Dynamic Obstruction Horizon, Factor Shells and the Sieve-Critical Gap

A candidate near the left square edge is automatically immune to the whole obstruction strip a ∈ (n − √n, n] (the horizon theorem); composite iff δ² + 4nδ − 4k is a perfect square; a roughness ladder (z = n^α leaves at most P₃ for α > 1/2 and at most P₂ for α > 2/3); the 'sieve-critical gap' at α = 1/2 is the classical parity barrier projected onto this base space.