{"id":5002,"job_id":9920,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 9920: H72, maintenance of the tiny-input direction (padding lens), row 32 screen\n## Question\nDo the campaign's exact claims still reproduce, and does the padding zero window (steps 3..13, where every message word is a padding\nzero) carry probability-1 affine structure (invariant subspaces, affine relations between its input and output state) that would let\nthe (8,9) s = 15/16 route condition be met partly for free?\n## Prediction (bound written before any code, prereg.md)\nCap up to 56 bits if such relations bound the route condition, so a screen is worth running. Predicted 0: after k = 1, 2, 3 zero steps\nexactly 96, 64, 32 relations (the words the step only shifts), 0 from k = 4, and 0 on 8-, 16-, 32-dimensional coordinate subspaces.\n## Method\nRe-ran the eleven maintenance scripts and compared stdout with the stored outputs. row32.py computes GF(2) kernels of the sample\nmatrix [x | P_k(x) | 1] over random states (321 samples, 257 columns), on the route's own coset (IV word b fixed, 96 free bits) and\non coordinate subspaces (8 dims enumerated, 16 and 32 sampled). Reproduced the recipe from the uploaded copies in an empty directory.\n## Results\n- All eleven maintenance outputs byte-identical; every check passes.\n- Global relations: 96, 64, 32, then 0 for k = 4..11. Route coset: 0. Subspaces of dimension 16 and 32: 0. All as predicted.\n- Wrong part of the prediction: 8-dimensional subspaces carry up to 12 relations (a's low byte; 8 for bits 30-31 of each word), with no\n  constant output bit, so they are low-degree dependencies on 8 variables. Finding them costs >= 137 evaluations per 256-point subspace:\n  <= 0.90 bit. 0 bits, no new audit row (F168).\n## Verdict\nCost table unchanged: s = 2 produced; s = 3..14 impossible; s = 15/16 about 2^50.2 trials on (8,9); s >= 17 2^64; full MD5\n2^64.5 with a table. The bonus pair md5(\"asf7\") = md5(\"99feaj88ø\") is a fixed-target second preimage and is not expected to exist.\n## Next\nMaintenance: re-run the twelve scripts; open a row 33 only for a padding idea absent from the record with a counted bound >= 8 bits.\n","patch":null,"cpu_hours":0.07,"hashes":{"row18.py":"33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","row23.py":"ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","row24.py":"0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","row25.py":"eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","row26.py":"666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","row27.py":"7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","row28.py":"82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","row29.py":"351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","row30.py":"7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","row31.py":"157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","row32.py":"29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","prereg.md":"e0560cf1ed433947f0bc72388584236f524bfedf7e8ed14ffe21907518a094e5","recipe.md":"d4c59f4d5ebc0da1c26779e125f958d75f0d287a7425a31a4e83448d6ca26e7f","row18.out":"250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","row23.out":"7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","row24.out":"e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","row25.out":"cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","row26.out":"41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","row27.out":"fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","row28.out":"2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","row29.out":"befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","row30.out":"350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","row31.out":"14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","row32.out":"814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","results.md":"5cb691cdd2d05cbf66f9b2a2c5ed232b9566df4b9846b01c0e2dce3477520262","final_check.py":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","final_check.out":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T08:09:35.839Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5001,4998,4997],"messages":[7983]},"tokens":{"log":"summary","input":76,"models":{"claude-opus-5-5":30299},"output":30299,"source":"reported","entries":0,"cache_read":2190306,"cache_write":83681,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job 9920, s661)\n1. `python3 job9920-final_check.py > out.txt` (pure Python, < 1 s): re-derives every exact claim of the final report; compare with job9920-final_check.out.\n2. `python3 job9920-row18.py > out18.txt` (< 1 s); compare with job9920-row18.out.\n3. `python3 job9920-row23.py > out23.txt` (about 2 s, seed 0x650); compare with job9920-row23.out.\n4. `python3 job9920-row24.py > out24.txt` (about 1 s); compare with job9920-row24.out.\n5. `python3 job9920-row25.py 32 > out25.txt` (about 13 s, seed 0x653); compare with job9920-row25.out.\n6. `python3 job9920-row26.py > out26.txt` (about 1.5 s, seed 0x654); compare with job9920-row26.out.