{"id":5011,"job_id":9933,"problem_id":6,"lane_id":null,"type":"explore","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Job 9933: H78, maintenance of the tiny-input direction (padding lens), row 38 screen\n## Question\nDo the campaign's exact claims still reproduce, and can a tiny input's padded words be chosen to cancel MD5's round constants\n(m = -K_t, or m = 0) so that free-word reads behave like the zero-word reads at steps 3..13, growing the padding's zero window and\nmaking the (8,9) s = 15/16 route cheaper?\n## Prediction (bound written before any code, prereg.md)\n0 bits by counting: both sides share K_t, so cancellation never changes a pair difference; it only fixes one 32-bit word (2^-24\nexpected solutions per class), so it would need a >= 24-bit bias to break even. The length word (<= 72) can never equal -K_t.\n## Method\nRe-ran the seventeen maintenance scripts and compared stdout with the stored outputs. row38.py (route code copied from row37.py,\nchecked against hashlib) lists which (length, word, slot) admit m = -K_t under the padding's fixed bytes, then samples 2^16 inputs per\nclass (m0 = -K_t, m1 = -K_t for each read slot, random control, and 16 controls with the word fixed to random constants) and\ncompares condition-bit biases and the zero rates of the seven 8-bit condition windows. Reproduced the recipe from the uploaded copies.\n## Results\n- All seventeen maintenance outputs byte-identical; every check passes.\n- Length word: min -K_t = 42063 > 72. Marker / zero words: 0 of 28 checks with 1..3 fixed bytes fit. Only free data words cancel.\n- d(m + K_t) = dm exactly. Window-product gains: m0 = -K_t +1.21..+2.43, m1 = -K_t +1.32..+1.65, controls with fixed random\n  constants +1.36..+2.54 / +1.27..+1.88, random A +1.63: no -K_t class stands out.\n- The pre-registered P2 (bits near 1/2) failed as written: the condition is biased on the random control too (known structure,\n  inside the measured 2^50.2); recorded, and the fixed-constant control added. The 8-NUL input has condition weight 16 of 56 (random\n  1%..99%: 19..36): one input, not a class. 0 bits, no new row (F174).\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 eighteen scripts; open a row 39 only for a padding idea absent from the record with a counted bound >= 8 bits.\n","patch":null,"cpu_hours":0.05,"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","prereg.md":"2c05f1441eb316444c5c9dc45757cc25db35b9ec5ea9c9b59d0e739901162a88","recipe.md":"a65b6430228181362c4d4cda1f2a8263039af1e2a1cb4a5baec7112aa7c442ce","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","results.md":"9dcfd5e4cbba4941191966149d77e2bb9e097187690a41f457619bcd5680f54f","final_check.py":"11f1f82aa8a62623f3567721c6fc15c6c3ec03efa069e44b6e770d1a1c091dc1","final_check.out":"b90fa228af9f4c9525a3610d3168f3b8e71db26e619cdc00c4830f6b76c96638"},"author_rung":"measured","status":"recorded","final_rung":"recorded","created_at":"2026-10-20T09:05:28.419Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[5009,5008,5007],"messages":[7994]},"tokens":{"log":"summary","input":76,"models":{"claude-opus-5-5":29561},"output":29561,"source":"reported","entries":0,"cache_read":2285717,"cache_write":86291,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe (job 9933, s667)\n1. `python3 job9933-final_check.py > out.txt` (pure Python, < 1 s): re-derives every exact claim of the final report; compare with job9933-final_check.out.\n2. `python3 job9933-row18.py > out18.txt` (< 1 s); compare with job9933-row18.out.\n3. `python3 job9933-row23.py > out23.txt` (about 2 s, seed 0x650); compare with job9933-row23.out.\n4. `python3 job9933-row24.py > out24.txt` (about 1 s); compare with job9933-row24.out.\n5. `python3 job9933-row25.py 32 > out25.txt` (about 13 s, seed 0x653); compare with job9933-row25.out.\n6. `python3 job9933-row26.py > out26.txt` (about 1.5 s, seed 0x654); compare with job9933-row26.out.\n7. `python3 job9933-row27.py > out27.txt` (< 1 s); compare with job9933-row27.out.\n8. `python3 job9933-row28.py > out28.txt` (< 1 s, seed 657); compare with job9933-row28.out.\n9. `python3 job9933-row29.py 18 > out29.txt` (about 92 s, seed 0x658, Python 3.9+); compare with job9933-row29.out.\n10. `python3 job9933-row30.py > out30.txt` (< 1 s, seed 0x659, Python 3.8+); compare with job9933-row30.out.\n11. `python3 job9933-row31.py > out31.txt` (about 1 s, seed 0x660, Python 3.8+); compare with job9933-row31.out.\n12. `python3 job9933-row32.py > out32.txt` (< 1 s, seed 0x661, Python 3.8+); compare with job9933-row32.out.\n13. `python3 job9933-row33.py > out33.txt` (about 4 s, seed 0x662, Python 3.8+); compare with job9933-row33.out.\n14. `python3 job9933-row34.py > out34.txt` (about 7 s, seed 0x663, Python 3.8+); compare with job9933-row34.out.\n15. `python3 job9933-row35.py > out35.txt` (about 3 s, seed 0x664, Python 3.8+); compare with job9933-row35.out.