{"id":2981,"job_id":6251,"problem_id":6,"lane_id":null,"type":"measure","user_id":73,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Smallest collision: 'tunnel-dead' L=63 instances fail at the Q4-tunnel stage (Q24). Adding Q24 to the Z3 instance filter predicts one of the two dead instances; the other is rare-but-possible\n\n**Measured + verified-model result** (step following #2979). No collision; the record stays 248 and the published reference 128.\n\n## Per-stage pass counts (class-filtered, witness-seeded, 60 s each; private md5sbc instrumentation)\n| instance | class Q23 | Q24 (Q4 tunnel) | Q25 (Q9 tunnel) | Q26 | Q27 | Q28 | Q29 conditions | Q29ok |\n|---|---|---|---|---|---|---|---|---|\n| 0x61630023 (dead) | 27 | **0** | 0 | 0 | 0 | 0 | 0 | 0 |\n| 0x6163004b (dead) | 17 | **0** | 0 | 0 | 0 | 0 | 0 | 0 |\n| 0x6163002f | 36 | 18 | 2,705,378 | 34,410,142 | 79,981,596 | 1,100,895 | 17,966 | 12,288 |\n| 0x61630042 | 14 | 11 | 2,159,385 | 26,056,057 | 51,694,086 | 945,359 | 17,204 | 12,288 |\n\n(Q24 counts states that pass in step 23. Q25..Q29 count tunnel candidates passing each check, so later columns can exceed earlier ones.)\n\n**Both dead instances fail entirely at Q24.** Each class Q23 state tries all 4,096 Q4-tunnel values and none satisfies Q24's conditions plus the step-23 rotation. On productive instances, 50–80% of class Q23 states pass Q24, and the rest of the pipeline then behaves normally.\n\n## Z3 filter extension (q24_z3.py)\n- #2968's live-coupling model was extended with the Q4 tunnel (Q4 = base ^ (x & 0x14872E23)), m4 from the round-1 inverse, Q24 from step 23, Q24's conditions and the step-23 rotation.\n- **Results over the 32 instances:**\n  - 14 are sat for class + Q23 + Q24 (D), against 15 for class + Q23 (C);\n  - the instance that drops out is **0x61630023, which was measured dead**;\n  - **0x6163004b stays sat**, so its live zero (17 class Q23 states × 4,096 tunnel values) reflects rarity in the reached region, not impossibility.\n- Without the class constraint (E), 30 of 32 are sat.\n- The filter therefore removes structural Q24-dead instances only. Live screening (a few seconds of seeded search) is still needed for rare-Q24 instances.\n\n## Effect on pricing\nSmall. The productive fraction among model-filtered instances rises from 13/15 to about 13/14. #2979's 1.4–2.1x Stevens estimate for a 126-byte pair stands.\n\n## OUTCOMES.md entry (proposed)\n| Track | Method | Budget and hardware | Best reached | What it shows |\n|---|---|---|---|---|\n| Smallest collision | Per-stage md5sbc counters + Z3 Q24 extension for L=63 instances | ~6 CPU-min | 248 (unchanged) | Dead instances fail at the Q4-tunnel stage (Q24); the Z3 Q24 filter predicts 1 of 2; pricing unchanged (~1.4–2.1x Stevens) |","patch":null,"cpu_hours":0.1,"hashes":{"q24_results.json":"878387adb378c750a32984e4430676d8a9694cc96ef738602b0ebf3ff1db2056"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-11T11:35:16.799Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2979,2978,2968,2891],"messages":[]},"tokens":{"log":"summary","input":6,"models":{"claude-opus-5-5":5424},"output":5424,"source":"reported","entries":0,"cache_read":2764646,"cache_write":5754,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. Model: `python q24_z3.py tables.json instances.txt q24_results.json` (#2968's model plus Q4 tunnel/m4/Q24 conditions/step-23 rotation; z3-solver 4.13.0.0). C/D/E per instance.\n2. Live: #2978's md5sbc_jump plus counters at step24()/step25() calls and after the Q26/Q27/Q28/Q29 checks in step25, tagged by class. Run `WFILE=wl_<seed>.txt STALL=3 FILTER63=1 ./md5sbc_st 60 <seed>` for 0x61630023, 0x6163004b, 0x6163002f, 0x61630042. The STAGES lines are in stage_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":"2026-10-11T11:35:16.799Z","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":"On instances where class Q23 states pass but no Q29 appears (0x61630023, 0x6163004b) versus productive ones (e.g. 0x6163002f, 0x61630042), at which tunnel stage (Q24 via the Q4 tunnel, Q25 via the Q9 tunnel, Q26..Q29 via the Q14 tunnels) do class states fail, and is the failure a fixed-bit condition that could be added to the Z3 instance filter?\n\nWhy this step: #2978/#2979 found ~13% of model-sat instances tunnel-dead; predicting them from bitconditions would remove that overhead and tighten the 126-byte price.\n\nStop when: Per-stage pass counts for >= 2 dead and >= 2 productive instances, plus a Z3 check of any candidate condition, or 20 CPU-minutes.","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":2984,"handle":"danieljmt","status":"pending"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2981/transcript","files":[{"sha256":"878387adb378c750a32984e4430676d8a9694cc96ef738602b0ebf3ff1db2056","name":"q24_results.json","bytes":16617},{"sha256":"68c7c99dae7259653f464826447a196b6a82baa669875d0e6d2f5274af5b2ec2","name":"q24_z3.py","bytes":8179},{"sha256":"fde9cd11f2394ff42142d349401030a629858e4daaf5c0c83155ef0395006e25","name":"stage_logs.txt","bytes":4173}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"d45e04866f91a2c4f301282e956578fe67309bd17a45d1e45373c5718e58c860","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}