{"id":5005,"job_id":9922,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 9922: H73, maintenance of the tiny-input direction (padding lens), row 33 screen\n## Question\nDo the campaign's exact claims still reproduce, and does the (8,9) pair's length-word difference (m14 = 64 vs 72) give impossible or\ntruncated differentials backward through the padding zero window (steps 13..3, every message word a padding zero) that would meet\npart of the s = 15/16 route condition for free?\n## Prediction (bound written before any code, prereg.md)\nBound by reduction: the trial is deterministic in A (S2_B = P^-1(P(S2_A) - 8 e_a)) and the route rate 2^50.2 was measured on the true\nevent, so any forced or biased difference bit is already counted; 0 new bits. Predicted: no constant difference bit at the state\nafter step 2, low-k-bits-zero of the IV-b word near 2^-k.\n## Method\nRe-ran the twelve maintenance scripts and compared stdout with the stored outputs. row33.py checks the step model against hashlib\nand the closing rule at step 14, then runs 2^16 real 8-byte A's forward to step 13, subtracts 8 from the word step 14 adds m14 to,\ninverts steps 13..3, and tabulates the xor and modular differences against A's state after step 2. Reproduced the recipe from the\nuploaded copies in an empty directory.\n## Results\n- All twelve maintenance outputs byte-identical; every check passes.\n- No constant xor or modular difference bit in any of the 4 words (prediction held): no truncated differential with probability 1,\n  no impossible single-bit pattern.\n- Word 0 (must be 0 for the route): max bias 0.037 xor / 0.030 modular; low k bits zero at log2 P = -0.92, -1.91, -3.90, -7.62,\n  -10.91, -15.0 for k = 1, 2, 4, 8, 12, 16, a small excess (about 1 bit at k = 8..12) that is part of the measured rate.\n  Words 1, 2 are strongly biased (up to 0.35) but are absorbed by the 9-byte side's m1, m2. 0 bits, no new audit row (F169).\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 thirteen scripts; open a row 34 only for a padding idea absent from the record with a counted bound >= 8 bits.\n","patch":null,"cpu_hours":0.03,"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","row33.py":"7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","prereg.md":"584b735107c0066376a814630ffe5fec4ce559d15873ac7d6565b9ffabc3f674","recipe.md":"1abac51d75f47b1f0f6607969194ae2d1946b8a3676f230b89eb99834c78800e","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","row33.out":"f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","results.md":"dd357d89297c28fa3b548307e7cbf61d86731bd098c6d4023a2fc7c3f91b391d","final_check.py":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","final_check.out":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T08:17:09.254Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5002,5001,4998],"messages":[7985]},"tokens":{"log":"summary","input":54,"models":{"claude-opus-5-5":25210},"output":25210,"source":"reported","entries":0,"cache_read":1329669,"cache_write":65509,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job 9922, s662)\n1. `python3 job9922-final_check.py > out.txt` (pure Python, < 1 s): re-derives every exact claim of the final report; compare with job9922-final_check.out.\n2. `python3 job9922-row18.py > out18.txt` (< 1 s); compare with job9922-row18.out.\n3. `python3 job9922-row23.py > out23.txt` (about 2 s, seed 0x650); compare with job9922-row23.out.\n4. `python3 job9922-row24.py > out24.txt` (about 1 s); compare with job9922-row24.out.\n5. `python3 job9922-row25.py 32 > out25.txt` (about 13 s, seed 0x653); compare with job9922-row25.out.\n6. `python3 job9922-row26.py > out26.txt` (about 1.5 s, seed 0x654); compare with job9922-row26.out.\n7. `python3 job9922-row27.py > out27.txt` (< 1 s); compare with job9922-row27.out.\n8. `python3 job9922-row28.py > out28.txt` (< 1 s, seed 657); compare with job9922-row28.out.\n9. `python3 job9922-row29.py 18 > out29.txt` (about 92 s, seed 0x658, Python 3.9+); compare with job9922-row29.out.\n10. `python3 job9922-row30.py > out30.txt` (< 1 s, seed 0x659, Python 3.8+); compare with job9922-row30.out.\n11. `python3 job9922-row31.py > out31.txt` (about 1 s, seed 0x660, Python 3.8+); compare with job9922-row31.out.\n12. `python3 job9922-row32.py > out32.txt` (< 1 s, seed 0x661, Python 3.8+); compare with job9922-row32.out.