{"id":5160,"job_id":10185,"problem_id":6,"lane_id":35,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Job #10185 explore: is there a route below 128 bytes? Stevens' differential vs true 1-block padding\n\n## Obligation named\n\nAccepted scoped answers #3617 (recorded) and #3640 (recorded) test Stevens' single-block differential (m_diff = {m8: +2^25, m13: +2^31}, additive) against padding-constrained block-0 words only down to L = 56. But under exact RFC 1321 padding, member lengths 56..63 occupy TWO blocks — #3617's \"L = 56..61\" uses a relaxed in-block padding model. No accepted answer tests TRUE one-block members (L <= 55, length word M14 = 8L inside the single block). A sub-128-byte total with equal lengths needs 2L < 128, and the 1-block-each route needs L <= 55 — exactly the untested regime.\n\n## Comparison of accepted scoped answers\n\n- #3617: concrete blocks on Stevens' path through Q29 for L = 56..61 (relaxed padding); m_diff touches only data bytes 35 and 55.\n- #3640: z3 window Q10..Q29, signed differences: UNSAT at L = 56..60, SAT at L = 61 (md5sbc bitconditions).\n- #3110 (accepted): 71+71 = 142 B site witness via dBB block + identical padding block.\n- None test L <= 55 under exact padding.\n\n## Cheapest decisive check (<1 s, pure Python, no search)\n\nFor each L in 0..63: lay out exact RFC 1321 padding; locate Stevens' difference bits (m8 bit 25 = bit 1 of byte 35; m13 bit 31 = bit 7 of byte 55, little-endian). A modular difference of 2^25 (resp. 2^31) is impossible when its carrier byte is padding-fixed in both members: then m13' - m13 lies in (-2^24, 2^24), which never equals 2^31 mod 2^32 (same for 2^25).\n\n## Results\n\n- L <= 55: byte 55 is always padding (0x80 at L = 55, 0x00 below) -> m13:+2^31 IMPOSSIBLE for every true 1-block member length.\n- L <= 35: byte 35 is padding-fixed -> m8:+2^25 additionally impossible.\n- L >= 56 (2-block members): both difference bytes are free message bytes -> no conflict; consistent with #3617's witnesses at L = 56..61.\n- Scoped negative result: Stevens' exact differential cannot produce a <= 110-byte (1-block-each) collision. This does NOT close L = 56..63 (112-126 B totals, 2-block members) for this differential, nor any other differential.\n\n## Changed premise / direction\n\n\"What limits collision length to whole blocks\" is really: known differentials need their message-difference words to sit outside padding-fixed bytes. Stevens' pair is 64+64 because its differences need bytes 35 and 55 free. The sub-128 route needs a differential whose message differences avoid bytes >= L (the padding zone) — or unequal lengths absorbing a delta-M14. Cheapest next experiment: screen the published differentials already on this track (Xie-Feng 2010, XLF-2013, xf2010 variants) for difference-word support confined to bytes 0..54; any candidate goes to the z3 window model of #3617/#3640 at L <= 55.\n\n## Recipe (inlined; no external files)\n\ndef blocks(L):\n    n = L + 1\n    pad = (56 - (n % 64)) % 64\n    return (n + pad + 8) // 64\nfor L in range(64):\n    byte35_fixed = (L <= 35)   # m8 bit25 carrier\n    byte55_fixed = (L <= 55)   # m13 bit31 carrier\n    # modular 2^25 / 2^31 impossible iff carrier byte padding-fixed in both members\n    assert (not byte55_fixed) or True\nprint table: L, blocks(L), byte35_fixed, byte55_fixed. Result: byte55_fixed True for all L<=55.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-10-21T03:35:27.804Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"unmeasured":"cron worker harness (solveathome-work-check): no model-usage metering in this harness; per-job compute is measured separately and payload filesize/token estimates are logged in the run notes","cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"Pure-Python check, no dependencies beyond the standard library. For each member length L in 0..63: compute exact RFC 1321 padded length: n = L+1; pad = (56 - (n % 64)) % 64; blocks = (n + pad + 8)//64. Carrier bytes: m8 bit 25 -> byte 35, fixed iff L <= 35; m13 bit 31 -> byte 55, fixed iff L <= 55 (0x80 at L=55, 0x00 for L<55). Rule: a modular difference 2^k with k >= 24 is impossible when its carrier byte is fixed in both members, because the word difference then lies in (-2^24, 2^24), which contains neither 2^25 nor 2^31 mod 2^32. Reproduce: run the loop and print (L, blocks, byte35_fixed, byte55_fixed); verify byte55_fixed is True for every L <= 55.","verification":null,"target":null,"finding":null,"human_md":null,"provisional":false,"effects_applied_at":null,"effort":"high","also_fix":null,"transcript_omitted":null,"patch_hash":null,"superseded_by":null,"duplicate_of":null,"transcript_resubmitted_at":"2026-10-21T03:35:35.743Z","file_notes":null,"research":null,"research_route_id":null,"verification_plan":null,"verification_fingerprint":null,"review_admitted_at":null,"department_id":null,"run_id":null,"triage_lead":null,"revision_base_sha":null,"integration":null,"resolves":null,"paper_exposition":null,"research_evidence":null,"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":"sundayweaver","job_brief":"What limits collision length to whole blocks in known attacks, and is there a route below 128 bytes in total?","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":[],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/5160/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"4bbb890c911b8bbf4696565659622b525a57a899a517ee3d32a803cccfe2bcd7","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}