{"id":2968,"job_id":6207,"problem_id":6,"lane_id":null,"type":"explore","user_id":73,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Smallest collision: with Stevens' live couplings modelled, L=63 class + Q23 is satisfiable on 15/32 instances and unsat on exactly the instances #2959 measured; a live filtered search on a predicted instance yields Q29 states at ~174/s (unconstrained ~180–220/s)\n\n**Verified finite result plus a measured live confirmation.** No collision; the record stays 248 and the published reference 128.\n\n## Model\nPer md5sbc collinit instance, a Z3 model of the search's own derivations (live_coupling_z3.py):\n- **Fixed:** the instance's Q14..Q21, with Q4 and Q5 forced by their conditions. m6, m11, m0, m5 and Q1 are derived as collinit derives them; the derived Q1 equals the value md5sbc printed for 0x6163000d.\n- **Free, within their masks:** Q3 and Q6 (table enumeration) and Q9, Q10, Q11, Q12 (main loop).\n- **Derived exactly as the code does:** Q7, Q2, m1, Q13 (table); Q8, m10, Q22, m15, Q23 (main loop).\n- **Checks:** Q7/Q13 table conditions, the step-13 rotation, the Q8 condition, both table-key matches (Qprev[11] and Qprev[16]), the Q22 condition, the step-21 rotation, then optionally the Q23 condition and step-22 rotation, and the L=63 class (m15 >> 24 == 0x80).\n- Every sat model is replayed in plain Python through the same derivation.\n\n## Results (32 instances from #2964)\n| (A) Q23, no class | (B) class, no Q23 | (C) class + Q23 | instances |\n|---|---|---|---|\n| sat | sat | **sat** | **15** |\n| sat | sat | unsat | 7 |\n| sat | unsat | unsat | 9 |\n| unsat | sat | unsat | 1 |\n\nAll sat witnesses are verified.\n\n**Agreement with live measurements.** The model reproduces every observation:\n- **#2959's three instances:** +5 (0x61630005) and +13 (0x6163000d) are (C) unsat, matching 0 Q23 passes among 91,136 and 35,904 class states. +24 (0x61630018) is (A) unsat, matching 0 Q23 passes among 40M states of any kind.\n- **Live confirmation on predicted-sat instances** (class-filtered, 60 s each, sandboxed):\n  - **0x6163002f:** 39,320 class states gave **32 Q23 passes** and **6,384 Q29 states by 31 s**, reaching 12,288 Q29 states at 70.6 s (**2^7.44 ≈ 174 Q29/s**). The unconstrained rate on #2959's instances was 182–218/s.\n  - **0x61630023 and 0x61630027:** the 60 s enumeration window reached only 2,560 and 8,960 class states, giving 0 passes; at 0x6163002f's rate (~8e-4) about 2 and 7 were expected, so this is not informative.\n  - **0x61630021:** no class states in the window.\n\n## What it changes\n- **The L=63 (126-byte) equal-length absorption route on Stevens' differential is open.** On about half of collinit instances the search couplings admit class states that pass Q23, and on such an instance the class-filtered search produces Q29 states at nearly the unconstrained rate. Cost per Q29 state is roughly 0.8–1.0x unconstrained, so choosing L=63 instances costs only the per-instance Z3 test (~0.1 s).\n- **#2959 and #2964 are reconciled:**\n  - #2959's measurement stands, but on unlucky instances;\n  - #2964's looser sat result was right in direction;\n  - #2959's mechanism hypothesis stays refuted, and the real cause is instance-specific coupling through Q7, Q8 and m10.\n- A full 126-byte pair still needs Stevens' downstream success probability, about 2^-33.85 per Q29 state, i.e. about 2^49.8 compressions overall (#2661/717). That is several CPU-years, unchanged by the padding constraint if Q29 states keep their downstream odds, which is untested.\n\n## Limits\n- Live confirmation on one instance (one window, 70 s).\n- Downstream (post-Q29) odds of class states versus unconstrained are not measured.\n- L=62 is not tested.\n\n## Next step\n1. Measure Q29 rate and post-Q29 survival (the tunnel stages to a full near-collision check) for class states against unconstrained on 3+ Z3-selected instances.\n2. Add an instance pre-filter (the Z3 class + Q23 test) and class-first enumeration (solve Q12 from m15 per table entry) to md5sbc, and measure the resulting Q29/s.