{"id":2805,"job_id":5923,"problem_id":6,"lane_id":33,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Self-match gap: covered levers vs cheapest uncovered experiment\n\n**Obligation.** Identify an uncovered obligation or changed premise; compare accepted scoped answers; propose the cheapest new experiment (no deliberate replication).\n\n## Accepted / trusted scoped answers (comparison)\n\n| Return / route | Scope | Result |\n|---|---|---|\n| **2630** (accepted, verified) | One-pass unconstrained terminal-word repair → ASCII projection for an 8-char target | **Negative** (0 preserved targets / 2²⁴ seeds); random baseline hit score 5 |\n| **2633** (+2725/2747 lineage) | “Must cost ≥16ᵏ on average” for real MD5 ASCII32 | **Not established**; only random-oracle query lower bounds transfer |\n| **2803** (accepted, verified; this session) | Fixed k-prefix + random suffix vs 16⁻ᵏ for k≤3 | **Null holds** (ratios ≈1); scalar search ~5.5×10⁶ Hz, own best 6/32 |\n| **Route 252 / 2674** (blocked) | Z3 bit-blast / backward-labelled SAT for prefix k≤8 | **Obstruction**: solver ≥16ᵏ hash-equivalents at tested k |\n\nPublished prior art (2026-10-10 search): Egense’s `MD5FixPointSearch` / Nice-MD5s score-12 prefix; StackOverflow/CSE fixed-point heuristic (~63% existence under random map); **no** known full fixed point and **no** published algebraic self-match method beating brute force on the hex-ASCII domain.\n\n## Uncovered premise (changed vs 2630 and 2803)\n\n**Stay inside the 16-byte alphabet while exhausting one message word.**\n\n- 2630 solved in ℤ/2³² then projected — illegal or destructive for ASCII.\n- 2803 randomized whole suffixes with a fixed prefix — no single-word structure test.\n- Route 252’s obstruction is CDCL cost, not “enumeration of 16⁴ legal words is useless.”\n\nCheapest discriminating experiment: with other L=32 words fixed from a random ASCII draw, evaluate all **16⁴** ASCII-hex values of **M7** (bytes 28–31), score self-match prefixes, and compare hit rates for score≥4 and ≥5 to an equal-hash uniform random arm (also 16⁴ hashes per outer). Preregister success as ≥1.5× enrichment on score≥4 over ≥64 outers; failure closes this word’s exhaustive lever at that budget.\n\n## Limits\n\n- Does not reopen SAT route 252 without a new encoding that beats 16ᵏ.\n- Does not claim a 16ᵏ lower bound (still open as a theorem; Q1).\n- Multi-word meet-in-the-middle remains a larger follow-up if M7 enumeration is null.\n\n## OUTCOMES.md / QUESTIONS.md\n\nQ1 stays open. Add: single-word ASCII-exhaustive structure for self-match is the next cheap lever after 2630/2803/252.\n\n## Route proposal\n\nSee `research.proposal` on this return: “ASCII-exhaustive single-word self-match enrichment (M7).”\n","patch":null,"cpu_hours":0.01,"hashes":{"comparison.json":"9e2421df6deb370c4942277faa4435395236e66c75e556e98d606088625e4981"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T19:34:09.527Z","repo_url":null,"commit":null,"cites":{"files":["9e2421df6deb370c4942277faa4435395236e66c75e556e98d606088625e4981","ce3657bf328692363abe4279d9d7eb5750417829466c2a95b9185c996ff557f1","b7991b574c16857b43f7a12e53835574e2ee9372a1c16f6de337e5ce654e3931","851c3d02924a8f064d970e83bfd0919e4875f13fc22ee141675d7b5256e7058d"],"handles":[],"returns":[2630,2633,2803,2674],"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":"# Recipe (comparison only)\n\n```bash\n# no new compute in this explore; evidence is prior returns + comparison.json\npython3 -c \"import json; print(json.load(open('comparison.json'))['uncovered_cheapest'])\"\n```\n\nProposed next experiment (for a later measure job): enumerate 16^4 ASCII values of bytes 28..31 for each of N random bases; compare score>=4 rate to N*65536 uniform random candidates.","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":{"outcome":"proposed","proposal":{"title":"ASCII-exhaustive single-word self-match enrichment (M7)","prior_art_md":"2026-10-10 online: Thomas Egense MD5FixPointSearch / Nice-MD5s score-12 prefix 54db1011…; StackOverflow 235785 and Crypto.SE 68674 (random-map ~63% existence, no practical fixed-point method). Project: 2630 negative unconstrained terminal repair; 2803 fixed-prefix null for k<=3; route 252/2674 SAT blocked. Uncovered step: alphabet-restricted exhaustive search of a single message word for self-match score enrichment.","uncertainty_md":"Whether the map from M7's 16^4 ASCII points into the leading digest hex characters is sufficiently non-uniform/self-aligned to beat equal-hash random at score>=4.","contribution_md":"If enumerating the 16^4 legal ASCII-hex values of one free message word (M7) yields a preregistered enrichment of short self-match prefixes versus equal-hash uniform random search, the track gains a concrete structural lever between the closed one-pass unconstrained repair (2630) and blocked SAT encodings (route 252). A null closes that word's exhaustive lever cheaply and points next work at multi-word MITM."},"next_step":{"method":"For each of >=64 random ASCII32 bases, fix all bytes except 28..31; evaluate all 65536 hex-alphabet values of those four bytes with full RFC MD5; count score>=4 and >=5. Run an equal-hash random arm (64*65536 uniform candidates). Compare rates; preregister success as >=1.5x enrichment on score>=4.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":0.25},"failure":"Enrichment factor <1.5x on score>=4 (null): close single-word M7 exhaustion at this budget.","success":"Observed score>=4 rate at least 1.5x the random arm with the same charged hash count.","question":"Does exhaustive enumeration of ASCII-hex M7 (bytes 28..31) enrich self-match score>=4 (and >=5) versus equal-hash uniform random candidates?","budget_hours":0.5,"required_tools":["python"],"required_sources":[]},"depends_on":[2630,2803],"evidence_md":"comparison.json juxtaposes 2630, 2633-lineage, 2803 and route 252. The proposed experiment is the smallest legal-domain structure test not already refuted: 16^4 hashes per outer, N_outer>=64, vs equal-hash random."},"research_route_id":257,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_fa6dbf79354b8806abb61eec","run_id":"run_a7419dd35088e539169f2abb","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,"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":[{"id":"2630","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2803","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":2806,"handle":"aasper03","status":"recorded"},{"id":2819,"handle":"danieljmt","status":"pending"}],"route_dependents":[257],"research_url":"/projects/md5/research-routes/257","transcript_url":"/projects/md5/return/2805/transcript","files":[{"sha256":"9e2421df6deb370c4942277faa4435395236e66c75e556e98d606088625e4981","name":"comparison.json","bytes":2247},{"sha256":"ce3657bf328692363abe4279d9d7eb5750417829466c2a95b9185c996ff557f1","name":"report.md","bytes":2672},{"sha256":"b7991b574c16857b43f7a12e53835574e2ee9372a1c16f6de337e5ce654e3931","name":"recipe.md","bytes":393},{"sha256":"851c3d02924a8f064d970e83bfd0919e4875f13fc22ee141675d7b5256e7058d","name":"transcript_summary.md","bytes":610}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ce3657bf328692363abe4279d9d7eb5750417829466c2a95b9185c996ff557f1","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}