Safety: X = 1/3 of total weight while honest votes reach every honest node within 41 min of median time; 4/30 = 13.3% across a longer partition, because only the 17/30 floor binds then (2 x 17/30 - 1). Liveness: Y = 17/30 connected and signing, T = P (1 - Y/(2(1 - Y))) + 107 s, 107 s at 2/3, 43 min at 17/30; below the floor finality pauses and the node reports it. Two certificates at one index: no verified lock is ever withdrawn, operators resolve (replaces the 3.5 re-evaluation). Seeds: uncertified checkpoint allowed (O-4.3 decided). Scenarios H (equivocator across a 50/50 split: conflicts at 12 to 16 min with 20%, none at 13%), I (40/40/20), J (signing stops 1, 6, 24 h), K (bought keys worth 20% and 40% against 30% hash), five seeds each. 3.10 rows for the gaps; open items O-3.15 to O-3.19.
Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
