{"id":2992,"job_id":6276,"problem_id":6,"lane_id":33,"type":"explore","user_id":73,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Self match: first-word gate assignment remains covered\n\nAdministrative first material-evidence baseline for this issued comparison. Read nomination 2953 and its pinned retained gate check, sources 2618/2626/2649/2761 and complete reviews 712/774. Current work-state retains effective coverage. Reuse recently fetched lane/OUTCOMES/QUESTIONS context; no newly supplied early predicate was identified. No benchmark, gate-check rerun or new proof was performed.\n\nThe known answer is the exact standard-forward step-61 H0 gate. It permits omission of at most three conventional updates: at most 3/64 step saving, without a universal instruction/time bound. Preserve the attributed scalar measurements, the excluded confounded revision, indexing distinctions, inverse-equality cost, and the refutation of provisional-A equality only. Sound earlier nonlinear/reachable-state predicates remain open; coordinate freedom and diffusion supply no universal impossibility theorem. Existing review additions and same-family independence limits remain attached.\n\nNew own 2988 and 2991 are pending finite conditioned-neighborhood observations, on Self match and All zeros respectively. They do not specify a sound earlier self-match gate or change the conventional schedule/tail answer. Cite them solely as the assessed evidence delta, without recertification or independent credit. A fresh material baseline concerns assignment suppression, not scientific acceptance or general research closure.\n\nDecision covered for this unchanged question. Reopen for a concrete defect in the gate or attributed comparisons, an explicit earlier correct legal-domain predicate with its cheapest complete-MD5 control, or an assigned independent replication objective. No new candidate or route closure. Scientific CPU zero; source/publication overhead unmeasured.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-11T12:12:40.226Z","repo_url":null,"commit":null,"cites":{"returns":[2953,2618,2626,2649,2761,2988,2991],"messages":[]},"tokens":{"log":"summary","input":17348,"models":{"gpt-6.1-sol":2839},"output":2839,"source":"reported","entries":0,"cache_read":875392,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","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_ef09d64fbbd7ddb34ab67f81","run_id":"run_0f3d096e134ebdae527426d8","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":{"task":{"intent":"consolidation","schema":"research-task-v1","domain_md":"self-match.methods: The candidate is exactly 32 lowercase ASCII characters from `0123456789abcdef`, in any order, repeats allowed. Its **32 literal ASCII bytes** are hashed; it is not decoded as hex. The score is the length of the common prefix of the candidate and its digest, 0 to 32, stopping at the first mismatch: later matches do not count. The final goal is a candidate equal to its own digest (a fixed point). None is known, and none is proven to exist: a random-map heuristic gives roughly a 63% chance that one exists.\n\nSubmit `candidate`. Fixture: `54db1011d76dc70a0a9df3ff3e0b390f` has digest `54db1011d76d137956603122ad86d762`, score 12. Distinguish input records, throughput, restricted facts and attack methods; compare identical domains, baselines, compute and luck.\nself-match.study-2: The candidate is exactly 32 lowercase ASCII characters from `0123456789abcdef`, in any order, repeats allowed. Its **32 literal ASCII bytes** are hashed; it is not decoded as hex. The score is the length of the common prefix of the candidate and its digest, 0 to 32, stopping at the first mismatch: later matches do not count. The final goal is a candidate equal to its own digest (a fixed point). None is known, and none is proven to exist: a random-map heuristic gives roughly a 63% chance that one exists.\n\nSubmit `candidate`. Fixture: `54db1011d76dc70a0a9df3ff3e0b390f` has digest `54db1011d76d137956603122ad86d762`, score 12. Full 64-step MD5, RFC IV, exact padding; reductions or different IVs are separate scopes. Negative evidence closes only its tested method and scope.","topic_ids":["self-match.methods","self-match.study-2"],"stop_if_md":"The exact obligation is already answered, a decisive counterexample defeats this attempt, or the required evidence cannot be obtained within actual consent and controls.","changed_premise_md":"Establish the exact uncovered difference from existing research before substantial work.","predecessor_returns":[],"expected_evidence_md":"An attributable scoped claim, source, measured comparison or negative result with its cheapest decisive check.","unresolved_obligation_md":"Can the first output word be computed early, or bounded, so most candidates are rejected before all 64 steps? Measure the saving and its limit."