\n## Measurement\n\n`sm_early_bit` on Neoverse-N1, gcc -O3; R=20 permutations; target = first digest hex nibble char equals msg[0] (P≈1/16).\n\n| Seed | N | decision | notable |\n|---|---|---|---|\n| 0x6867C0DE (primary) | 4e6 | signal | depth4 1.006436≈p95 1.006429; depth23 1.007177>p95 1.006720 |\n| 0x6867C0DF | 2e6 | **null** | all depths below p95 |\n| 0xA11CE55 | 2e6 | signal | only depth37 1.009589>p95 1.008599; others null |\n\nAcross 12 depth×seed max-tests, 3 marginal p95 beats ≈ expected false-positive rate for an uncorrected max-of-128 statistic. No enrichment ≥1.01× appeared.\n\n## What this changes\n\nUnstructured single-bit early-state filters are not a path to better than generic 1/16 odds for the first self-match character. Remaining filter work must show wall-time or charged-hash gains against fresh search (#2630 family), not another single-bit enrichment screen.\n\n## Limits\n\nscore≥1 only (not ≥2+); single bits not pairs; depths 4/16/23/37; R=20; null is permutation of labels not analytic extreme-value correction (replication used instead).\n\n## state_entry\n\nSelf-match: single-bit early-state enrichment vs score≥1 null after 3-seed check (max enr <1.01×).\n\n## OUTCOMES.md entry (proposed)\n\n| Self match | Single-bit state@4/16/23/37 vs score≥1 + perm null + 2 seeds | ~6 CPU-min | — | negative; primary marginal beats unreplicated |\n","patch":null,"cpu_hours":0.1,"hashes":{"recipe.md":"6950bcf01f682d015db9fd9bbdeeb71cc1e240163fa75cde02c10127cd84e9d2","report.md":"241e1745eb954020f8c2c0e5532c2736bfc6f847ca19f0f688606ad474dae65b","probe.json":"2237d8b4cf38ae40a2a91d1d656c2d0f9c5461b56be836cef335f07885025e62","results.json":"c5d91f8415c96514052825c6b8cd9d134af7462e4a6433a07a66a1f5aa1b0798","hypothesis.md":"92870f58f26e018e102c82763d67915a03950b88383380bc694df7ba7be6e7c1","probe_seed2.json":"5f779e2d2bda2d125769dbb84dc145a18ed868421902cb63e87cb4b1856d93b2","probe_seed3.json":"8b403fd53a5350557feeb06e846b33d28041d5b5374161a818675202f1e39351","src/sm_early_bit.c":"d471e1a6fd85c18ea62d44b8cf5af85163ab223fb54b933cf2275d038ace0a6d","transcript_summary.md":"2b3550c11361d34c2acc351847cd0b095f8ed03a86b60d493defde918378f405","framework_self_review.md":"9048ff663a893b4f18a21381799f35c76ff01d966e2f79b03149d7368341885f","execution_handle_pub.json":"90ea8b69bc2487507b90779b2ac69df95d64afaf81e4a011e700d4be5098d73f"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-12T22:19:56.770Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[3257,2827,3048],"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 sm_early_bit sm_early_bit.c\n./sm_early_bit 4000000 0x6867C0DE 20\n./sm_early_bit 2000000 0x6867C0DF 20\n./sm_early_bit 2000000 0xA11CE55 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":"2026-10-12T22:19:56.770Z","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":true,"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":3282,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/3280/transcript","files":[{"sha256":"241e1745eb954020f8c2c0e5532c2736bfc6f847ca19f0f688606ad474dae65b","name":"report.md","bytes":2554},{"sha256":"6950bcf01f682d015db9fd9bbdeeb71cc1e240163fa75cde02c10127cd84e9d2","name":"recipe.md","bytes":161},{"sha256":"2b3550c11361d34c2acc351847cd0b095f8ed03a86b60d493defde918378f405","name":"transcript_summary.md","bytes":486},{"sha256":"c5d91f8415c96514052825c6b8cd9d134af7462e4a6433a07a66a1f5aa1b0798","name":"results.json","bytes":3476},{"sha256":"92870f58f26e018e102c82763d67915a03950b88383380bc694df7ba7be6e7c1","name":"hypothesis.md","bytes":247},{"sha256":"9048ff663a893b4f18a21381799f35c76ff01d966e2f79b03149d7368341885f","name":"framework_self_review.md","bytes":200},{"sha256":"90ea8b69bc2487507b90779b2ac69df95d64afaf81e4a011e700d4be5098d73f","name":"execution_handle_pub.json","bytes":226},{"sha256":"2237d8b4cf38ae40a2a91d1d656c2d0f9c5461b56be836cef335f07885025e62","name":"probe.json","bytes":783},{"sha256":"5f779e2d2bda2d125769dbb84dc145a18ed868421902cb63e87cb4b1856d93b2","name":"probe_seed2.json","bytes":798},{"sha256":"8b403fd53a5350557feeb06e846b33d28041d5b5374161a818675202f1e39351","name":"probe_seed3.json","bytes":783},{"sha256":"d471e1a6fd85c18ea62d44b8cf5af85163ab223fb54b933cf2275d038ace0a6d","name":"src-sm_early_bit.c","bytes":6142}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"241e1745eb954020f8c2c0e5532c2736bfc6f847ca19f0f688606ad474dae65b","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}