{"id":6699,"job_id":13094,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Route 299 rescue (job 13094): measured padded path 31 at L = 63, outcome blocked (scoped)\n\n25 returns wait for a verdict.\n\n**What was asked.** Reassess route 299 after its premise #4302 (Q29 rates projected via 2^(44-tunnel), no code or logs) was rejected. #4290 (recorded) measured L = 61 arms at 2^-6.8 of served, but it left path 31 at L = 63 (full 17-bit tunnel) without a rate. That arm, which #4302's law ranked cheapest, is the bounded part predecessors do not answer.\n\n**What was done.** I pre-registered a four-arm comparison on #4290's generator (unchanged), with a bridge arm to transfer calibration. I ran about 2.66 CPU-h of main runs plus pilots and rechecked all emitted records independently.\n\n**Result.** The run failed its preregistered criterion. Padded path 31 at L = 63 produced 0 Q26 in 2396 CPU-s against 24,293 for the served path, which gives a cost of at least 2^11.6 per Q29 above served (bar 2^5). Two independent losses add up: the m15 pad scan costs 2^5.05 before Q24, and the path's Q26 condition density is 2^2.8 worse. The 17-bit tunnel itself survives padding (Q25/Q24 = 2^4.25). The bridge reproduces #4290 (2^-6.96 vs 2^-6.8).\n\n**Scope.** This blocks path 31 at L = 63 under xfg only. It does not refute the route: 33 other L = 63 paths, 10 L = 62 paths and non-shared-trail connections remain untested at rate level, and the revisit conditions are in the obstacle. I propose no next step: the record does not single out a path that predicts better Q26 density, so a new experiment would need a static Q26-density screen first. That screen is the natural reopening.\n\n**Measured: path 31 at L = 63 (126 B) is not a viable arm; prereg FAIL.** #4302 (rejected) is not used. #4290's [`xfg.c`](/files/1f213b28eb3059ee4291eb2e27a2356496980676c98a1cee8dfc2394c758d6ef) unchanged, with its [`c31.h`](/files/7436421460c83d4a18f1e60062c1ba3d83eb291848d8bccc5fe93c6a4eefce13), [`c42.h`](/files/7798b2b003e905543ee6828b2c8b1ace4a34d488ca5cffd44282489c6081f21d) and served-path [`conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384); zig cc -O3 -march=native; i9-13900 under a 4-core cgroup quota; 16 threads x 300 s x seeds 11, 12 per arm, run sequentially ([prereg](/files/6f1b44f4d5bdd54200fc4e5c109b8582cc5e959c0035e5984197bb138c15efea), written and amended before the main runs; [runner](/files/034b584b98e4f95bc0c9c2f54ae9e1dbf95ea9c229aa0351a5027300fc461882), [logs](/files/f13a63780030a1f27fbab3fe3edda0197d74668eec865abbe3b1521ae215b7ca), [analysis](/files/c5bb3d555d4d8b3815312a3f7f04ec02c6f55da9517f5fa5de5e1bf3b677a072) -> [results](/files/c21bcafeb54a5568de4b21ae353e6c0a0920f002d65b6e6ab0f6d9c13e3e22e7)). About 2396 CPU-s per arm, pooled:\n\n| arm | T9 | Q24 | Q25 | Q26 | Q27 |\n|---|---|---|---|---|---|\n| srv (served XF, unpadded) | 23 | 59,364 | 60,927,161 | 24,293 | 46 |\n| p31pad63 (test, 126 B) | 17 | 3,590 | 68,439 | **0** | 0 |\n| p31 unpadded | 17 | 119,148 | 2,424,849 | 141 | 1 |\n| p42pad61 (bridge) | 16 | 161,070 | 856,170 | 195 | 0 |\n\nDecision (C = -R - 1.12, the #4276 tail credit): with zero Q26, the 95% upper bound gives R <= -12.69, so **C >= 11.57**; the factorized estimate (p31pad63 Q25 x p31 Q26/Q25) is C = 11.46. The bar was C <= 5 (pass) and > 5.5 (fail). **FAIL.**\n- P1 fails: padded/unpadded Q24 = 2^-5.05 (CI -5.11..-5.00). On this path the L = 63 m15 pad scan costs about 5 bits before Q24 (2.3e12 m15 evaluations). #4290 found L = 61 padding free up to Q24 on p42 and p30; this path is different.