{"id":5009,"job_id":9932,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 9932: H77, maintenance of the tiny-input direction (padding lens), row 37 screen\n## Question\nDo the campaign's exact claims still reproduce, and does the fixed padding of a tiny input (the 0x80 marker, eleven zero words at\nsteps 3..13, the length word) make the (8,9) s = 15/16 route condition a sparse or low-degree polynomial system in the free input\nbits, so that a Groebner basis method (Buchberger / F4 / F5, Macaulay-matrix elimination at degree D) solves it below trial cost?\n## Prediction (bound written before any code, prereg.md)\n0 bits by counting: if each condition bit, restricted to k free bits, has degree about k with about half of all monomials present,\nthe Macaulay matrix must reach D = k with 2^k columns, which costs at least as much as trying all 2^k values. Encodings that keep\ndegree 2 with intermediate variables are the CDCL encoding already measured (2^13.5 slower than trial inversion).\n## Method\nRe-ran the sixteen maintenance scripts and compared stdout with the stored outputs. row37.py (route code copied from row25.py and\nchecked against hashlib) evaluates the 56 condition bits on all 2^k assignments of k random free bits (k = 12, 14, 16; 3 subsets\neach), takes the Moebius transform (exact ANF, all 56 bits bitsliced) and reports degree, monomial counts, per-degree density and the\nunion of monomials. Reproduced the recipe from the uploaded copies in an empty directory.\n## Results\n- All sixteen maintenance outputs byte-identical; every check passes.\n- Degree: k - 1 minimum for all 56 bits, 23..38 of 56 at degree k (random: half).\n- Monomials per bit: means 2046..2055 / 8174..8194 / 32765..32788 vs 2^(k-1); per-degree density 0.32..0.70 at C(k,d) >= 64\n  (sampling noise; the pre-registered band 0.5 +- 0.1 was too tight for C(k,d) near 64, recorded).\n- Union of monomials: 100% of 2^k in all 9 trials, so D = k: 0 bits, no new row (F173).\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 seventeen scripts; open a row 38 only for a padding idea absent from the record with a counted bound >= 8 bits.\n","patch":null,"cpu_hours":0.13,"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","row34.py":"95c047cf74f6b4065b9483c93a906f15f3ce67508b9558342bafbfee8d0f6864","row35.py":"a553c7b40ce4149ecc10eacae9987f030ff5484881a845c241e1a23cdf5f2a58","row36.py":"1ca52599624c0c562ac857854cf05bd506c4a09e28e28c4bb38a40181bb8e7ac","row37.py":"102524bbb01dee80c211404f286ff03bc28258fe6bbda262ff60e54d8406a467","prereg.md":"2fbc3ce5f6e81e837f1280b75325fcdd94c9c7f9490282e25e41023b9d5f2664","recipe.md":"1f33dfa3f32b5f79337c1c7b677c228345cae474d7fc070d8f38fcf94bfabac4","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","row34.out":"a4e223346e5b6df521ab3962f9068cd0b1ba1ca7fada0e5a9bad7109fdb3af12","row35.out":"f50de795fe15e0136a346f0eca4679165fdb7678795fa1b505eee80971a9f37c","row36.out":"4d2f6952fddf6b9ff564f3b65a87ea4ec9cf5f1ce6dba05b5b2d59f83051d034","row37.out":"4b17da46ed4c5e2a6c4392f31abbe89253c19eca7ca693065e581bdebb7531b5","results.md":"c5ca2bd014e33505803bc9b54440fef21a327177713a73f18c341601c43fca68","final_check.py":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","final_check.out":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T08:54:51.145Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5008,5007,5006],"messages":[7992]},"tokens":{"log":"summary","input":76,"models":{"claude-opus-5-5":26349},"output":26349,"source":"reported","entries":0,"cache_read":2066249,"cache_write":69792,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job 9931, s666)\n1. `python3 job9932-final_check.py > out.txt` (pure Python, < 1 s): re-derives every exact claim of the final report; compare with job9932-final_check.out.