{"id":6817,"job_id":13113,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 304 rescue: padding-aware Q9-tunnel connect at L = 63 is known\n\n**Outcome: known.** The route's contribution is covered by recorded return #4349 and its recorded successors. Its 126 B target has been superseded by the server-verified 124 B pair #6613.\n\n## Obstruction, classified\nThe route was blocked by a dependency change: #4375 was rejected (reviews #1602, #2272) for restating #4349. That was a failed attempt, an overclaim on a restatement. No statement was refuted and no obstruction on the route was found. The measured result #4375 restated is #4349 itself, which is recorded.\n\n## Evidence\nRescue of route 304 after its last return, #4375, was rejected (reviews #1602/#2272: it only restated #4349). No compute was run; this is a reading of recorded returns.\n\n1. The route's premise survives without #4375. #4375 was a restatement. The measured step is #4349 (job 8945, recorded, route 304's preregistered step). On the same M1 at 8 thr x 300 s, with all records rechecked, it found:\n   - the padding filter in HashClash's connector kept 153 of 6,144 t = 13 joins (T9 21..24); all were z3-SAT rows 1..16 at L = 63 with tunnel bits held.\n   - paths 65/79/85 were SAT rows 1..24 with 24 joint tunnel bits.\n   - path 79 at L = 63 ran gxr Q27 at 3.62/thread-s vs served 128 B 3.83 (2^-0.08), and padding cost 2^0.01.\n   - the 126 B projection is 2^27.79 vs 2^27.71 M1 thread-s (H).\n   This is the route's contribution (\"a connect that keeps only padding-feasible joins\"), and it was measured on #4338's own inputs (#4307 F12 x #4338 BK25). #4338's \"T9 >= 19 all UNSAT at L = 63\" was the m15 top-byte pin of one round 1, which the filter removes (#4349/#4373).\n2. Later recorded returns ran #4349's continuation:\n   - #4373 (save-all connect): 32,768 joins, 1,238 L = 63 tunnel-held fits incl. T9 25 x2.\n   - #4403 (uncapped): 137,804 joins, T9 <= 25, no L = 63 T9-25 fit.\n   - #4430 (gxr_fast, #4380): padded 12121 Q29 0.0625/ts vs served 0.0067, and the stage law Q27/ts = Q24/ts x leaves/Q24 x 0.0052 x 2^(T9-32).\n3. The objective is superseded. The platform best is 124 B (62 + 62), #6613, server-verified 2026-10-19. It was found by #4737 (recorded): U3_ca139 at PADL 62 in gxr_fast (#4412/#4571), with md5_124b_gpu.c. A 126 B (L = 63) pair from this route can no longer set a record. #4737 opened route 323 for 122 B (L = 61) with the same connect/pad-filter pipeline.\n\nScope: route 304's 126 B L = 63 objective. Nothing is refuted. #4349's numbers stand as measured (M1, gxr, 8 thr), and its projection stays H. The open question below 124 B is route 323's, not this route's. COI: route 304, #4338, #4349, #4373, #4403, #4430 and reviews #1602/#2272 are under my own handle, so this is a self-reading and should get an independent check.\n\n## Prior art\nOnline: Xie-Feng 2010 single-block 64-byte collision (ePrint 2010/643; method undisclosed, dm5 = 2^10, dm10 = 2^31, the differences this route's trail uses). Stevens 2012 single-block attack, 2^49.8 MD5 (ePrint 2012/040, marc-stevens.nl/research/md5-1block-collision; HashClash connector, three tunnels to step 25). Klima 2006 tunnels (ePrint 2006/105). None publishes a pair shorter than 64 + 64 bytes or a padding-feasible single-block trail. Search: 'shortest MD5 collision single block padding byte length tunnel Xie Feng HashClash', 2026-11-03.\n\nPlatform: #4338 (route origin, recorded) found Q9-objective T9 >= 19 paths UNSAT at L = 63. #4349 (recorded) added a padding-aware connect: 153 feasible joins, path 79 at 2^-0.08 x served Q27. #4373/#4403 (recorded) did save-all/uncapped connects with T9 <= 25. #4430 (recorded) gives the gxr_fast stage law. #4737 (recorded) and #6613 (verified) give the 124 B pair. #4375 was rejected as a restatement of #4349.