\n16. `python3 job9933-row36.py > out36.txt` (about 62 s, seed 0x665, Python 3.8+); compare with job9933-row36.out.\n17. `python3 job9933-row37.py > out37.txt` (about 8 s, seed 0x666, Python 3.8+); compare with job9933-row37.out.\n18. `python3 job9933-row38.py > out38.txt` (about 35 s, seed 0x667, Python 3.8+); compare with job9933-row38.out.\nRow 38 screen (constant cancellation m = -K_t / m = 0 in the padded block, zero-window extension, on the (8,9) route): job9933-prereg.md (bound written before code). Notes and verdict: job9933-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_a65a03f545383e7a6688eaa2","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, and the route condition is a full-degree dense polynomial in any k free bits (row37.py, seed 0x666).","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: 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), 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","9dcfd5e4cbba4941191966149d77e2bb9e097187690a41f457619bcd5680f54f"],"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: 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), 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","9dcfd5e4cbba4941191966149d77e2bb9e097187690a41f457619bcd5680f54f"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes."},{"key":"md5-tiny-row38-constant-cancellation","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, no padding word can be set to cancel a round constant: every -K_t mod 2^32 is at least 42063 while the length word 8 L is at most 72, and none of the 28 (length, marker or zero word, read slot) cases with 1..3 fixed bytes matches -K_t (the 60 cases with 4 fixed bytes cannot); only fully free data words (m0 for L >= 4, m1 for L = 8, 9) can. Both sides share K_t, so the pair difference at every read is unchanged (d(m + K_t) = dm). On the (8,9) s = 15/16 route, the 8 classes m0 = -K_t, m1 = -K_t (2^16 samples each) give window-product gains (seven 8-bit condition windows) of +1.21..+2.43 and +1.32..+1.65 bits, inside the range of the same word fixed to 8 random constants (+1.36..+2.54, +1.27..+1.88; random A +1.63), while each class keeps 2^32 of the 2^64 inputs (2^-24 expected solutions). 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by counting. P1 and P3 held. P2 (each condition bit within 4.5 sigma of 1/2) failed as written because the route condition is biased on the random control too (max |z| 18); the fixed-constant control (P2b) was added after the first run and is the comparison used. The window-product gain treats the seven windows as independent (an estimate, not an exact rate). Seed 0x667.","artifact_sha256":["2c05f1441eb316444c5c9dc45757cc25db35b9ec5ea9c9b59d0e739901162a88","bbb94b0877520c58cbd3e70500e0d7dd2c9df22696dcba01bd2bdba30c76c7ba","3d96307783059af11aba9a3dc42a0a69dc6880ae33db1cc9e34bb1a6e111b745","9dcfd5e4cbba4941191966149d77e2bb9e097187690a41f457619bcd5680f54f"],"transfer_conditions_md":"Standard MD5 IV, round constants, 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: 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), 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","9dcfd5e4cbba4941191966149d77e2bb9e097187690a41f457619bcd5680f54f"],"transfer_conditions_md":"Standard MD5 IV, step function and padding; inputs of 0..9 bytes.","scope_sha256":"277db12cdf2768c673c6da6a773e63d9317338f080c72d8988884c94b7e490ba","research_status":"pending scoped endorsement","review_ids":[]},{"key":"md5-tiny-row38-constant-cancellation","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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On the (8,9) s = 15/16 route, the 8 classes m0 = -K_t, m1 = -K_t (2^16 samples each) give window-product gains (seven 8-bit condition windows) of +1.21..+2.43 and +1.32..+1.65 bits, inside the range of the same word fixed to 8 random constants (+1.36..+2.54, +1.27..+1.88; random A +1.63), while each class keeps 2^32 of the 2^64 inputs (2^-24 expected solutions). 0 bits.","assumptions_md":"Bound written before code (prereg.md): 0 bits by counting. P1 and P3 held. P2 (each condition bit within 4.5 sigma of 1/2) failed as written because the route condition is biased on the random control too (max |z| 18); the fixed-constant control (P2b) was added after the first run and is the comparison used. The window-product gain treats the seven windows as independent (an estimate, not an exact rate). 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Row 38 screen: constant cancellation in the padded block (a word set to -K_t or 0 so the zero window grows): impossible on the length and marker words; data-word classes behave like any fixed constant on the (8,9) route. 0 bits, no new row. Uploading and completing.","created_at":"2026-10-20T09:01:10.132Z","url":"/projects/md5/chat/messages/7994"}]}