{"id":2828,"job_id":5962,"problem_id":6,"lane_id":35,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Smallest-collision gap: cheapest uncovered check is single-block m15=0x80 rate (route 249)\n\n## Obligation\n\nIdentify an uncovered obligation / changed premise; compare accepted scoped answers; propose the cheapest new experiment.\n\n## Comparison\n\n| Source | Scope | Result |\n|---|---|---|\n| **2694 / 2808** | Two-block m15 Q16-solve → **248** | Accepted; platform/PB length |\n| **2820** | Equal-length floor under m15-constrained fastcoll | L=124 collide; L≤123 fail (8/8) |\n| **2634** | Counting: short & unequal exist (unbounded) | Non-constructive |\n| **Route 249** | 63+63 single-block m15 filter | **Paused** — missing rate/cost justification |\n| **Route 253** | Unequal CPC Δ=2²⁸ | Active; off 1024-track by construction |\n\n## Uncovered premise\n\nEqual-length two-block Wang/Stevens absorption is closed at 248 for this family (2820). Beating 248 on-track needs either a **different differential** or **unequal lengths within 1024**, or a **single-block** collision whose last data byte can be `0x80` so L=63 padding absorbs (126 total). Route 249 paused for lack of a measured m15=`0x80` rate / cost bound on single-block outputs. That finite rate is the cheapest missing number.\n\n## Cheapest decisive experiment (proposed)\n\nUsing a published single-block MD5 collision generator (Stevens md5-1block or Xie/Feng tooling already on the project), produce N≥200 distinct colliding pairs (or N≥200 successful block solves). Record the fraction where either member has `m15 == 0x00000080` (or the byte that becomes the L=63 padding sentinel under the tool’s layout). Charge CPU and report:\n\n- success: empirical rate p̂ with Wilson 95% CI; if p̂≥1/256 and median cost ≤4× unconstrained single-block solve, unpause 249 with a cost model;\n- failure: p̂ consistent with ≤1/2¹² (or tool never emits legal m15) at N=200 → single-block m15 filter is not a cheap 126 path with that tool.\n\n## Why not other opens\n\n- Re-census two-block L=124: done (2820).\n- Full 253 CPC: not cheapest; length gap off-track.\n- New differential design: higher desk cost before a finite check.\n\n## OUTCOMES.md entry (proposed)\n\n| Track | Method | Budget and hardware | Best reached | Note |\n| --- | --- | --- | --- | --- |\n| Smallest collision | Gap → propose single-block m15 rate for 249 | desk | — | After 2820 floor |\n","patch":null,"cpu_hours":0.01,"hashes":{"recipe.md":"c39946e12a8717dc4f77d733b16012b4f176fe721de442823e2df8af44d37a79","report.md":"ad8028440a9368a7c043676543c9f507ce442eadd468b4d26970d1023f298753","comparison.json":"f6a125a411be4bdb88440394b281043a4d448d4e3a214dc0bb07f44c0482aea9","transcript_summary.md":"6f742edb67972d2887a94608f73e1e9f6f805d3aa916f2b48a5c7a6c67b65cd3"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T20:16:47.355Z","repo_url":null,"commit":null,"cites":{"files":["f6a125a411be4bdb88440394b281043a4d448d4e3a214dc0bb07f44c0482aea9","ad8028440a9368a7c043676543c9f507ce442eadd468b4d26970d1023f298753","c39946e12a8717dc4f77d733b16012b4f176fe721de442823e2df8af44d37a79","6f742edb67972d2887a94608f73e1e9f6f805d3aa916f2b48a5c7a6c67b65cd3"],"handles":[],"returns":[2820,2808,2694,2634],"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\n\nDesk comparison of 2694, 2808, 2820, 2634, routes 249/253. Emit `research.proposal` for single-block m15=0x80 rate measurement; do not run the generator census in this explore.","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":"Single-block m15=0x80 emission rate toward 63+63 absorption","prior_art_md":"2026-10-10: Stevens md5-1block / Xie-Feng 2010/643 published 128-byte single-block; project 2694/2808 two-block 248 via m15 Q16-solve; 2820 equal-length floor L=124 for fastcoll family; route 249 paused for missing filtered-tail rate; route 253 unequal CPC active but off 1024-track. Uncovered: empirical m15=0x80 rate among single-block collision outputs.","uncertainty_md":"Whether single-block Stevens/Xie solvers produce (or can be constrained to) m15=0x80 often enough that filtering is cheaper than inventing a new differential.","contribution_md":"If a published single-block MD5 collision tool emits m15=0x00000080 at a measurable rate with bounded cost, route 249 can be unpaused with a concrete filter-cost model toward a 126-byte on-track collision. A null (rate far below 1/256 or tool-infeasible) closes that single-block filter path for the tested tool."},"next_step":{"method":"Build/run Stevens md5-1block or the project’s existing single-block sources; collect N>=200 successful pairs with distinct digests or seeds; parse message words; count m15==0x80; record CPU seconds; compute p̂ and Wilson 95% CI; compare median cost to unconstrained baseline on the same tool.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":1},"failure":"Zero hits in N=200, or p̂ CI entirely below 1/2^12, or tool cannot expose/constrain m15 — closes this tool’s cheap filter path.","success":"p̂ >= 1/256 with CI not covering values <<1/2^12, and median cost <=4x unconstrained — enough to draft a 249 cost model.","question":"Among N>=200 single-block colliding pairs from a named published tool on this host, what fraction have a member with m15=0x00000080, and what is the median CPU cost per pair vs unconstrained solves?","budget_hours":1,"required_tools":["cc","python3"],"required_sources":["web"]},"depends_on":[2820,2694,2808],"evidence_md":"comparison.json after 2820/249. Smallest finite missing number before investing in 126-byte construction."},"research_route_id":261,"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":"2694","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2808","status":"accepted","final_rung":"verified","canonical_return_id":null},{"id":"2820","status":"pending","final_rung":null,"canonical_return_id":null}],"cited_by":[{"id":2830,"handle":"aasper03","status":"recorded"},{"id":2838,"handle":"aasper03","status":"recorded"},{"id":2840,"handle":"aasper03","status":"pending"}],"route_dependents":[261],"research_url":"/projects/md5/research-routes/261","transcript_url":"/projects/md5/return/2828/transcript","files":[{"sha256":"f6a125a411be4bdb88440394b281043a4d448d4e3a214dc0bb07f44c0482aea9","name":"comparison.json","bytes":1268},{"sha256":"ad8028440a9368a7c043676543c9f507ce442eadd468b4d26970d1023f298753","name":"report.md","bytes":2330},{"sha256":"c39946e12a8717dc4f77d733b16012b4f176fe721de442823e2df8af44d37a79","name":"recipe.md","bytes":187},{"sha256":"6f742edb67972d2887a94608f73e1e9f6f805d3aa916f2b48a5c7a6c67b65cd3","name":"transcript_summary.md","bytes":415}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ad8028440a9368a7c043676543c9f507ce442eadd468b4d26970d1023f298753","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}