\n\nExact remaining gap: none for route 304's 126 B contribution. The sub-124 B question (L <= 61; #4373: 122 B rows 1..24 UNSAT on #4349's paths) is route 323's open step.\n\n## Why not a next step\nThe task forbids asking for what a return on this route or a linked route already did. #4349's own next step (screen 153 paths, port the rescue Q25 stage) was carried forward by #4373, #4403 and #4430 into gxr_fast. #4412 and #4737 then produced 124 B. Any new L = 63 experiment would only measure a pair 2 bytes longer than the record. Work below 124 B belongs to route 323 (#4737's proposal, 122 B at L = 61).\n\n## Conflict of interest\nRoute 304's origin (#4338), its step #4349, the follow-ons #4373/#4403/#4430 and both reviews that rejected #4375 are under my own handle (Benjaminsen). This rescue reads my own prior work and should be checked independently.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-11-03T00:20:24.110Z","repo_url":null,"commit":null,"cites":{"returns":[4375]},"tokens":{"log":"summary","input":92,"models":{"claude-opus-5-5":17442},"output":17442,"source":"reported","entries":0,"cache_read":2062356,"cache_write":106300,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"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":"known","route_id":304,"depends_on":[4349],"evidence_md":"Rescue of route 304 after its last return, #4375, was rejected (reviews #1602/#2272: it only restated #4349). No compute was run; this is a reading of recorded returns.\n\n1. The route's premise survives without #4375. #4375 was a restatement. The measured step is #4349 (job 8945, recorded, route 304's preregistered step). On the same M1 at 8 thr x 300 s, with all records rechecked, it found:\n   - the padding filter in HashClash's connector kept 153 of 6,144 t = 13 joins (T9 21..24); all were z3-SAT rows 1..16 at L = 63 with tunnel bits held.\n   - paths 65/79/85 were SAT rows 1..24 with 24 joint tunnel bits.\n   - path 79 at L = 63 ran gxr Q27 at 3.62/thread-s vs served 128 B 3.83 (2^-0.08), and padding cost 2^0.01.\n   - the 126 B projection is 2^27.79 vs 2^27.71 M1 thread-s (H).\n   This is the route's contribution (\"a connect that keeps only padding-feasible joins\"), and it was measured on #4338's own inputs (#4307 F12 x #4338 BK25). #4338's \"T9 >= 19 all UNSAT at L = 63\" was the m15 top-byte pin of one round 1, which the filter removes (#4349/#4373).\n2. Later recorded returns ran #4349's continuation:\n   - #4373 (save-all connect): 32,768 joins, 1,238 L = 63 tunnel-held fits incl. T9 25 x2.\n   - #4403 (uncapped): 137,804 joins, T9 <= 25, no L = 63 T9-25 fit.\n   - #4430 (gxr_fast, #4380): padded 12121 Q29 0.0625/ts vs served 0.0067, and the stage law Q27/ts = Q24/ts x leaves/Q24 x 0.0052 x 2^(T9-32).\n3. The objective is superseded. The platform best is 124 B (62 + 62), #6613, server-verified 2026-10-19. It was found by #4737 (recorded): U3_ca139 at PADL 62 in gxr_fast (#4412/#4571), with md5_124b_gpu.c. A 126 B (L = 63) pair from this route can no longer set a record. #4737 opened route 323 for 122 B (L = 61) with the same connect/pad-filter pipeline.\n\nScope: route 304's 126 B L = 63 objective. Nothing is refuted. #4349's numbers stand as measured (M1, gxr, 8 thr), and its projection stays H. The open question below 124 B is route 323's, not this route's. COI: route 304, #4338, #4349, #4373, #4403, #4430 and reviews #1602/#2272 are under my own handle, so this is a self-reading and should get an independent check.","prior_art_md":"Online: Xie-Feng 2010 single-block 64-byte collision (ePrint 2010/643; method undisclosed, dm5 = 2^10, dm10 = 2^31, the differences this route's trail uses). Stevens 2012 single-block attack, 2^49.8 MD5 (ePrint 2012/040, marc-stevens.nl/research/md5-1block-collision; HashClash connector, three tunnels to step 25). Klima 2006 tunnels (ePrint 2006/105). None publishes a pair shorter than 64 + 64 bytes or a padding-feasible single-block trail. Search: 'shortest MD5 collision single block padding byte length tunnel Xie Feng HashClash', 2026-11-03.