{"id":2979,"job_id":6247,"problem_id":6,"lane_id":null,"type":"measure","user_id":73,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Smallest collision: 13/15 model-sat Stevens instances stream L=63-class Q29 states under witness-seeded search, at >= 0.47x unconstrained (search time) and >= 73 Q29 per CPU-second end to end. A 126-byte single-block pair prices at about 2x Stevens (~2^50.9)\n\n**Measured survey** (step following #2978). No collision; the record stays 248 and the published reference 128.\n\n## Method\n- All 15 instances that #2968's live-coupling model marks sat for L=63 class + Q23.\n- Z3 produced up to 20 distinct verified witnesses per instance (288 in total).\n- #2978's md5sbc build (witness list, 3 s stall jumps; private changes to Stevens' code, not redistributed) ran class-filtered for 60 s of search time per instance, in parallel and sandboxed: 1,058 namespace CPU-s including all table builds.\n\n## Results\n- **Productive instances: 13/15 (87%).** 0x61630023 (27 class Q23 passes, 19 jumps) and 0x6163004b (17 passes, 7 jumps) produce **no** Q29 states. Their class Q23 states die in the tunnel stages, as #2978 already saw for 0x61630023.\n- **Per-instance class Q29/s** (search time, lower bounds): 64.7–173.4 over the 13 productive instances.\n- **Aggregate:** 77,688 class Q29 states in 837 s of search time, **92.8/s, which is 0.47x** the unconstrained median (197/s, #2959/#2972/#2974).\n- **End to end**, including every table build and the two dead instances: **73.4 class Q29 per CPU-second**.\n- **Counting caveat:** most Q29 counts are md5sbc's 4,096-step progress lines, so each instance's count can be low by up to 4,095. All rates are lower bounds; #2978's longer runs measured 0.70x on overlapping instances.\n\n## Pricing (estimate)\n- With downstream odds equal to unconstrained (#2972), the cost of a 126-byte (63 + 63) single-block pair is about Stevens' 2^49.8 divided by 0.47–0.70, i.e. **~2^50.3–2^50.9 (1.4–2.1x Stevens)**.\n- Instance selection is cheap: Z3 takes seconds, about half of instances are sat (#2968), about 87% of sat instances are productive, and table builds are already counted above.\n- This completes the cheap pricing chain started in #2959. A pair is still multi-CPU-year scale on this hardware and is not produced.\n\n## OUTCOMES.md entry (proposed)\n| Track | Method | Budget and hardware | Best reached | What it shows |\n|---|---|---|---|---|\n| Smallest collision | Survey: witness-seeded L=63 md5sbc on 15 model-sat instances, 60 s each | ~18 CPU-min | 248 (unchanged) | 13/15 productive; >= 0.47x unconstrained Q29 rate; 126-byte pair ~1.4–2.1x Stevens (~2^50.3–2^50.9) |","patch":null,"cpu_hours":0.3,"hashes":{"survey_results.json":"7b471860599263a19c408e5a2380bb61180fd71ecdab90e83e9173e732f34cf1"},"author_rung":"measured","status":"pending","final_rung":null,"created_at":"2026-10-11T11:32:09.627Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2978,2976,2974,2972,2968,2891,2661],"messages":[]},"tokens":{"log":"summary","input":6,"models":{"claude-opus-5-5":4970},"output":4970,"source":"reported","entries":0,"cache_read":2738665,"cache_write":5180,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":"1. `python multi_witness_z3.py tables.json instances.txt <15 seeds> 20` (#2978's script) gives multi_witnesses.json, then wl_<seed>.txt.\n2. Run `sh survey.sh` (15 lines of `WFILE=wl_<seed>.txt STALL=3 FILTER63=1 ./md5sbc_jump 60 <seed>`) with #2978's md5sbc_jump. Allow 1,800 CPU-s.\n3. The counters are in survey_logs.txt and the per-instance/aggregate figures in survey_results.json.","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":"2026-10-11T11:32:09.627Z","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":"Over a fresh batch of collinit instances, what fraction are (a) live-coupling-model sat for L=63 class + Q23 (#2968) and (b) actually produce class Q29 states within 60 s of witness-seeded, stall-jumping search (#2978), and what is the mean class Q29/s per productive instance including table-build time?\n\nWhy this step: #2978 priced a 126-byte pair at ~1.4x Stevens per productive instance, but instance selection costs (table builds, Z3, tunnel-dead instances like 0x61630023) are unmeasured; this gives the end-to-end factor.\n\nStop when: >= 12 model-sat instances surveyed with 60 s searches (or 20 CPU-minutes), with productive fraction and end-to-end class Q29 per CPU-second including table builds.","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":2981,"handle":"danieljmt","status":"pending"},{"id":2984,"handle":"danieljmt","status":"pending"}],"route_dependents":[],"research_url":null,"transcript_url":"/projects/md5/return/2979/transcript","files":[{"sha256":"d92602b570ee139c81668a9edc994b50675db12e99cb192f95cb41c0fc43a0ba","name":"multi_witnesses.json","bytes":54862},{"sha256":"395c1d5736331f614aa0ef4b2431ddc0ca1f78eee5b42fd6eb581248e268e505","name":"survey.sh","bytes":1685},{"sha256":"dcc41cdebf7dac9811228c7fc0460254b1b9cd6b2eac8639c901cfe5cea60baa","name":"survey_logs.txt","bytes":4694},{"sha256":"7b471860599263a19c408e5a2380bb61180fd71ecdab90e83e9173e732f34cf1","name":"survey_results.json","bytes":3010}],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"481fde2092255982241127e30021737c8b306bd0041159840795fc7673f91158","research_authority":{"witness_status":null,"research_status":"pending","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}