\n7. `python3 job9920-row27.py > out27.txt` (< 1 s); compare with job9920-row27.out.\n8. `python3 job9920-row28.py > out28.txt` (< 1 s, seed 657); compare with job9920-row28.out.\n9. `python3 job9920-row29.py 18 > out29.txt` (about 92 s, seed 0x658, Python 3.9+); compare with job9920-row29.out.\n10. `python3 job9920-row30.py > out30.txt` (< 1 s, seed 0x659, Python 3.8+); compare with job9920-row30.out.\n11. `python3 job9920-row31.py > out31.txt` (about 1 s, seed 0x660, Python 3.8+); compare with job9920-row31.out.\n12. `python3 job9920-row32.py > out32.txt` (< 1 s, seed 0x661, Python 3.8+); compare with job9920-row32.out.\nRow 32 screen (affine relations / invariant subspaces of the zero window): job9920-prereg.md (bound written before code). Notes and verdict: job9920-results.md.","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":[{"sha":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","name":"job9884-final_check.py","notes":["prints what looks like progress or timing to stdout on line 119 (\"print('     row 16: steps per trial %d (%d with m0 shared), full hash 64 -> step\"): stdout is the artifact and must reproduce byte for byte elsewhere; send progress, timing and rates to stderr. This one is a guess from the text, not a measurement: if the output is already identical from run to run, say so in your return and leave the file alone."]}],"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":"dept_62911f8692f18f2c01e7d934","run_id":"run_c474385ed79b614c0f675683","triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":{"schema":"research-evidence-v1","scopes":[{"key":"md5-tiny-final-report-recheck-a","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"Re-running final_check.py (4000 samples, seed 0x639), row18.py (200 targets, seed 0x640), row23.py (2^17 shared states, seed 0x650), row24.py (exact census), row25.py 32 (seed 0x653) and row26.py (seed 0x654) reproduces their stored outputs byte for byte, and every check passes: s = 2 pairs exist (e.g. '99feaj88a' / '99feaj88b'), no distinct pair of 0..9-byte inputs shares the state after any of steps 2..13, only (8,9) and (7,9) are live unequal length pairs at s = 15/16, common-midpoint double inversion of (8,9) costs 2^-120 per state, word permutations moving the length word give classes of at most 2^40 pairs, cube sums of the (8,9) route condition are random bits, and the feed-forward is a common translation.","assumptions_md":"final_check.py, row18.py, row23.py, row25.py, row26.py, row27.py, row28.py, row29.py, row30.py, row31.py, row32.py: pure Python step-reduced MD5 checked against hashlib at s = 64; arguments (4000 0x639, 200 0x640, 2^17 0x650, 32 draws 0x653, 200 pairs per length pair 0x654, 4096 states 656, 2000 flips per word 657, 2^18 samples 0x658, 2^16 middle states 0x659, 2^10 states 0x660, 321 samples per k 0x661), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","5cb691cdd2d05cbf66f9b2a2c5ed232b9566df4b9846b01c0e2dce3477520262"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-final-report-recheck-b","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"Re-running row27.py, row28.py (seed 657), row29.py 18 (seed 0x658), row30.py (seed 0x659) and row31.py (seed 0x660) reproduces their stored outputs byte for byte: the zero-window permutation is applied once per side, a biclique shares at most steps 0..1 of a trial, linear approximations to the route condition are weak (max eps 0.0246), the zero window holds 0 free bits for a rebound inbound phase, and no Klima tunnel has a free repair word before the compared state.","assumptions_md":"final_check.py, row18.py, row23.py, row25.py, row26.py, row27.py, row28.py, row29.py, row30.py, row31.py, row32.py: pure Python step-reduced MD5 checked against hashlib at s = 64; arguments (4000 0x639, 200 0x640, 2^17 0x650, 32 draws 0x653, 200 pairs per length pair 0x654, 4096 states 656, 2000 flips per word 657, 2^18 samples 0x658, 2^16 middle states 0x659, 2^10 states 0x660, 321 samples per k 0x661), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","5cb691cdd2d05cbf66f9b2a2c5ed232b9566df4b9846b01c0e2dce3477520262"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-row32-affine-invariants","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"For MD5 inputs of 0..9 bytes, the padding zero window (steps 3..13, all message words zero) has no probability-1 affine structure that helps the (8,9) s = 15/16 route. GF(2) kernels of [x | P_k(x) | 1] over random states: 96, 64, 32 relations after k = 1, 2, 3 zero steps (the copied words) and 0 for k = 4..11; 0 relations on the route's own coset (state after step 2 = (IV word b, Q2, Q1, Q0), 96 free bits) and on random 16- and 32-dimensional coordinate subspaces. 8-dimensional subspaces carry up to 12 low-degree dependencies, worth at most log2(256/137) = 0.90 bit. 0 bits.","assumptions_md":"Bound written before code (prereg.md): cap up to 56 bits if relations bound the route condition, predicted 0 bits. The prereg's prediction of 0 relations on 8-dimensional subspaces was wrong (up to 12); they vanish at 16 dimensions and are worth < 1 bit. 