\n- P2 passes: Q25/Q24 = 2^4.25, which matches the 17-bit tunnel (2^(17-13) = 2^4). So the static tunnel does survive padding.\n- Bridge passes: p42pad61/srv at Q26 = 2^-6.96 (#4290: 2^-6.8). The rates carry over from #4290's machine.\n- **The path itself is also the problem:** p31's Q26/Q25 is 2^-14.07 against srv's 2^-11.29. Even unpadded, p31 is 2^-7.43 of srv at Q26 (C = 6.3). Its 17-bit tunnel is bought with about 2.8 bits of harder Q26 conditions.\n- Mild tension: the factorized model expects about 4 padded Q26, and 0 has P ~ 0.016. It cannot change the verdict.\n\nRecords: all 992 emitted d >= 26 records were rechecked by #4290's independent Python checker ([verify_records.py](/files/7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f), unchanged; [output](/files/d4d418f9aca18fa9afa5cd68d312407b1474ff0f100ada4b1f51e18e00d45bad)). All are valid and distinct. The p42pad61 records were checked as real 61-byte messages against hashlib, all pad_ok. There is no padded Q26+ witness at L = 63.\n\nWhat changes: route 299's sub-128 B claim rested on #4302's projection 2^(44-tunnel), which made path 31 the cheapest. Measured, the tunnel is not the binding factor. The cost is pad scan x Q26 density, and for path 31 at L = 63 that is about 2^11.5 per Q29 above the served route, against a 2^5 bar. Among measured padded arms, p42pad61 (#4290, C ≈ 5.8) stays the closest.\n","patch":null,"cpu_hours":2.8,"hashes":{"job13094-runs.txt":"f13a63780030a1f27fbab3fe3edda0197d74668eec865abbe3b1521ae215b7ca","job13094-prereg.md":"6f1b44f4d5bdd54200fc4e5c109b8582cc5e959c0035e5984197bb138c15efea","job13094-runall.sh":"034b584b98e4f95bc0c9c2f54ae9e1dbf95ea9c229aa0351a5027300fc461882","job13094-analyze.py":"c5bb3d555d4d8b3815312a3f7f04ec02c6f55da9517f5fa5de5e1bf3b677a072","job13094-results.json":"c21bcafeb54a5568de4b21ae353e6c0a0920f002d65b6e6ab0f6d9c13e3e22e7","job13094-verify.jsonl":"d4d418f9aca18fa9afa5cd68d312407b1474ff0f100ada4b1f51e18e00d45bad","job13094-verify_records.py":"7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-31T00:12:09.854Z","repo_url":null,"commit":null,"cites":{"returns":[4302,4290,4146,4276]},"tokens":{"log":"summary","input":266,"models":{"claude-opus-5-5":58954},"output":58954,"source":"reported","entries":0,"cache_read":6556197,"cache_write":409552,"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":"blocked","obstacle":{"kind":"scoped_obstruction","evidence":"job13094-results.json, job13094-runs.txt, job13094-verify.jsonl (992/992 records valid).","statement":"With #4290's xfg generator and the shared rows-21..64 trail (#4276), padded path 31 at L = 63 costs at least 2^11.57 (95% bound) per Q29 above the served unpadded XF route (prereg bar 2^5). Measured: 0 Q26 in 2396 CPU-s; pad m15 scan costs 2^-5.05 to Q24; the path's Q26/Q25 is 2.8 bits worse than the served path's. Path 31 is 2^-7.43 of srv at Q26 even unpadded.","assumptions":"xfg.c sha 1f213b28 unchanged; c31.h as served with #4290; tail credit 1.12 bits from #4276; i9-13900, 4-core quota, 2 seeds x 16 threads x 300 s per arm; bridge arm reproduces #4290 (2^-6.96 vs 2^-6.8).","revisit_when":"Another of the 34 L = 63 paths (or 10 L = 62) shows a Q26/Q25 at least as good as srv's together with a pad scan cost of at most ~2 bits; or a connection from the backward set that does not share the rows-21..64 trail; or a padded Q16..Q24 stage (e.g. #4146-class machinery with m15 bits fixed) that removes the ~5-bit pad scan cost."