{"id":5014,"job_id":9936,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 9936: H79, maintenance of the tiny-input direction (padding lens), row 39 screen\n## Question\nDo the campaign's exact claims still reproduce, and since every padding constant of a tiny input (length word <= 72, markers 0x80 /\n0x8000) and the (8,9) differences (dm14 = +8, dm2) sit in low bits while modular addition is a T-function, can the (8,9) s = 15/16\nroute condition be solved bit-slice by bit-slice (mod 2^k, low bits first), so that costs add over slices instead of multiplying?\n## Prediction (bound written before any code, prereg.md)\n0 bits by proof: a bit set closed under the dependence of modular addition is a low slice {0..k-1}; the step's rotation by s_t\n(4..23) maps the top bits onto the bottom, so a low slice is closed only for k = 0 or 32. No proper slice survives one step.\n## Method\nRe-ran the eighteen maintenance scripts and compared stdout with the stored outputs. row39.py (route code copied from row38.py,\nchecked against hashlib) flips one random free bit above position k and tests whether the low k bits of the state change: forward on\nthe 8-byte side after steps 1..16, backward through the inverse steps from step 14, and on the 56 route-condition bits; it also tracks\nwhere the +8 length difference lands. Reproduced the recipe from the uploaded copies.\n## Results\n- All eighteen maintenance outputs byte-identical; every check passes.\n- 0 closed low slices forward (t = 1..16, k = 1..31) and backward (t = 1..15, k = 1..31).\n- Low-slice route-condition bits change under an A flip above k in >= 46.7% of samples for every k (minimum at k = 1, one bit).\n- The +8 length difference lands at Q15 bits 20..23 (rotl 17) with carries to 24, 25. P1..P4 held. 0 bits, no new row (F175).\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 nineteen scripts; open a row 40 only for a padding idea absent from the record with a counted bound >= 8 bits.\n","patch":null,"cpu_hours":0.15,"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","row38.py":"bbb94b0877520c58cbd3e70500e0d7dd2c9df22696dcba01bd2bdba30c76c7ba","row39.py":"97ae9627e2aa57981f86c9cfc0c572e15b5dad947c97d56820eb4bd1d1b125ec","prereg.md":"81e6f6f372223955fe7a1b70ae8446a73a22e0fc587dea77a4cb953549681c26","recipe.md":"38ac8b8cce049226e94dda324b85b8b6e5e3c306f4bc3b4d48b6ca21e9baa31e","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","row38.out":"3d96307783059af11aba9a3dc42a0a69dc6880ae33db1cc9e34bb1a6e111b745","row39.out":"8663c41ba0499542896ffe50d78b2a16471bc3877497193bb13e4d9aac6ebdbf","results.md":"4d1569448f61be49e037487a96648da5341e00e1a025d18bca5527bc09897128","final_check.py":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","final_check.out":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T09:16:51.857Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5011,5009,5008],"messages":[7998]},"tokens":{"log":"summary","input":70,"models":{"claude-opus-5-5":25541},"output":25541,"source":"reported","entries":0,"cache_read":1922234,"cache_write":74183,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job 9936, s668)\n1. `python3 job9936-final_check.py > out.txt` (pure Python, < 1 s): re-derives every exact claim of the final report; compare with job9936-final_check.out.\n2. `python3 job9936-row18.py > out18.txt` (< 1 s); compare with job9936-row18.out.\n3. `python3 job9936-row23.py > out23.txt` (about 2 s, seed 0x650); compare with job9936-row23.out.\n4. `python3 job9936-row24.py > out24.txt` (about 1 s); compare with job9936-row24.out.\n5. `python3 job9936-row25.py 32 > out25.txt` (about 13 s, seed 0x653); compare with job9936-row25.out.\n6. `python3 job9936-row26.py > out26.txt` (about 1.5 s, seed 0x654); compare with job9936-row26.out.\n7. `python3 job9936-row27.py > out27.txt` (< 1 s); compare with job9936-row27.out.\n8. `python3 job9936-row28.py > out28.txt` (< 1 s, seed 657); compare with job9936-row28.out.\n9. `python3 job9936-row29.py 18 > out29.txt` (about 92 s, seed 0x658, Python 3.9+); compare with job9936-row29.out.\n10. `python3 job9936-row30.py > out30.txt` (< 1 s, seed 0x659, Python 3.8+); compare with job9936-row30.out.\n11. `python3 job9936-row31.py > out31.txt` (about 1 s, seed 0x660, Python 3.8+); compare with job9936-row31.out.\n12. `python3 job9936-row32.py > out32.txt` (< 1 s, seed 0x661, Python 3.8+); compare with job9936-row32.out.\n13. `python3 job9936-row33.py > out33.txt` (about 4 s, seed 0x662, Python 3.8+); compare with job9936-row33.out.\n14. `python3 job9936-row34.py > out34.txt` (about 7 s, seed 0x663, Python 3.8+); compare with job9936-row34.out.\n15. `python3 job9936-row35.py > out35.txt` (about 3 s, seed 0x664, Python 3.8+); compare with job9936-row35.out.\n16. `python3 job9936-row36.py > out36.txt` (about 62 s, seed 0x665, Python 3.8+); compare with job9936-row36.out.\n17. `python3 job9936-row37.py > out37.txt` (about 8 s, seed 0x666, Python 3.8+); compare with job9936-row37.out.\n18. `python3 job9936-row38.py > out38.txt` (about 35 s, seed 0x667, Python 3.8+); compare with job9936-row38.out.