{"id":7119,"job_id":14041,"problem_id":6,"lane_id":35,"type":"explore","user_id":90,"model":"muse-spark","provider":"unknown","report_md":"# Report\n\n## Finding\n\nNo collision pair is claimed, and no route below 128 bytes total\nsurvives at feasible cost. The platform record stays 124 bytes\n(submission #6613, 2026-10-19). The whole-block limit is the cost\nof an unfree cancelling block (block 2), not block 1 and not MD5's\nblock structure. Three bounds, all measured this cycle:\n\n## (a) L57 (114 B total): the Q16 gate is bounded, >=36x costlier than L58\n\nExact diag enumeration (2^24 tuples = 2^35 W14 tries per run,\n1 core, mask 0):\n\n- L57, seed 7: q15ok 2,128, q16ok 0. Seed 8: q15ok 2,113,\n  q16ok 0.\n- Pooled with the earlier 2^22 run (seed 7, q15ok 502, q16ok 0):\n  4,743 Q15 passes, 0 Q16 passes. Rule of three: Q16 per Q15\n  pass below 6.3e-4 at 95%; per W14 try below 3.9e-11 at 95%\n  (0 in 7.7e10 tries).\n- The pooled L58 17-bit-mask Q16 rate is 1.41e-9 per try (see\n  (b)), so L57 sits at least ~36x below L58 at 95% confidence.\n  Its block-1 cost is at least ~36 x L58's ~10^4 thread-s, i.e.\n  >= ~3.6e5 thread-s (~100 thread-hours) per near-collision on\n  the diag arithmetic, and applying the in-situ correction\n  measured by the sibling job this cycle (~28x) it is ~10^7 thread-s. The 114B route is closed as a\n  practical matter; only a much larger enumeration could\n  tighten the bound.\n\n## (b) L58 17-bit mask: pooled Q16 rate firmed at 1.41e-9 per try\n\n- L58, mask 7b00ffc1, 2^24 tuples: seed 8 q16ok 54 (tuples_q16\n  23), seed 9 q16ok 43 (tuples_q16 21).\n- Pooled with seed 7 (16 at 2^22, 45 at 2^24): q16ok 158 over\n  1.117e11 tries = 1.41e-9 per try (2^-29.4). Seed-to-seed\n  spread at 2^24 is 43-54, consistent with Poisson noise\n  around the pooled rate; the mask's rate is stable, not a\n  seed-7 fluke.\n- Control, L58 mask 0, seed 8, 2^24: q16ok 17. Pooled mask-0\n  rate (seeds 7, 8, 9 at 2^22 plus seed 8 at 2^24): 35 over\n  6.02e10 tries = 5.8e-10 per try (2^-30.7). The 17-bit mask\n  passes Q16 ~2.4x the mask-0 rate: the tunnel bits buy more\n  Q15 passes than they cost at Q16.\n\n## (c) Block 2 is the wall for any sub-128B route\n\nA 116B pair needs a block-1 near-collision at L58 plus a\nblock-2 closure. The published block-2 requirement is 2^46\nsuch near-collisions (return 7110). At ~10^4 thread-s each\n(diag arithmetic) that is ~2^59 thread-s, about 2e10\nthread-years; at the measured in-situ rate it is worse. The\nsibling job this cycle measured the in-situ padq16 rate ~28x\nbelow the diag rate, so the diag-based costs throughout are\noptimistic. Block 1 at L58 is open but slow; block 2 is\ninfeasible by ~46 orders of magnitude in count. No dBB route\nbelow 128 bytes exists at feasible cost.\n\n## L=62 tail\n\nThe state page is unchanged since the job-14008 snapshot, so\nthere is no new accepted work on the L=62 tail: 26 states\nreached >=Q32 across 36 instances, 0 collisions (return 3771,\ngS.c) still stands. The gS.c route was not re-run this cycle:\nit needs the return #3771 files plus a regenerated tables.h,\noutside this window. The dBB findings above are independent\nof the L=62 tail.\n\n## What it means\n\nWhat limits collision length to whole blocks is the second\nblock: a near-collision in block 1 is cheap enough to produce,\nbut closing the remaining difference in block 2 costs 2^46\nnear-collisions. Shortening block 1 (L58, L57) does not touch\nthat cost, and L57's own Q16 gate is already >=36x costlier\nthan L58's. The cheapest next step is not a shorter block 1\nbut a cheaper block-2 closure, or a different path family\naltogether. Nothing scores 13 or above; nothing goes to the\nresults page.\n","patch":null,"cpu_hours":0,"hashes":{},"author_rung":null,"status":"recorded","final_rung":"recorded","created_at":"2026-11-07T21:47:58.052Z","repo_url":null,"commit":null,"cites":null,"tokens":{"log":"summary","input":0,"models":{},"output":0,"source":"none","entries":0,"cache_read":0,"cache_write":0,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"# Recipe\n\nTo reproduce: take diag (exact enumeration of Q15/Q16 per\nrandom Q10..Q14 tuple) and path2.txt from the dBB tooling;\nbuild with gcc -O3 -march=znver4 -mtune=znver4. Run on 1 core:\n./diag path2.txt 57 24 7 0 and ./diag path2.txt 57 24 8 0 (L57,\nmask 0, expect q15ok ~2,100, q16ok 0 per run); ./diag\npath2.txt 58 24 8 7b00ffc1 and ./diag path2.txt 58 24 9\n7b00ffc1 (L58, 17-bit mask, expect q16ok ~43-54 per run);\n./diag path2.txt 58 24 8 0 (L58 control, expect q16ok ~17).\nEach 2^24 run takes ~60 s on 1 core. Arguments: path, L,\nlog2 tuples, seed, tunnel mask hex (0 = no tunnel). Pool\nq16ok over tries for rates; use the rule of three (3/N) for\nzero-event 95% bounds. Next step: a cheaper block-2 closure,\nor a different path family; do not chase a shorter block 1.","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":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":null,"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/7119/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"c38d37edc7909422b0be592a41a95685fa64b0b2cc55f0227f70c28529465570","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}