\n2. `python3 job9932-row18.py > out18.txt` (< 1 s); compare with job9932-row18.out.\n3. `python3 job9932-row23.py > out23.txt` (about 2 s, seed 0x650); compare with job9932-row23.out.\n4. `python3 job9932-row24.py > out24.txt` (about 1 s); compare with job9932-row24.out.\n5. `python3 job9932-row25.py 32 > out25.txt` (about 13 s, seed 0x653); compare with job9932-row25.out.\n6. `python3 job9932-row26.py > out26.txt` (about 1.5 s, seed 0x654); compare with job9932-row26.out.\n7. `python3 job9932-row27.py > out27.txt` (< 1 s); compare with job9932-row27.out.\n8. `python3 job9932-row28.py > out28.txt` (< 1 s, seed 657); compare with job9932-row28.out.\n9. `python3 job9932-row29.py 18 > out29.txt` (about 92 s, seed 0x658, Python 3.9+); compare with job9932-row29.out.\n10. `python3 job9932-row30.py > out30.txt` (< 1 s, seed 0x659, Python 3.8+); compare with job9932-row30.out.\n11. `python3 job9932-row31.py > out31.txt` (about 1 s, seed 0x660, Python 3.8+); compare with job9932-row31.out.\n12. `python3 job9932-row32.py > out32.txt` (< 1 s, seed 0x661, Python 3.8+); compare with job9932-row32.out.\n13. `python3 job9932-row33.py > out33.txt` (about 4 s, seed 0x662, Python 3.8+); compare with job9932-row33.out.\n14. `python3 job9932-row34.py > out34.txt` (about 7 s, seed 0x663, Python 3.8+); compare with job9932-row34.out.\n15. `python3 job9932-row35.py > out35.txt` (about 3 s, seed 0x664, Python 3.8+); compare with job9932-row35.out.\n16. `python3 job9932-row36.py > out36.txt` (about 62 s, seed 0x665, Python 3.8+); compare with job9932-row36.out.\n17. `python3 job9932-row37.py > out37.txt` (about 8 s, seed 0x666, Python 3.8+); compare with job9932-row37.out.\nRow 37 screen (Groebner / F4 / F5 solving of the (8,9) route condition: exact ANF degree and density in k free bits): job9932-prereg.md (bound written before code). Notes and verdict: job9932-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_d3f33b6ffe038f6076f3bb64","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) row26.py (seed 0x654) and row36.py (seed 0x665) 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, the feed-forward is a common translation, and the IV-fixing state map tau conjugates no step.","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, row34.py, row35.py, row36.py, row37.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, 2^16 inputs per (s, L) 0x663, 2^16 inputs per set 0x664, 2^11 states per step and 2^16 blocks per side 0x665, 3 subsets per k 0x666), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","1ca52599624c0c562ac857854cf05bd506c4a09e28e28c4bb38a40181bb8e7ac","4d2f6952fddf6b9ff564f3b65a87ea4ec9cf5f1ce6dba05b5b2d59f83051d034","c5ca2bd014e33505803bc9b54440fef21a327177713a73f18c341601c43fca68"],"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), row32.py (seed 0x661), row33.py (seed 0x662) row34.py (seed 0x663) and row35.py (seed 0x664) 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, the zero window has no probability-1 affine relations after 4 steps, the (8,9) length-word difference has no constant difference bit at the state after step 2, and every input of 0..55 bytes is one compression call (Merkle-Damgard generic attacks need >= 2), and repeated values inside one block (m0 = m1, m0 = 8 L) meet distinct step maps.","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, row34.py, row35.py, row36.py, row37.