},"schema":"work-disposition-v3","sources":{"topic_ids":["self-match.methods","self-match.study-2"],"review_ids":[712,774],"message_ids":[],"predecessor_returns":[2618,2626,2649,2761]},"trusted":true,"decision":"covered","effective":true,"input_sha256":"fbabb1330e733b8d7d3a1275bcf0108c2ac73d26cc0ffb6f4307e8ba585e792b","rationale_md":"First material baseline: conventional step-61 gate and scoped tail savings remain covered. New conditioned-neighborhood finite observations supply no earlier correct self-match predicate or defect in the covered answer. Administrative decision only.","scope_sha256":"e343a1a0e527a4be85a3c42cd780cb8ddf15fe3bddd1ab8670d63bab73ef2a1a","allow_covered":true,"input_version":"material-evidence-v1","reopen_when_md":"Concrete gate/comparison defect, explicit earlier correct legal-domain predicate with a full-MD5 control, or assigned independent 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evidence delta from the prior decision: Legacy or first comparison: establish one material baseline; historical raw fingerprints cannot establish which evidence changed.. Read only these changes and the prior rationale first. If unchanged, a short reaffirmation suffices; do not re-prove identities or regenerate coverage artifacts.\n\nCompare this exact assignment with its predecessors and corrections before further investment. This is an assignment decision, not scientific acceptance. Read the cited messages and the lane's current claims; chat is evidence only.  Nomination: return #2953, message #none, review #none. Use existing packages and the cheapest source check; do not repeat large experiments.\n\nQuestion: Can the first output word be computed early, or bounded, so most candidates are rejected before all 64 steps? Measure the saving and its limit.\nDomain: self-match.methods: The candidate is exactly 32 lowercase ASCII characters from `0123456789abcdef`, in any order, repeats allowed. Its **32 literal ASCII bytes** are hashed; it is not decoded as hex. The score is the length of the common prefix of the candidate and its digest, 0 to 32, stopping at the first mismatch: later matches do not count. The final goal is a candidate equal to its own digest (a fixed point). None is known, and none is proven to exist: a random-map heuristic gives roughly a 63% chance that one exists.\n\nSubmit `candidate`. Fixture: `54db1011d76dc70a0a9df3ff3e0b390f` has digest `54db1011d76d137956603122ad86d762`, score 12. Distinguish input records, throughput, restricted facts and attack methods; compare identical domains, baselines, compute and luck.\nself-match.study-2: The candidate is exactly 32 lowercase ASCII characters from `0123456789abcdef`, in any order, repeats allowed. Its **32 literal ASCII bytes** are hashed; it is not decoded as hex. The score is the length of the common prefix of the candidate and its digest, 0 to 32, stopping at the first mismatch: later matches do not count. The final goal is a candidate equal to its own digest (a fixed point). None is known, and none is proven to exist: a random-map heuristic gives roughly a 63% chance that one exists.\n\nSubmit `candidate`. Fixture: `54db1011d76dc70a0a9df3ff3e0b390f` has digest `54db1011d76d137956603122ad86d762`, score 12. Full 64-step MD5, RFC IV, exact padding; reductions or different IVs are separate scopes. Negative evidence closes only its tested method and scope.\nPremise: Establish the exact uncovered difference from existing research before substantial work.\nReturns: 2618, 2626, 2649, 2761; reviews: 712, 774; messages: none nominated.\n\nCovered means only this unchanged obligation need not be dispatched again.\nReturn work_disposition:{decision:\"covered|open\",scope_sha256:\"e343a1a0e527a4be85a3c42cd780cb8ddf15fe3bddd1ab8670d63bab73ef2a1a\",input_sha256:\"fbabb1330e733b8d7d3a1275bcf0108c2ac73d26cc0ffb6f4307e8ba585e792b\",rationale_md,reopen_when_md,next_task?:<research-task-v1>}. Name replication explicitly. Only a fresh trusted open decision explicitly reopens this exact scope. Changed evidence or chat requests reconsideration and never removes prior suppression. A changed source snapshot or superseded base decision makes this response ineffective; it grants no scientific authority.","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/2992/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"3d6bcfbb3ae68a4412ff6346f250e46380ae30fc351fb0400db01e01ea73c512","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}