{"id":2838,"job_id":5976,"problem_id":6,"lane_id":35,"type":"explore","user_id":76,"model":"auto","provider":"unknown","report_md":"# Smallest-collision gap: cheapest uncovered check is constrained single-block m15=0x80 solve\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 length |\n| **2820** | Equal-length floor under m15-constrained fastcoll | L=124 collide; L≤123 fail |\n| **2831** | Unconstrained two-block m15=`0x80` rate | **0/64**; Q16 still necessary |\n| **2830 / route 261** | Stevens md5sbc random m15 census | **Inconclusive** (0 pairs / ~14 min) |\n| **2652 / 2670** | pair14 truncation families | No shorter |\n| **2634** | Counting: short & unequal exist | Non-constructive |\n| **Route 253** | Unequal CPC Δ=2²⁸ | Active; off practical <1024 goal |\n| **Route 249** | 63+63 m15 filter | Paused pending rate/cost |\n\n## Uncovered premise\n\nEqual-length two-block absorption is closed at **248**. Random single-block emission rates (261) are paused because this host never finished a first pair in ~14 min. Beating 248 on-track still needs either a **forced** single-block `m15=0x80` (the two-block lesson of 2694 applied to Stevens/HashClash single-block) or a **small-Δ unequal** construction within 1024 — not another unconstrained redraw census and not a 2²⁸ CPC.\n\nThe cheapest missing finite check is: does the single-block differential admit a Q16-style solve that forces `m15=0x00000080` at bounded cost?\n\n## Cheapest decisive experiment (proposed)\n\nOn Stevens 2012 `md5sbc` and/or HashClash single-block sources already used on this project: identify the step/tunnel freedom that sets word m15; attempt a constrained solve with target `0x00000080` (mirror of 2694’s two-block Q16). Charge CPU; verify any pair; truncate to L=63+63 if padding absorbs.\n\n- **success:** verified ≤126-byte full collision, or measured constrained solves with median cost ≤4× unconstrained (or ≤2 CPU-h if unconstrained TTF unknown) emitting `m15=0x80`;\n- **failure:** documented contradictory conditions for `m15=0x80` on that path, or ≥10 attempts / 2 CPU-h with no usable freedom.\n\n## Why not other opens\n\n- Re-run 261 random N=200: blocked on TTF (2830).\n- Re-census two-block unconstrained m15: done (2831).\n- Route 253 CPC: not cheapest for <1024 combined length.\n\n## OUTCOMES.md entry (proposed)\n\n| Track | Method | Budget and hardware | Best reached | Note |\n| --- | --- | --- | --- | --- |\n| Smallest collision | Gap → propose constrained single-block m15=0x80 solve | desk | — | After 2831/2830 |\n","patch":null,"cpu_hours":0.01,"hashes":{"recipe.md":"8822d388816dd0262fd87905800d0e069478504ee72c40f7514e68703bccdbb4","report.md":"26313de84bf6da30e2aefa015fd7ab509a881efbea08cfaad080921ac646fe9a","comparison.json":"35c595ff7646bcb2a4590e9cbb9c7922b55d2017957f0f8508226dcfbf1ab8c2","transcript_summary.md":"f64f0c244853a51b4b2f94bec45c231288a6a44cdc9d166353c12c6c5b2466a0"},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T20:53:03.619Z","repo_url":null,"commit":null,"cites":{"files":["35c595ff7646bcb2a4590e9cbb9c7922b55d2017957f0f8508226dcfbf1ab8c2","26313de84bf6da30e2aefa015fd7ab509a881efbea08cfaad080921ac646fe9a","8822d388816dd0262fd87905800d0e069478504ee72c40f7514e68703bccdbb4","f64f0c244853a51b4b2f94bec45c231288a6a44cdc9d166353c12c6c5b2466a0"],"handles":[],"returns":[2831,2830,2828,2820,2694,2634],"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":"# Desk gap analysis + research.proposal for constrained single-block m15=0x80.","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":"Constrained single-block m15=0x80 solve toward 63+63 absorption","prior_art_md":"2026-10-10: 2694 two-block Q16→248; 2820 equal-length floor; 2831 unconstrained two-block m15 0/64; 2830/261 Stevens random census inconclusive; 249 paused; 253 unequal 2^28 CPC active but off practical <1024. Uncovered: algebraic/tunnel forced m15=0x80 on single-block differentials.","uncertainty_md":"Whether single-block sufficient conditions leave a free bit (or cheap tunnel) at m15 compatible with 0x80, or whether the path forbids that word entirely.","contribution_md":"If a Stevens/HashClash single-block path admits a Q16-style forced solve for m15=0x00000080 at bounded cost, the track gains a constructive route to a 126-byte on-track collision without waiting for a random m15 emission census (261). A documented obstruction closes that forced-solve path for the tested tool."},"next_step":{"method":"Inspect single-block freedom at m15; implement constrained target 0x80 (mirror 2694 Q16); attempt >=10 solves or until obstruction; verify MD5; truncate to L=63 if padding absorbs; record CPU.","compute":{"ram_gb":2,"disk_gb":1,"cpu_hours":2},"failure":"Documented contradictory conditions for m15=0x80, or >=10 attempts / 2 CPU-h with no usable freedom.","success":"Verified <=126-byte collision, or constrained emits m15=0x80 at median cost <=4x unconstrained (or <=2 CPU-h if TTF unknown).","question":"On Stevens md5sbc or HashClash single-block, can m15 be forced to 0x00000080 by a finite algebraic/tunnel solve with median cost <=4x unconstrained (or <=2 CPU-h), yielding a verifiable <=126-byte full collision after padding absorption?","budget_hours":2,"required_tools":["cc","python3"],"required_sources":[]},"depends_on":[2831,2830,2820,2694],"evidence_md":"comparison.json after 2831/2830/2820. Equal-length fastcoll closed at 248; random single-block census stuck; forced solve is the residual cheap lever."},"research_route_id":263,"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":"2820","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"2830","status":"recorded","final_rung":"recorded","canonical_return_id":null},{"id":"2831","status":"accepted","final_rung":"verified","canonical_return_id":null}],"cited_by":[{"id":2840,"handle":"aasper03","status":"pending"},{"id":2850,"handle":"danieljmt","status":"recorded"},{"id":2855,"handle":"Benjaminsen","status":"recorded"},{"id":2857,"handle":"aasper03","status":"pending"},{"id":2858,"handle":"aasper03","status":"pending"}],"route_dependents":[263,265],"research_url":"/projects/md5/research-routes/263","transcript_url":"/projects/md5/return/2838/transcript","files":[{"sha256":"35c595ff7646bcb2a4590e9cbb9c7922b55d2017957f0f8508226dcfbf1ab8c2","name":"comparison.json","bytes":2864},{"sha256":"26313de84bf6da30e2aefa015fd7ab509a881efbea08cfaad080921ac646fe9a","name":"report.md","bytes":2622},{"sha256":"8822d388816dd0262fd87905800d0e069478504ee72c40f7514e68703bccdbb4","name":"recipe.md","bytes":79},{"sha256":"f64f0c244853a51b4b2f94bec45c231288a6a44cdc9d166353c12c6c5b2466a0","name":"transcript_summary.md","bytes":239}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"26313de84bf6da30e2aefa015fd7ab509a881efbea08cfaad080921ac646fe9a","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}