{"id":2949,"job_id":6177,"problem_id":6,"lane_id":33,"type":"explore","user_id":73,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Self match: the 16^k lower-bound question is still covered (re-issue after #2937)\n\n**Decision: covered.** This is an assignment decision, not scientific acceptance. The same scope (0349a1df...) was decided covered by #2898, my #2915, #2932 and #2937; nothing has changed between them.\n\n**Covered answer** (#2633, reviews 705/769; #2657, reviews 715/777):\n- **Classical random-map model** (advice-free, charged distinct queries): success <= 1-(1-16^-k)^min(q,N). This is a query-model statement, not an actual-MD5 runtime bound.\n- **Coherent quantum model:** the O(4^k) BBHT construction.\n- **Open:** transfer to actual MD5 and fixed-point existence (Q1/Q5).\n\n**Since #2915:** only #2932 and #2937, both covered re-issues. The reviews on 2633 and 2657 are unchanged.\n\n**Source check (reused).** #2915's formula_check.json (attached by hash) shows the closed forms equal the direct sums exactly at k = 1..3, with the existence probability tending to 1-1/e. Repeating it would duplicate it.\n\n**Mechanism.** This is the fifth issue of this comparison in about 4 hours with no new evidence.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-11T09:35:23.085Z","repo_url":null,"commit":null,"cites":{"files":["678385f9bd65b8466b1a350246786f6e25bedda8463225e4b28cd0b39888ca8a"],"handles":["Benjaminsen"],"returns":[2937,2932,2915,2898,2633,2657],"messages":[]},"tokens":{"log":"summary","input":2,"models":{"claude-opus-5-5":801},"output":801,"source":"reported","entries":0,"cache_read":694045,"cache_write":1586,"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_c2ccb63b450f473296a41c24","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-3: 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-3"],"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":"Is there an argument that self-match prefixes cannot be found faster than 16^k on average? A sound negative answer closes a route."},"schema":"work-disposition-v2","sources":{"topic_ids":["self-match.methods","self-match.study-3"],"review_ids":[705,769,715,777],"message_ids":[],"predecessor_returns":[2633,2657]},"trusted":true,"decision":"covered","effective":true,"input_sha256":"32be056560ec01ef7e401128f7d4dd67d3fb8e3f56f0fa4a5c439e89ee0c2bbf","rationale_md":"The question is unchanged. The model-scope answer of 2633 (705/769) and 2657 (715/777) stands: the classical distinct-query cap and the quantum O(4^k) construction, with actual-MD5 transfer open. Since #2915 only the covered re-issues #2932 and #2937 appeared. The exact formula check is reused by hash.","scope_sha256":"0349a1dfb02211911ccdcf4e456d18de0761ba93312dab033c75485eb7f16b11","allow_covered":true,"reopen_when_md":"Reopen only for an explicit finite-resource actual-MD5 theorem on the ASCII32 domain, a legal structural construction with setup-charged cost, or a concrete correction to 2633/2657. Re-issues do not reopen it.","work_check_job_id":6177,"base_decision_return_id":2937},"handle":"danieljmt","job_brief":"Compare 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 #2937, message #none, review #none. Use existing packages and the cheapest source check; do not repeat large experiments.\n\nQuestion: Is there an argument that self-match prefixes cannot be found faster than 16^k on average? A sound negative answer closes a route.\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-3: 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: 2633, 2657; reviews: 705, 769, 715, 777; messages: none nominated.\n\nCovered means only this unchanged obligation need not be dispatched again.\nReturn work_disposition:{decision:\"covered|open\",scope_sha256:\"0349a1dfb02211911ccdcf4e456d18de0761ba93312dab033c75485eb7f16b11\",input_sha256:\"32be056560ec01ef7e401128f7d4dd67d3fb8e3f56f0fa4a5c439e89ee0c2bbf\",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":[{"id":2989,"handle":"danieljmt","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2949/transcript","files":[{"sha256":"678385f9bd65b8466b1a350246786f6e25bedda8463225e4b28cd0b39888ca8a","name":"formula_check.json","bytes":618}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"1a210764bfde6f4458f8b8860f462a6e5990383b3a7ec0f4d52af7145617c5c9","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}