\nThis prices a 126-byte pair against the 248 record.\n\n## OUTCOMES.md entry (proposed)\n| Track | Method | Budget and hardware | Best reached | What it shows |\n|---|---|---|---|---|\n| Smallest collision | Z3 live-coupling model of md5sbc per instance (32), plus a class-filtered live run on a predicted instance | ~4 CPU-min | 248 (unchanged) | L=63 class + Q23 sat on 15/32 instances (unsat exactly where #2959 measured 0); filtered search yields ~174 Q29/s on a selected instance: the 126-byte route is open at ~Stevens cost |","patch":null,"cpu_hours":0.08,"hashes":{"live_coupling_z3.py":"af2f06f6a8a1463f58f55bf2eea13ed95e1788120de99e5d55f3b312e6287cb8","live_coupling_z3.json":"34e0cc27891fcbda7e8c74da2acb0f0fc9f9894a5ca0ffc3b1dc68ec6d0e3641"},"author_rung":"verified","status":"pending","final_rung":null,"created_at":"2026-10-11T10:36:49.412Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2964,2959,2891,2934,2938,2661],"messages":[]},"tokens":{"log":"summary","input":10,"models":{"claude-opus-5-5":15343},"output":15343,"source":"reported","entries":0,"cache_read":4056929,"cache_write":20672,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Instances: as #2964 (instances.txt has fixed Q14..Q21 per seed). Tables: #2891's tables.json (92aeb9ed...).\n2. Run `python live_coupling_z3.py tables.json instances.txt` (z3-solver 4.13.0.0, about 4 s). It writes live_coupling_z3.json: per seed, queries A/B/C with Python-replayed witnesses.\n3. Live check: #2959's instrumented md5sbc (recipe in #2959), `FILTER63=1 ./md5sbc_q29 60 0x6163002f`. Expected: q23_cls > 0 and q29_cls in the thousands within about 30 s; the Q29ok lines report ~2^7.4/s. The logs are in live_filter_logs.txt.","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":"2026-10-11T10:36:49.412Z","department_id":"dept_ef09d64fbbd7ddb34ab67f81","run_id":"run_c2ccb63b450f473296a41c24","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,"handle":"danieljmt","job_brief":"With each md5sbc instance's fixed round-1/2 states (Q1,Q4,Q5,Q14..Q21, m0,m5,m6,m11), and free Q3,Q6 (table) and Q9..Q12 (enumerated) under their CONSTTABLES conditions, with Q7, Q2, m1, Q13, Q8, m10, Q22, m15, Q23 derived exactly as the search derives them: is m15 in the L=63 class together with the Q22 and Q23 conditions and rotations satisfiable?\n\nWhy this step: #2964 showed class+Q23 is sat when Q12, Q13, Q22 are free (32/32), while live search found 0/127,040 (#2959). The free variables in #2964 are coupled in live search through Q7/Q8/m10; this decides whether stock collinit search can ever emit a Q23-passing L=63 state.\n\nStop when: sat/unsat for the 32 instances of #2964 (witnesses verified by recomputing the search derivations in Python), or 1 CPU-hour solver time.","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":[{"id":2972,"handle":"danieljmt","status":"pending"},{"id":2974,"handle":"danieljmt","status":"pending"},{"id":2975,"handle":"danieljmt","status":"pending"},{"id":2976,"handle":"danieljmt","status":"pending"},{"id":2978,"handle":"danieljmt","status":"pending"},{"id":2979,"handle":"danieljmt","status":"pending"},{"id":2981,"handle":"danieljmt","status":"pending"},{"id":2984,"handle":"danieljmt","status":"pending"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2968/transcript","files":[{"sha256":"af2f06f6a8a1463f58f55bf2eea13ed95e1788120de99e5d55f3b312e6287cb8","name":"live_coupling_z3.py","bytes":7670},{"sha256":"34e0cc27891fcbda7e8c74da2acb0f0fc9f9894a5ca0ffc3b1dc68ec6d0e3641","name":"live_coupling_z3.json","bytes":9209},{"sha256":"259d0f56c8d1664dff3617e5b4ea7168569574502ce268a9903dcb2a03c4d8cb","name":"instances.txt","bytes":4291},{"sha256":"373ca3f4c0cb7e12cfc6c1ef4c8cb0a665cad6ac21f4efde793125e099cdc5ee","name":"live_filter_logs.txt","bytes":3185}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"18b8c43e0da95f44d0e80a6fda990a68d0e9a519afbb4f87a71f2c7524c0b3f2","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}