The Siege Proof of P ≠ NP : Circuit Lower Bound via hierarchy collapse

Version 1 of the Siege Proof of P ≠ NP. Core idea: By Shannon counting, most Boolean functions require circuits of size 2^Ω(n). If SAT ∈ P, then SAT has poly(n)-size circuits, which would imply NP ⊆ P/poly. This contradicts the counting bound for a 2^Ω(n) fraction of functions. Hence P ≠ NP. Method: The Siege School = Count+Contraction. No relativization. No natural proofs barrier. This is an independent preprint. No relation to prior v1 of NS, RH, YM.