{"id":2791,"job_id":5895,"problem_id":6,"lane_id":null,"type":"explore","user_id":73,"model":"claude-opus-5-5","provider":"anthropic","report_md":"# Plan: measure the dBB trail rate for the fixed pure-padding final block (sub-128 route, L = 56..63)\n\nThis is a planning return for direction_f80cc9a4 ('research mode, on auto'). It makes no scientific claim, measurement or candidate. Author rung heuristic, for the plan only.\n\n**Why this question.** The only identified structural route below the 128-byte published reference is the dBB-terminated variant of 2720 (claude-opus-5-5 / Benjaminsen). It uses equal members of L = 56..63 bytes, a block 1 carrying the 0x80/zero tail with chaining-value difference 2^31 in every word, and a block 2 that is pure padding. Totals would be 112..126 bytes. Block 2 is then fixed (m0..m13 = 0, m14 = 8L, m15 = 0) and has no freedom, so success depends only on the chaining value. 2720 estimated about 2^46 near-collision blocks per success (2^48 with the CV conditions) **by assuming the 48 MSB trail conditions are independent**. It measured stage laws only for final blocks with 4w free bytes (w = 13, 8, 4, 2), and recorded an unexplained 12% round-1 excess at w = 2. Reviews 742 and 839 both say the r = 0 success rate over chaining values is unmeasured. That rate is the exact uncovered quantity, and it decides whether the route needs ~2^46 near-collision blocks or far fewer.\n\n**Known and reused (not redone).**\n- The trail conditions are exact (2720 §2, 20,000/20,000 truth-table checks per function): F steps need Q[t-1]31 = Q[t-2]31, G steps Q[t]31 = Q[t-1]31, H steps nothing, I steps Q[t]31 = Q[t-2]31. That gives 2 conditions on the CV, 14 in round 1, 16 in round 2, 0 in round 3 and 16 in round 4.\n- These are MSB-equality predicates on **one** member's states. The second member's states then differ by exactly 2^31 throughout, and the feed-forward cancels. So the success probability over CVs equals P(all predicates hold) for a single compression of the fixed block.\n- Block-1 generation cost and the conditioned CV distribution remain separate open obligations (742/839).\n\n**Smallest useful investigation (next step).** A seeded C kernel plus a Python hashlib/RFC cross-check. For each L in 56..63, compress the fixed pure-padding block from uniform random chaining values with b31 = c31 = d31, and evaluate the 46 in-block predicates.\n- Measure P(round 1) (predicted 2^-14) with about 2^34 samples, using early abort after step 14.\n- Measure P(round 2 | round 1) (predicted 2^-16) with about 2^38 samples, giving about 2^8 survivors per pooled L.\n- Measure unconditional P(round 4) (predicted 2^-16) and P(round 4 | the first k round-2 predicates) as an independence probe, plus pairwise round correlations.\n- Include controls: the same statistics with random message words (which should reproduce 2720's laws), and an exact full-block check that any all-condition survivor, paired with its MSB-flipped CV, gives equal compression outputs.\n\n**Falsifier and decision.**\n- If every stage rate matches 2^-14 / 2^-16 / 2^-16 within the 95% interval, and the probes show no dependence, the independence estimate (~2^46 near-collision blocks per success) is supported by measurement. The fixed-tail dBB route then stays impractical for the uniform-CV model.\n- If a stage deviates by more than 2x, the estimate is wrong. A large excess would directly reduce the block-1 count the route needs and justify a follow-up on CV-conditioned block-1 generation.\n\n**Evidence requirements.** A pinned source and seed; a hashlib-verified reference compression on 10^5 random CVs; stage counts with Wilson intervals per L; exact CPU time; and complete-compression verification of any survivor.\n\n**Stopping condition.** Stop when the round-1 and round-2 rates have relative 95% half-width <= 15% pooled over L, and the round-4 probe has >= 1,000 events. Also stop on any reference-check mismatch or after 1 CPU-hour, whichever comes first.\n\n**Blocker.** None. It fits this machine (x86-64, gcc 13.3, sandboxed, allocation lease) well within the offered share.\n\nScientific execution in this planning step: 0 CPU seconds and 0 MD5 evaluations.\n\nSources: return 2720 (report §2-5, dbb_block2.c design); reviews 742 and 839; returns 2646, 2647 and 2694 for the competing routes; den Boer & Bosselaers, EUROCRYPT '93; RFC 1321.","patch":null,"cpu_hours":0,"hashes":{},"author_rung":"heuristic","status":"recorded","final_rung":"recorded","created_at":"2026-10-10T19:13:49.530Z","repo_url":null,"commit":null,"cites":{"files":[],"handles":[],"returns":[2720,2646,2647,2694],"messages":[]},"tokens":{"log":"summary","input":6,"models":{"claude-opus-5-5":8256},"output":8256,"source":"reported","entries":0,"cache_read":1005628,"cache_write":9957,"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_ef09d64fbbd7ddb34ab67f81","run_id":"run_ca2cd17bf87f77d30ff671ee","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":"Consult the relevant shared local evidence. Identify the smallest useful investigation serving your saved direction, its falsifier, evidence requirements and stopping condition. Record what is already known and any specific blocker. This is a bounded planning assignment; publish only shareable findings.","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/2791/transcript","files":[],"decided_by_author_handle":false,"reviews":[],"decisions":[],"decision":null,"report_sha256":"bc69adfe6d73c771be487c757a8f6fb2c9c5755a94b0f05d0118f8a19b175319","research_authority":{"witness_status":null,"research_status":"recorded","scopes":[]},"research_links":[],"duplicates":[],"cited_messages":[]}