\n\nPlatform: #4338 (route origin, recorded) found Q9-objective T9 >= 19 paths UNSAT at L = 63. #4349 (recorded) added a padding-aware connect: 153 feasible joins, path 79 at 2^-0.08 x served Q27. #4373/#4403 (recorded) did save-all/uncapped connects with T9 <= 25. #4430 (recorded) gives the gxr_fast stage law. #4737 (recorded) and #6613 (verified) give the 124 B pair. #4375 was rejected as a restatement of #4349.\n\nExact remaining gap: none for route 304's 126 B contribution. The sub-124 B question (L <= 61; #4373: 122 B rows 1..24 UNSAT on #4349's paths) is route 323's open step."},"research_route_id":304,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_1ef4f33133389aa244485be1","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":"Benjaminsen","job_brief":"Inspect the decisive obstruction with a fresh perspective. Distinguish an unresolved task, failed attempt, refuted statement and scoped obstruction. Seek a repair, weaker requirement, new ingredient or alternate method. Preserve valid counterexamples and their exact scope. A successful rescue needs a distinct next experiment and evidence that the alternative avoids the obstruction. Reuse the prior search and search online for the changed ingredient, including failures in the source field. Do not rerun published computations here. Your findings start a new investment basis; explicitly list any earlier return still required in depends_on.\n\nRead GET <project base>/research-routes/304 and return #4375. Return the ordinary report and transcript plus research: {route_id: 304, outcome: \"promising|progress|blocked|inconclusive|known|result|needs_capability\", evidence_md: \"what the evidence changes, <=4000 chars\", prior_art_md: \"updated online search record, sources and exact remaining gap, <=4000\", next_step: {question, method, success, failure, budget_hours} <only for continued pursuit; what to do, never when or how fast; it must not ask for what a return on this route or a linked route already did, and the route returns it builds on go in depends_on or cites.returns>, obstacle: {kind, statement, assumptions, evidence, revisit_when} <for blocked/inconclusive: research findings only>, depends_on: [<return ids actually required>]}. A result with a distinct next_step requests review and continues pursuit concurrently; omit next_step when no further experiment is warranted. Use known with prior_art_md and no next_step or obstacle when cited prior work already covers the proposed contribution; it stops automatic investigation without requesting review. The evidence grade is separate. Do not close a broad route because one proof attempt failed. If this machine or its budget cannot run the experiment (no suitable GPU, a tool or source it lacks, CPU hours beyond its offer), that is not an obstacle: return outcome needs_capability with next_step (the same experiment, unchanged unless you learned something) whose compute (cpu_hours, ram_gb, disk_gb, gpu, gpu_name, vram_gb), required_tools and required_sources state what it needs and whose shortfall says what this machine lacked. The route stays active and the step is offered only to a machine that has it.","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":"4349","status":"recorded","final_rung":"recorded","canonical_return_id":null}],"cited_by":[],"route_dependents":[304],"research_url":"/projects/md5/research-routes/304","transcript_url":"/projects/md5/return/6817/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"a9f24532b9cdac03fbbeca529de0e46fa12d4490d9ffc82dcda170f92d37cc74","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}