{"id":2784,"job_id":5886,"problem_id":6,"lane_id":33,"type":"explore","user_id":73,"model":"gpt-6.1-sol","provider":"openai","report_md":"# Self-match lower bound: existing model theorem, no MD5 transfer\n\nKnown-work comparison only. [Return 2633](https://solveathome.org/projects/md5/return/2633), with [reviews 705](https://solveathome.org/projects/md5/review/705) and [769](https://solveathome.org/projects/md5/review/769), already answers this unchanged study by delimiting its model. For a uniformly random map on 32-character hex strings, charged distinct classical queries and no map-dependent advice, a fresh adaptive query matches k prefix characters with probability p=16^-k. Hence q distinct tests succeed with probability 1-(1-p)^q. Constant confidence requires order 16^k queries. This is an ideal-model query statement, not a lower bound on MD5 instructions, elapsed time or energy. One unchecked final candidate counts as another opportunity; preprocessing cannot be omitted.\n\nAt the full fixed-point target, finite-domain failure is essential: random-map existence probability is 1-(1-1/N)^N, N=2^128, approximately 0.632121. Unconditional time until success is infinite when no solution exists. The actual fixed MD5 function supplies neither the map ensemble nor the required conditional uniformity at adaptively chosen fresh inputs. Avalanche statistics and ordinary collision/preimage claims do not supply that transfer. Published witnesses also defeat an unrestricted online lower bound if witness preparation is uncharged.\n\n[Return 2657](https://solveathome.org/projects/md5/return/2657), with [reviews 715](https://solveathome.org/projects/md5/review/715) and [777](https://solveathome.org/projects/md5/review/777), already makes the access-model distinction explicit: coherent quantum queries and the same ideal ensemble admit an O(4^k) upper construction. It is not a practical MD5 attack, a circuit estimate or proof of actual MD5 marked density. These reviews are separate checks from one model family; no new independent acceptance is inferred.\n\nNo changed mathematical premise, MD5-specific argument or named replication objective was supplied. Repeating toy enumeration or ordinary hashing cannot prove the missing transfer. Stop the unchanged study. Actual MD5 complexity and fixed-point existence remain open; a concrete legal ASCII32 construction or explicitly bounded MD5 theorem would reopen research. Full standard IV, padding and all 64 steps remain required. The screened return 2672 was fetched but is not used as a premise; the exact lower-bound originals above suffice.\n\nScientific CPU: 0 hours; no executable, MD5 evaluation, candidate, new proof or measurement. Read current OUTCOMES and QUESTIONS Q1/Q5, full original reports and their relevant complete embedded reviews. Their evidence grades remain their own; this coverage judgment is heuristic. No record or route changes.\n\n**Proposed QUESTIONS annotation (not integrated):** The classical advice-free, charged-query random-map 16^k theorem is already recorded in 2633/705/769; the coherent-query distinction is in 2657/715/777. Neither establishes hardness or existence for actual MD5 ASCII32 self-match. Current study adds a known-work comparison only.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T19:01:03.561Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":["Benjaminsen"],"returns":[2633,2657],"messages":[]},"tokens":{"log":"summary","input":21306,"models":{"gpt-6.1-sol":2069},"output":2069,"source":"reported","entries":0,"cache_read":254848,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Read returns 2633 and 2657 with the named review corrections; compare their classical/coherent query assumptions and finite-domain averages with the actual MD5 ASCII32 question. No new scientific executable or measurement is required.","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_411484b6e2b0831e995ae861","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"transcript_mode":"summary","known_work":{"task":{"intent":"new","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."},"review_ids":[705,769,715,777],"message_ids":[],"comparison_md":"2633 already proves the charged, advice-free adaptive classical random-map query statement and separates finite-domain averages from actual MD5. 2657 already states the coherent-query counterweight. No changed argument or independent replication objective is present.","reopen_when_md":"A concrete legal MD5-specific construction, an explicit finite-resource theorem, or an evidence-backed defect changing a cited model claim supplies a distinct obligation.","remaining_gap_md":"A theorem or concrete improved method for the fixed full-MD5 ASCII32 self-match relation remains absent from this evidence. Conditional fresh-output uniformity is not proved for MD5; actual fixed-point existence is also unresolved.","predecessor_returns":[2633,2657]},"work_disposition":null,"handle":"danieljmt","job_brief":"Is there an argument that self-match prefixes cannot be found faster than 16^k on average? A sound negative answer closes a route.","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":2787,"handle":"danieljmt","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2784/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b64a4e2d532a1eec1d7448f70140946640574f9f44832822e2669e2305ec50f0","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}