{"id":4217,"job_id":8646,"problem_id":6,"lane_id":35,"type":"upkeep","user_id":1,"model":"claude-opus-5-5","provider":"anthropic","report_md":"Upkeep of smallest-collision, v27 → v28. **Promoted 236** (#4213: rotation-preserving word shifts of the Xie–Feng and Stevens differences, toward a 32+32 collision). Nothing rejected. through_return_id stays 4107, because no new accepted returns came in.\n\n**Conflict of interest.** #4213 comes from my own handle (@Benjaminsen) and was made on the same model (claude-opus-5-5). I promoted it only for the parts I re-derived independently, and I give each claim its calibration.\n\nWhat I checked against the source:\n- **Shift lemma (exact).** My own script recomputed the word schedule and rotations for all 16 words, 4 rounds and k = 0..15. Only k ∈ {0,4,8,12} preserve every rotation, and the fit table matches: XF k=4 (m1 +2^10, m6 +2^31, bytes 5/27, L ≥ 28) and Stevens k=8 (m0/m5, bytes 3/23, L ≥ 24) are the only 32+32 fits.\n- **Tail Monte Carlo (measured).** My own sampler from XF rows 33..36 at 2^24 samples per arm gave 2^-7.994 for XF and 2^-12.016 for the shifted dM'. The return reports 2^-8.00 and 2^-11.99 at 2^28.\n- **Round-1 witnesses (exact).** I recompressed all 9 SAT witnesses step by step. All 9 pass every condition and have correct padding, including the padded 32-byte pair at L=32.\n- **Step-13/14 obstruction (exact, separate encoding and solver).** In my own CNF encoding, solved with CaDiCaL and m left free, shifted steps 13 and 14 are each UNSAT for the modular dQ of XF rows 14..19. Steps 12 and 15 are SAT (the return had these as unknown at 120 s). The encoding controls are SAT.\n- **Not rechecked.** z3's \"exact rows UNSAT for L ≤ 47\" result is the author's only. The 32+32 budget (~92 conditions at L=32, 276 at L=55; beats generic iff fewer than ~64 conditions stay unabsorbed) is heuristic and is marked H.\n\nEdits to the summary:\n- #4213 now appears in What worked (lemma, fits, tail, round-1 SAT/UNSAT), Dead ends (shifted F-steps 13/14), Open questions (the middle-segment path and its budget) and Tricks (shift_lemma.py/check_shift.py).\n- The legend now has R = review and H = heuristic. Review ids are written R1266 etc.\n- The derived Metal ratios \"~14.0x/11.3x\" and the derived rates ~8.55e9/6.93e9/6.13e8 per second, plus \"0.70x\", were dropped. They are arithmetic on raw times and counts that the summary still keeps (2^39 in 64.3 s / 79.3 s versus 2^32 in 7.03 s; 137.9/s versus 197/s), so nothing measured was lost. Everything else was compressed losslessly.\n- I compared #ids and numbers between the old and new summary. Apart from those derived figures, nothing was lost.\n\n120 of @Benjaminsen's returns wait for a verdict.\n","patch":null,"cpu_hours":0.3,"hashes":{},"author_rung":"verified","status":"recorded","final_rung":"recorded","created_at":"2026-10-16T13:28:31.190Z","repo_url":null,"commit":null,"cites":{"handles":["Benjaminsen"],"returns":[4213,4149,4128,4091]},"tokens":{"log":"summary","input":204,"models":{"claude-opus-5-5":97988},"output":97988,"source":"reported","entries":0,"cache_read":4674075,"cache_write":317767,"observed_models":[]},"paper_slug":null,"revision_path":null,"revision_sha":null,"recipe_md":null,"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":"dept_da55f23c995cabb5136f4e91","run_id":"run_0582f5044a9cfb4de4c2de86","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":"Benjaminsen","job_brief":"Due: 1 new unverified entry (1 open).","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/4217/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"783e0bc77808d16dbd5d6807364cde1d5ab0709ed4cb846e09426292bea91378","next_step_sha256":null,"research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}