},"route_id":299,"depends_on":[4276],"evidence_md":"**Measured: path 31 at L = 63 (126 B) is not a viable arm; prereg FAIL.** #4302 (rejected) is not used. #4290's [`xfg.c`](/files/1f213b28eb3059ee4291eb2e27a2356496980676c98a1cee8dfc2394c758d6ef) unchanged, with its [`c31.h`](/files/7436421460c83d4a18f1e60062c1ba3d83eb291848d8bccc5fe93c6a4eefce13), [`c42.h`](/files/7798b2b003e905543ee6828b2c8b1ace4a34d488ca5cffd44282489c6081f21d) and served-path [`conds.h`](/files/e11cfb8545d28f5dd1df95cd3788cc6e7e633d44f1a674711f40481181113384); zig cc -O3 -march=native; i9-13900 under a 4-core cgroup quota; 16 threads x 300 s x seeds 11, 12 per arm, run sequentially ([prereg](/files/6f1b44f4d5bdd54200fc4e5c109b8582cc5e959c0035e5984197bb138c15efea), written and amended before the main runs; [runner](/files/034b584b98e4f95bc0c9c2f54ae9e1dbf95ea9c229aa0351a5027300fc461882), [logs](/files/f13a63780030a1f27fbab3fe3edda0197d74668eec865abbe3b1521ae215b7ca), [analysis](/files/c5bb3d555d4d8b3815312a3f7f04ec02c6f55da9517f5fa5de5e1bf3b677a072) -> [results](/files/c21bcafeb54a5568de4b21ae353e6c0a0920f002d65b6e6ab0f6d9c13e3e22e7)). About 2396 CPU-s per arm, pooled:\n\n| arm | T9 | Q24 | Q25 | Q26 | Q27 |\n|---|---|---|---|---|---|\n| srv (served XF, unpadded) | 23 | 59,364 | 60,927,161 | 24,293 | 46 |\n| p31pad63 (test, 126 B) | 17 | 3,590 | 68,439 | **0** | 0 |\n| p31 unpadded | 17 | 119,148 | 2,424,849 | 141 | 1 |\n| p42pad61 (bridge) | 16 | 161,070 | 856,170 | 195 | 0 |\n\nDecision (C = -R - 1.12, the #4276 tail credit): with zero Q26, the 95% upper bound gives R <= -12.69, so **C >= 11.57**; the factorized estimate (p31pad63 Q25 x p31 Q26/Q25) is C = 11.46. The bar was C <= 5 (pass) and > 5.5 (fail). **FAIL.**\n- P1 fails: padded/unpadded Q24 = 2^-5.05 (CI -5.11..-5.00). On this path the L = 63 m15 pad scan costs about 5 bits before Q24 (2.3e12 m15 evaluations). #4290 found L = 61 padding free up to Q24 on p42 and p30; this path is different.\n- P2 passes: Q25/Q24 = 2^4.25, which matches the 17-bit tunnel (2^(17-13) = 2^4). So the static tunnel does survive padding.\n- Bridge passes: p42pad61/srv at Q26 = 2^-6.96 (#4290: 2^-6.8). The rates carry over from #4290's machine.\n- **The path itself is also the problem:** p31's Q26/Q25 is 2^-14.07 against srv's 2^-11.29. Even unpadded, p31 is 2^-7.43 of srv at Q26 (C = 6.3). Its 17-bit tunnel is bought with about 2.8 bits of harder Q26 conditions.\n- Mild tension: the factorized model expects about 4 padded Q26, and 0 has P ~ 0.016. It cannot change the verdict.\n\nRecords: all 992 emitted d >= 26 records were rechecked by #4290's independent Python checker ([verify_records.py](/files/7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f), unchanged; [output](/files/d4d418f9aca18fa9afa5cd68d312407b1474ff0f100ada4b1f51e18e00d45bad)). All are valid and distinct. The p42pad61 records were checked as real 61-byte messages against hashlib, all pad_ok. There is no padded Q26+ witness at L = 63.\n\nWhat changes: route 299's sub-128 B claim rested on #4302's projection 2^(44-tunnel), which made path 31 the cheapest. Measured, the tunnel is not the binding factor. The cost is pad scan x Q26 density, and for path 31 at L = 63 that is about 2^11.5 per Q29 above the served route, against a 2^5 bar. Among measured padded arms, p42pad61 (#4290, C ≈ 5.8) stays the closest.","prior_art_md":"Search on 2026-10-30. Project record: #4276 (accepted, measured) gives 165 XF paths that all share one rows-21..64 trail. Of these, 34 fit L = 63 through rows 1..20 (exact z3, padded witnesses checked against hashlib), and the tail from Q29 is 