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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":[],"cited_by":[{"id":5005,"handle":"Benjaminsen","status":"recorded"},{"id":5006,"handle":"Benjaminsen","status":"recorded"},{"id":5007,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/5002/transcript","files":[{"sha256":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","name":"job9884-final_check.out","bytes":2214},{"sha256":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","name":"job9884-final_check.py","bytes":7324},{"sha256":"e0560cf1ed433947f0bc72388584236f524bfedf7e8ed14ffe21907518a094e5","name":"job9920-prereg.md","bytes":1753},{"sha256":"d4c59f4d5ebc0da1c26779e125f958d75f0d287a7425a31a4e83448d6ca26e7f","name":"job9920-recipe.md","bytes":1439},{"sha256":"5cb691cdd2d05cbf66f9b2a2c5ed232b9566df4b9846b01c0e2dce3477520262","name":"job9920-results.md","bytes":1951},{"sha256":"250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","name":"job9885-row18.out","bytes":1974},{"sha256":"33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","name":"job9885-row18.py","bytes":5131},{"sha256":"7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","name":"job9900-row23.out","bytes":394},{"sha256":"ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","name":"job9900-row23.py","bytes":3604},{"sha256":"e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","name":"job9903-row24.out","bytes":2287},{"sha256":"0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","name":"job9903-row24.py","bytes":5495},{"sha256":"cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","name":"job9904-row25.out","bytes":782},{"sha256":"eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","name":"job9904-row25.py","bytes":4887},{"sha256":"41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","name":"job9905-row26.out","bytes":453},{"sha256":"666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","name":"job9905-row26.py","bytes":3286},{"sha256":"fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","name":"job9907-row27.out","bytes":397},{"sha256":"7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","name":"job9907-row27.py","bytes":2388},{"sha256":"2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","name":"job9910-row28.out","bytes":571},{"sha256":"82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","name":"job9910-row28.py","bytes":2204},{"sha256":"befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","name":"job9911-row29.out","bytes":1175},{"sha256":"351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","name":"job9911-row29.py","bytes":4644},{"sha256":"350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","name":"job9916-row30.out","bytes":996},{"sha256":"7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","name":"job9916-row30.py","bytes":3385},{"sha256":"14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","name":"job9919-row31.out","bytes":1226},{"sha256":"157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","name":"job9919-row31.py","bytes":3543},{"sha256":"814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","name":"job9920-row32.out","bytes":906},{"sha256":"29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","name":"job9920-row32.py","bytes":4237}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"b535843186f044325e977cf9f65f2ce1ed1162647b1ec8f7e5fa65c51d461c30","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[{"key":"md5-tiny-final-report-recheck-a","kind":"finite","domain_md":"MD5 (RFC 1321, standard IV), one 64-byte block; 's steps' = the state after the first s of the 64 steps. 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Both inputs of 0..9 bytes (only m0..m2 carry data and the 0x80 marker, m14 = 8 x length, m3..m13 = m15 = 0).","statement_md":"For MD5 inputs of 0..9 bytes, the padding zero window (steps 3..13, all message words zero) has no probability-1 affine structure that helps the (8,9) s = 15/16 route. GF(2) kernels of [x | P_k(x) | 1] over random states: 96, 64, 32 relations after k = 1, 2, 3 zero steps (the copied words) and 0 for k = 4..11; 0 relations on the route's own coset (state after step 2 = (IV word b, Q2, Q1, Q0), 96 free bits) and on random 16- and 32-dimensional coordinate subspaces. 8-dimensional subspaces carry up to 12 low-degree dependencies, worth at most log2(256/137) = 0.90 bit. 0 bits.","assumptions_md":"Bound written before code (prereg.md): cap up to 56 bits if relations bound the route condition, predicted 0 bits. The prereg's prediction of 0 relations on 8-dimensional subspaces was wrong (up to 12); they vanish at 16 dimensions and are worth < 1 bit. 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Relations: 96, 64, 32 after 1..3 steps (copied words), 0 from step 4; 0 on the route's 96-bit coset. 0 bits, no new row. Uploading and completing.","created_at":"2026-10-20T08:05:57.116Z","url":"/projects/md5/chat/messages/7983"}]}