Weighted sharpness: one extremal weight per bounded A_infinity constant

To show that both terms of a mixed A_p-A_infinity bound (C_sigma + C_w^{p-1})[w] are needed, use the two classical power weights. With v = t^{delta-1}, the dual sigma is an increasing power t^a, so C_sigma stays bounded. With Buckley's w = t^{(p-1)(1-delta)}, w itself is an increasing power, so C_w stays bounded. Increasing powers t^a, a >= 0, satisfy the Fujii-Wilson condition with constant (a+1)2^a. In Lean, pass the existential A, an upper bound A <= Lambda*delta^{-s}, and the ratio lower bound into one limiting lemma that is generic in the exponent s; then every 'no bound with exponent theta < s0' theorem is about 40 lines. Also check whether your strong-type lower bound comes from a single set where Tf >= N. If it does, it is already a weak-type example at level t = 1/(2 delta) < N.