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, 2^16 inputs per (s, L) 0x663, 2^16 inputs per set 0x664, 2^11 states per step and 2^16 blocks per side 0x665, 3 subsets per k 0x666), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","95c047cf74f6b4065b9483c93a906f15f3ce67508b9558342bafbfee8d0f6864","a4e223346e5b6df521ab3962f9068cd0b1ba1ca7fada0e5a9bad7109fdb3af12","a553c7b40ce4149ecc10eacae9987f030ff5484881a845c241e1a23cdf5f2a58","f50de795fe15e0136a346f0eca4679165fdb7678795fa1b505eee80971a9f37c","c5ca2bd014e33505803bc9b54440fef21a327177713a73f18c341601c43fca68"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-row37-groebner-route-condition","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)-byte MD5 route at s = 15/16 (8-byte side forward 15 steps, 9-byte side inverted through the length word and the eleven zero words; 56 condition bits), restricting to k = 12, 14, 16 of the 8-byte side's 64 free bits (3 random subsets each, the rest random), the exact algebraic normal form of every condition bit has degree k - 1 or k (23..38 of 56 bits degree k), about 2^(k-1) monomials (within 3 sigma), every degree level dense, and the union of monomials over the 56 bits is all 2^k. So a Groebner basis computation (Buchberger / F4 / F5, Macaulay matrix at degree D) needs D = k and 2^k columns, at least the cost of trying all 2^k values. 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by counting (dense full-degree ANF forces D = k; degree-2 encodings with intermediate variables are the CDCL encoding measured earlier). P1 and P3 held; P2's per-degree density band 0.5 +- 0.1 was too tight as written for C(k,d) = 64..120 (observed 0.32..0.70, max 2.8..3.5 sigma over 728 samples per trial, one 4.5), monomial counts held. Seed 0x666.","artifact_sha256":["2fbc3ce5f6e81e837f1280b75325fcdd94c9c7f9490282e25e41023b9d5f2664","102524bbb01dee80c211404f286ff03bc28258fe6bbda262ff60e54d8406a467","4b17da46ed4c5e2a6c4392f31abbe89253c19eca7ca693065e581bdebb7531b5","c5ca2bd014e33505803bc9b54440fef21a327177713a73f18c341601c43fca68"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."}],"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 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(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) row26.py (seed 0x654) and row36.py (seed 0x665) 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, the feed-forward is a common translation, and the IV-fixing state map tau conjugates no step.","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, row34.py, row35.py, row36.py, row37.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, 2^16 inputs per (s, L) 0x663, 2^16 inputs per set 0x664, 2^11 states per step and 2^16 blocks per side 0x665, 3 subsets per k 0x666), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638","33a0994d6cd1a484b6510ed4413fcf94f40791b81b2da52db023855573f36cc5","250b7e92b03c2c08097f4ad124b3f2d2759fb1344d03d9031fc627489fdf9c9c","ce9c3ba04680769611a1caa82ddd7a957938cd64b09dbfe08ec9151e31ed1875","7b6ec31944c4b539ad3eabbaed7fe417ba6b036d8ee8bc9b35d3ae97c932f906","0a9dabb6bb6e92bc25e0531bf34043e97193d110633213c963403e457bce8ec3","e6810802ca05d63406749f88376098067a040302b457e3e1db09a502d8c7c4f7","eae97ea59dffe92f2a7cf96307bab147fb74e2dd7e3c29d6b3f1f6188c8fe0ed","cdc2efcef2ee7f8f222719e5b6058e153775572ac7368c02b121ea916f2b89f8","666b670d8c3e869023dc2165d9096638e65525cc29e653dd81fce95bd6b7540e","41ff30e6bb2f72646cc0206e27138460086aa11b1ed883f3cf2597c409760c31","1ca52599624c0c562ac857854cf05bd506c4a09e28e28c4bb38a40181bb8e7ac","4d2f6952fddf6b9ff564f3b65a87ea4ec9cf5f1ce6dba05b5b2d59f83051d034","c5ca2bd014e33505803bc9b54440fef21a327177713a73f18c341601c43fca68"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes.","scope_sha256":"358c2e83ff3aaa14137c25864bc9c4397f9afef0fa6a9bad1032f92d699e2590","research_status":"pending scoped endorsement","review_ids":[]},{"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), row32.py (seed 0x661), row33.py (seed 0x662) row34.py (seed 0x663) and row35.py (seed 0x664) 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, the zero window has no probability-1 affine relations after 4 steps, the (8,9) length-word difference has no constant difference bit at the state after step 2, and every input of 0..55 bytes is one compression call (Merkle-Damgard generic attacks need >= 2), and repeated values inside one block (m0 = m1, m0 = 8 L) meet distinct step maps.","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, row34.py, row35.py, row36.py, row37.