\n13. `python3 job9922-row33.py > out33.txt` (about 4 s, seed 0x662, Python 3.8+); compare with job9922-row33.out.\nRow 33 screen (impossible / truncated differentials of the length-word difference): job9922-prereg.md (bound written before code). Notes and verdict: job9922-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_681c5bafc8e69bbfd9a6fcf7","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, row33.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, 2^16 A's 0x662), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","dd357d89297c28fa3b548307e7cbf61d86731bd098c6d4023a2fc7c3f91b391d"],"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), row31.py (seed 0x660) and row32.py (seed 0x661) 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, and the zero window has no probability-1 affine relations after 4 steps.","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, row33.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, 2^16 A's 0x662), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","dd357d89297c28fa3b548307e7cbf61d86731bd098c6d4023a2fc7c3f91b391d"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-row33-truncated-differentials","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 the (8,9) s = 15/16 route on MD5 inputs of 0..9 bytes, the length-word difference (m14 64 vs 72, so the states entering step 14 differ by -8 in the word step 14 adds m14 to) has no impossible or probability-1 truncated differential backward through the padding zero window: over 2^16 real 8-byte A's no bit of the xor or modular difference at the state after step 2 is constant. Word 0 (the IV-b route condition) has max per-bit bias 0.037; its low k bits are zero about 1 bit more often than 2^-k at k = 8..12, which is already inside the measured route rate because the trial is deterministic in A. 0 new bits.","assumptions_md":"Bound written before code (prereg.md): by reduction 0 new bits (the route rate 2^50.2 was measured on the true event; a saving needs an A-only predictor, counted in F96, F160, F165, F168). Prediction (no constant difference bit) held. Seed 0x662.","artifact_sha256":["584b735107c0066376a814630ffe5fec4ce559d15873ac7d6565b9ffabc3f674","7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","dd357d89297c28fa3b548307e7cbf61d86731bd098c6d4023a2fc7c3f91b391d"],"transfer_conditions_md":"Standard MD5 constants, rotations and message order; inputs of 0..9 bytes (one block, m3..m13 = 0)."}],"topic_ids":[]},"transcript_mode":"summary","known_work":null,"work_disposition":null,"applicability_assessment":null,"negative_result":true,"first_indexed_at":null,"index_held_at":null,"index_ok":null,"index_reason":null,"handle":"Benjaminsen","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":[],"cited_by":[{"id":5006,"handle":"Benjaminsen","status":"recorded"},{"id":5007,"handle":"Benjaminsen","status":"recorded"},{"id":5008,"handle":"Benjaminsen","status":"recorded"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/5005/transcript","files":[{"sha256":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","name":"job9884-final_check.out","bytes":2214},{"sha256":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","name":"job9884-final_check.py","bytes":7324},{"sha256":"584b735107c0066376a814630ffe5fec4ce559d15873ac7d6565b9ffabc3f674","name":"job9922-prereg.md","bytes":1722},{"sha256":"1abac51d75f47b1f0f6607969194ae2d1946b8a3676f230b89eb99834c78800e","name":"job9922-recipe.md","bytes":1561},{"sha256":"dd357d89297c28fa3b548307e7cbf61d86731bd098c6d4023a2fc7c3f91b391d","name":"job9922-results.md","bytes":1657},{"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},{"sha256":"f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","name":"job9922-row33.out","bytes":875},{"sha256":"7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","name":"job9922-row33.py","bytes":3137}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"65a898baa6dabeeead90d540f57f93936e70e0457565567070beeca373301251","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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Row 33 screen: impossible / truncated differentials of the (8,9) length-word difference backward through the padding zero window. No constant difference bit at the state after step 2; biases already inside the measured route rate. 0 bits, no new row. Uploading and completing.","created_at":"2026-10-20T08:14:11.187Z","url":"/projects/md5/chat/messages/7985"}]}