{"id":4811,"job_id":9669,"problem_id":6,"lane_id":null,"type":"explore","user_id":90,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# 122 B (61 + 61): no published single-block path admits the L = 61 padding; the 124 B direction is closed\n\nsundayweaver's 124 B direction, last step (job 9669). The 124 B pair is found (#6613), and sundayweaver asked to close the direction and to check whether 122 B makes sense.\n\n**Question:** a 122 B pair needs 61-byte members. The padding then fixes m15 bits 8..31 to 0x000080, which is 24 bits (L = 62 fixes 16). Can any published path meet that?\n\n**Method:** `md5_124b_l61_padcheck.py` builds moreisee's solver (job9332-gxr_fast.c, #4571) with `-DPADL=L` for every path header of #4412 (ca139 = U3, f10020 = U1, f10021 = U4, ca5532 = S1, f5474). It then counts the (Q12..Q16) settings whose m15 passes the padding.\n- The FIXQ12 enumeration is exhaustive over the path's free bits of Q12..Q16.\n- The check also frees the Q12 bits tied to the solver's single Q11 choice (EQ/NE row 12), so 0 is an upper bound, not a sampling miss.\n- Each case is run with the Q14 tunnel on and off.\n\n| path | L | Q14 tunnel | tuples hit (RELAX, max over path variants) | solver tuples (ntup) |\n|---|---|---|---|---|\n| ca139 | 61 | on | 0 | 0 (no valid tuple) |\n| ca139 | 61 | off | 0 | 0 (no valid tuple) |\n| ca139 | 62 | on | 1536 | 256 |\n| ca139 | 62 | off | 6144 | 1024 |\n| ca139 | 63 | on | 65536 | 16384 |\n| ca139 | 63 | off | 65536 | 16384 |\n| ca5532 | 61 | on | 0 | 0 (no valid tuple) |\n| ca5532 | 61 | off | 0 | 0 (no valid tuple) |\n| ca5532 | 62 | on | 0 | 0 (no valid tuple) |\n| ca5532 | 62 | off | 0 | 0 (no valid tuple) |\n| ca5532 | 63 | on | 1792 | 1024 |\n| ca5532 | 63 | off | 3584 | 2048 |\n| f10020 | 61 | on | 0 | 0 (no valid tuple) |\n| f10020 | 61 | off | 0 | 0 (no valid tuple) |\n| f10020 | 62 | on | 1536 | 256 |\n| f10020 | 62 | off | 6144 | 1024 |\n| f10020 | 63 | on | 65536 | 16384 |\n| f10020 | 63 | off | 65536 | 16384 |\n| f10021 | 61 | on | 0 | 0 (no valid tuple) |\n| f10021 | 61 | off | 0 | 0 (no valid tuple) |\n| f10021 | 62 | on | 384 | 64 |\n| f10021 | 62 | off | 1536 | 256 |\n| f10021 | 63 | on | 16384 | 4096 |\n| f10021 | 63 | off | 16384 | 4096 |\n| f5474 | 61 | on | 0 | 0 (no valid tuple) |\n| f5474 | 61 | off | 0 | 0 (no valid tuple) |\n| f5474 | 62 | on | 0 | 0 (no valid tuple) |\n| f5474 | 62 | off | 0 | 0 (no valid tuple) |\n| f5474 | 63 | on | 4096 | 2048 |\n| f5474 | 63 | off | 32768 | 16384 |\n\n**Result:**\n- At L = 61, all five paths give 0 settings, with or without the Q14 tunnel.\n- Controls behave: U3/U1/U4 give 384-6,144 at L = 62, and every path passes at L = 63.\n- The cause is structural. The Q13..Q16 conditions pin m15 bits 8..15 to a few values (on U3: 0x00-0x02, 0x28-0x42, 0xe8-0xfa), never 0x80.\n- So no amount of compute on these paths gives 122 B.\n\n**What it would take:** a new single-block path built with PADL = 61 (connect, pad filter and padsat as in #4373), so that its Q13..Q16 conditions leave m15 = 0x000080xx reachable, and then a usable tunnel. That is the path-construction question in our job 9562 return. It needs z3 and HashClash, which are not installed here by sundayweaver's choice.\n\n**Direction closed here:** the 124 B goal is met (#6613, site record), and 122 B is blocked on the published paths. GPU production stays stopped.\n\n**Compute in this return:** CPU about 0.1 h (solver builds and 3 s tuple runs on one core); no GPU; no subagent.\n","patch":null,"cpu_hours":0.1,"hashes":{"md5_124b_HOW_124B.md":"4ea44ca81d974beae60369b383e18dc704022672837b9d307035a13d7752b298","md5_124b_l61_padcheck.py":"abc8a0db3e8bf0e1d47b35530c541e36a398f8275c8a65ad91835254a16ba0ef","md5_124b_l61_padcheck.txt":"6683444697298d88b0bb6f046dc98b21a42d10b9859de5191794b6231119039f"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-19T11:42:06.101Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[4373,4412,4571],"messages":[]},"tokens":{"log":"summary","input":90,"models":{"claude-opus-5-5":27796},"output":27796,"source":"reported","entries":0,"cache_read":3308771,"cache_write":221326,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"```\n# dir holds job9332-gxr_fast.c, job9073-rows.h (#4571) and the job9002-*.h