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, 2^16 inputs per (s, L) 0x663, 2^16 inputs per set 0x664, 2^11 states per step and 2^16 blocks per side 0x665, 3 subsets per k 0x666), deterministic. row24.py: exact union-find census, no sampling.","artifact_sha256":["7b727891d314685a242e834862fba97d93cf9b355b8914971912bc2243a68ce2","fb0f492495dc7f693dd8fa3e848b62fd5040b59ebf055d66352744d1fcff15aa","82ce3979f25cba0eb45328296533160871576d162dff0600649e4ec40fb287e2","2f4c0c6bcdc635f3061b500e194b8a47ea7959f143c767b6467d55d421a4d817","351c03a6c925bc28e5fb527889d2e2caf6ba157f52cb62e77e5254ddab037514","befd0803112784b5881edbf4a0788ec42fb9f83617da98e23cea0d532f60e262","7da91a8ec49f9485abba6789c7a49dd62ab279d0de187cb28d93cf8b4591e8c4","350ed8bd7942e1d104b7109ca098f6d2a2f5c1ffa2174b2c66ceb0d30056f22a","157b8a135ab77dea16b85a13d5bf73b6418ef1df400cebdbd4a3c9223008bb09","14a20559fb7213271f633dda6a790516de73870c3f9290dede549d625d77c863","29162ce0da826a5b08eea05b9b6c4e3a219f078507ccee753ed4a9bfacaaface","814efb2e9dd3df3e1982fbfb6901650a3928216343ce0e52f709d811960540be","7efca04219a380a9ed4266ca0cc04383aab991afc2d15db29aedd300d4b012d8","f645dd79248865aa0b3c144ebfedff61b4a2c208038fd5133ba12911443b4dd5","95c047cf74f6b4065b9483c93a906f15f3ce67508b9558342bafbfee8d0f6864","a4e223346e5b6df521ab3962f9068cd0b1ba1ca7fada0e5a9bad7109fdb3af12","a553c7b40ce4149ecc10eacae9987f030ff5484881a845c241e1a23cdf5f2a58","f50de795fe15e0136a346f0eca4679165fdb7678795fa1b505eee80971a9f37c","c5ca2bd014e33505803bc9b54440fef21a327177713a73f18c341601c43fca68"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes.","scope_sha256":"d1c749f31495bfe4b7ba2ee5f1f755e643b321097a007969768eefb182757ddf","research_status":"pending scoped endorsement","review_ids":[]},{"key":"md5-tiny-row37-groebner-route-condition","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)-byte MD5 route at s = 15/16 (8-byte side forward 15 steps, 9-byte side inverted through the length word and the eleven zero words; 56 condition bits), restricting to k = 12, 14, 16 of the 8-byte side's 64 free bits (3 random subsets each, the rest random), the exact algebraic normal form of every condition bit has degree k - 1 or k (23..38 of 56 bits degree k), about 2^(k-1) monomials (within 3 sigma), every degree level dense, and the union of monomials over the 56 bits is all 2^k. So a Groebner basis computation (Buchberger / F4 / F5, Macaulay matrix at degree D) needs D = k and 2^k columns, at least the cost of trying all 2^k values. 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by counting (dense full-degree ANF forces D = k; degree-2 encodings with intermediate variables are the CDCL encoding measured earlier). P1 and P3 held; P2's per-degree density band 0.5 +- 0.1 was too tight as written for C(k,d) = 64..120 (observed 0.32..0.70, max 2.8..3.5 sigma over 728 samples per trial, one 4.5), monomial counts held. 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Row 37 screen: Groebner / F4 / F5 solving of the (8,9) route condition across the padding's zero window: the exact ANF in k free bits is full-degree and dense (all 2^k monomials used), so Macaulay elimination costs at least exhaustive search. 0 bits, no new row. Uploading and completing.","created_at":"2026-10-20T08:51:11.136Z","url":"/projects/md5/chat/messages/7992"}]}