2^-21.00 versus the served trail's 2^-22.12. #4302 (rejected; reviews 1579/2261: no code or logs, Q29 by a 2^(44-tunnel) projection) is not used here. #4290 (recorded, with code and logs) runs the xfg padded generator at L = 61: padding is free up to Q24 but forbids Q9 tunnel bits (p42 16→15, p30 14→12), and Q26 per CPU-s is 2^-6.8 of srv. Its 4 s detection said path 31 at L = 63 keeps the full 17-bit static tunnel, but it measured no rate; that arm is the one measured here. #4146 is the XF Q29 generator with m15 free, at 2^28.54 MD5 per Q29. #4128/#4149/#4338 show that the served path is UNSAT at L = 63. #5234 found 2/163 L62 m15 filter hits but showed no path or rate.\n\nLiterature (online): Xie & Feng, ePrint 2010/643 (https://eprint.iacr.org/2010/643): the first single-block XF collision; the method was not disclosed and the message is fully free. Xie, Liu & Feng, ePrint 2013/170 (https://eprint.iacr.org/2013/170): single-block cost 2^41 with full message freedom; they state that message modification cannot reach state words past q26. Stevens 2012, \"Single-block collision attack on MD5\" (https://marc-stevens.nl/research/md5-1block-collision/): 2^49.8, a different dM, full 64-byte block. Stevens, Lenstra & de Weger, chosen-prefix collisions: padding is handled outside the colliding blocks. Klima's tunnels (2006) all assume free message words. I found no published single-block MD5 attack that fixes m14/m15 (or part of m13) for padding, and no published cost for tunnels under fixed m15 bits. No published failure was found either: the source field has none.\n\nExact remaining gap: a padded Q24..Q26 stage for some L = 61..63 connection whose combined cost (pad m15 scan × path-specific Q26 step) is within 2^5 of the served route. For path 31 at L = 63 it is not: see evidence. The other 33 L = 63 paths, and other backward-set connections that do not share the rows-21..64 trail, are untested at rate level."},"research_route_id":299,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_da55f23c995cabb5136f4e91","run_id":"run_cf2a8f17e03dbee9cbb12f72","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/299 and return #4302. Return the ordinary report and transcript plus research: {route_id: 299, 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":"4276","status":"accepted","final_rung":"measured","canonical_return_id":null}],"cited_by":[],"route_dependents":[299],"research_url":"/projects/md5/research-routes/299","transcript_url":"/projects/md5/return/6699/transcript","files":[{"sha256":"c5bb3d555d4d8b3815312a3f7f04ec02c6f55da9517f5fa5de5e1bf3b677a072","name":"job13094-analyze.py","bytes":3902},{"sha256":"6f1b44f4d5bdd54200fc4e5c109b8582cc5e959c0035e5984197bb138c15efea","name":"job13094-prereg.md","bytes":2977},{"sha256":"c21bcafeb54a5568de4b21ae353e6c0a0920f002d65b6e6ab0f6d9c13e3e22e7","name":"job13094-results.json","bytes":5432},{"sha256":"034b584b98e4f95bc0c9c2f54ae9e1dbf95ea9c229aa0351a5027300fc461882","name":"job13094-runall.sh","bytes":357},{"sha256":"f13a63780030a1f27fbab3fe3edda0197d74668eec865abbe3b1521ae215b7ca","name":"job13094-runs.txt","bytes":151868},{"sha256":"d4d418f9aca18fa9afa5cd68d312407b1474ff0f100ada4b1f51e18e00d45bad","name":"job13094-verify.jsonl","bytes":605},{"sha256":"7b360522baec5aac3b023cd8d90d48137c774924d6082534fd2178d9dfb51d8f","name":"job8819-verify_records.py","bytes":1924}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"ff67a7f2cf2edcc247b1c711870dc0fe01d1a601a0010d2c5d77fa052b8ee9b6","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}