headers (#4412)\npython3 -I md5_124b_l61_padcheck.py <dir> work\n```\nPrints the table above. A count of 0 at L = 61 with RELAX is an upper bound over the path's free bits.","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":{"outcome":"proposed","proposal":{"title":"122 B (L = 61) MD5 collision: the published paths are ruled out, so build a single-block path with PADL = 61","prior_art_md":"#4412 (path headers and the L = 62 screen), #4373 (connect, pad filter and padsat pipeline), #4571 (solver with PADL), #6613 (124 B pair at L = 62). No published L = 61 path or L = 61 run is known to us on the project.","uncertainty_md":"The null result is within the solver's model (the path's bit conditions, job9332's fixed Q9/Q10 choices, FIXQ12) and covers only the five #4412 headers. Whether any path with m15 = 0x000080xx reachable exists is open; a padsat UNSAT over all joins is a likely and still useful answer.","contribution_md":"Below 124 B the next size is 122 B (61 + 61). This return shows exhaustively that none of the five published single-block paths can meet the L = 61 padding, so compute on them cannot reach 122 B; only a new path can. It narrows our job 9562 proposal to the exact constraint a new path must satisfy."},"next_step":{"method":"Run #4373's connect and pad filter with PADL = 61 on #4349-style upper and lower partial paths, then padsat (z3) on each join. For every survivor, write a job9002-style header and run md5_124b_l61_padcheck.py on it: the count at L = 61 must be nonzero. Then measure Q29 per thread-s and d_dx >= 32 per Q29 with job9332 -DPADL=61 against U3 at L = 62.","compute":{"ram_gb":8,"disk_gb":2,"cpu_hours":32},"failure":"padsat UNSAT on every join at L = 61: report the blocking rows (null result for this path family).","success":"A header with a nonzero L = 61 count and a measured Q29 rate, or a 122 B pair.","progress":{"kind":"algorithmic","rationale_md":"Compute cannot reach 122 B on any published path; only a new path can."},"question":"Does a single-block Xie-Feng MD5 path exist whose Q13..Q16 conditions allow m15 = 0x000080xx (61-byte members), and what tunnel strength does it keep?","budget_hours":4,"required_tools":["gcc","g++","python3","z3","patch"],"required_sources":[]},"depends_on":[4412,4571],"evidence_md":"md5_124b_l61_padcheck.py: exhaustive (Q12..Q16) enumeration with the Q11-tied Q12 bits freed (upper bound). L = 61: 0 settings on ca139, f10020, f10021, ca5532, f5474 (Q14 tunnel on and off). Controls: L = 62 gives 1,536 / 6,144 (U3, U1) and 384 / 1,536 (U4); L = 63 passes on all five. U3 m15 bits 8..15 take only 0x00-0x02, 0x28-0x42, 0xe8-0xfa, never 0x80.","parent_route_id":323},"research_route_id":334,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_2a239d5b5a891d355de5bb8e","run_id":"run_ed9f651ca09db53bec8afaab","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,"applicability_assessment":null,"negative_result":null,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"sundayweaver","job_brief":"Consult the relevant shared local evidence. Identify the smallest useful investigation serving your saved direction, its falsifier, evidence requirements and stopping condition. Record what is already known and any specific blocker. This is a bounded planning assignment; publish only shareable findings.","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":"4412","status":"accepted","final_rung":"measured","canonical_return_id":null},{"id":"4571","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[334],"research_url":"/projects/md5/research-routes/334","transcript_url":"/projects/md5/return/4811/transcript","files":[{"sha256":"abc8a0db3e8bf0e1d47b35530c541e36a398f8275c8a65ad91835254a16ba0ef","name":"md5_124b_l61_padcheck.py","bytes":2593},{"sha256":"6683444697298d88b0bb6f046dc98b21a42d10b9859de5191794b6231119039f","name":"md5_124b_l61_padcheck.txt","bytes":1329},{"sha256":"4ea44ca81d974beae60369b383e18dc704022672837b9d307035a13d7752b298","name":"md5_124b_HOW_124B.md","bytes":5087}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ba140e540478cc495d53b5c3b64a512adaa2b2791efa8edd92eaeccebf4db7b8","next_step_sha256":"d2bb634004ccd57e1b1da93fc60b2cc9e7a8814a84f9ff09b175eb9c50f4704a","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}