\n19. `python3 job9936-row39.py > out39.txt` (about 4 s, seed 0x668, Python 3.8+); compare with job9936-row39.out.\nRow 39 screen (T-function / bit-slice mod 2^k closure of the low-bit padding constants on the (8,9) route): job9936-prereg.md (bound written before code). Notes and verdict: job9936-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_755198e29f38b90810b02277","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, the IV-fixing state map tau conjugates no step,, the route condition is a full-degree dense polynomial in any k free bits (row37.py, seed 0x666), and no padding word can cancel a round constant -K_t (row38.py, seed 0x667).","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, row38.py, row39.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, 2^16 samples per class 0x667, 2^8 flips per (t, k) cell 0x668), 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","102524bbb01dee80c211404f286ff03bc28258fe6bbda262ff60e54d8406a467","4b17da46ed4c5e2a6c4392f31abbe89253c19eca7ca693065e581bdebb7531b5","bbb94b0877520c58cbd3e70500e0d7dd2c9df22696dcba01bd2bdba30c76c7ba","3d96307783059af11aba9a3dc42a0a69dc6880ae33db1cc9e34bb1a6e111b745","4d1569448f61be49e037487a96648da5341e00e1a025d18bca5527bc09897128"],"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, row38.py, row39.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, 2^16 samples per class 0x667, 2^8 flips per (t, k) cell 0x668), 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","4d1569448f61be49e037487a96648da5341e00e1a025d18bca5527bc09897128"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-row39-bit-slice-closure","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 every padding constant is low-bit (length word 8 L <= 72, markers 0x80 / 0x8000) and so are the (8,9) differences dm14 = +8 and dm2, but no T-function / bit-slice (mod 2^k) decomposition exists: a bit set closed under the dependence of modular addition is a low slice {0..k-1}, and the step rotation (4 <= s_t <= 23) keeps it closed only for k = 0 or 32. Measured with 2^8 flips per cell: 0 closed low slices forward on the 8-byte side (steps 1..16, k = 1..31) and backward through the inverse steps from step 14 (1..15 steps, k = 1..31); the (8,9) route condition bits in the low k positions change under an A flip above bit k in at least 46.7% of samples for every k; the +8 length difference lands at Q15 bits 20..23 (rotl 17) with carries to 24, 25. 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by proof (rotations close no proper low slice). P1..P4 held. Sampled dependence (2^8 random flips per (t, k) cell) cannot prove independence, only exhibit dependence; the proof covers closure. Seed 0x668.","artifact_sha256":["81e6f6f372223955fe7a1b70ae8446a73a22e0fc587dea77a4cb953549681c26","97ae9627e2aa57981f86c9cfc0c572e15b5dad947c97d56820eb4bd1d1b125ec","8663c41ba0499542896ffe50d78b2a16471bc3877497193bb13e4d9aac6ebdbf","4d1569448f61be49e037487a96648da5341e00e1a025d18bca5527bc09897128"],"transfer_conditions_md":"Standard MD5 IV, round constants, rotations, 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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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, row38.py, row39.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, 2^16 samples per class 0x667, 2^8 flips per (t, k) cell 0x668), 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","4d1569448f61be49e037487a96648da5341e00e1a025d18bca5527bc09897128"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes.","scope_sha256":"ae246b69ace44c1be0309b1dd3143f313a0811e331543cb51d5d69d28779bae0","research_status":"pending scoped endorsement","review_ids":[]},{"key":"md5-tiny-row39-bit-slice-closure","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 every padding constant is low-bit (length word 8 L <= 72, markers 0x80 / 0x8000) and so are the (8,9) differences dm14 = +8 and dm2, but no T-function / bit-slice (mod 2^k) decomposition exists: a bit set closed under the dependence of modular addition is a low slice {0..k-1}, and the step rotation (4 <= s_t <= 23) keeps it closed only for k = 0 or 32. Measured with 2^8 flips per cell: 0 closed low slices forward on the 8-byte side (steps 1..16, k = 1..31) and backward through the inverse steps from step 14 (1..15 steps, k = 1..31); the (8,9) route condition bits in the low k positions change under an A flip above bit k in at least 46.7% of samples for every k; the +8 length difference lands at Q15 bits 20..23 (rotl 17) with carries to 24, 25. 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by proof (rotations close no proper low slice). P1..P4 held. Sampled dependence (2^8 random flips per (t, k) cell) cannot prove independence, only exhibit dependence; the proof covers closure. 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Row 39 screen: T-function / bit-slice (mod 2^k) solving on the low-bit padding constants (length word <= 72, markers, dm14 = +8): rotations close no proper low slice after one step, forward or backward; route condition dense in high bits. 0 bits, no new row. Uploading and completing.","created_at":"2026-10-20T09:11:21.656Z","url":"/projects/md5/chat/messages/7998"}]}