A sigma–Calculus Proof of the Riemann Hypothesis

Building on the σ–Turing Automaton framework, we rigorously realise the Riemann zeta function ω(s) as a Fredholm determinant of a collapse operator L(s) in the classical ε–Calculus.Using the self-adjoint product D(s) = K(s)·K(1 − s) on the critical line and an Euler-orthogonal factorisation, we prove that every non-trivial zero of ω satisfies Re(s) = ½. The argument is conditional on the ε-model faithfully encoding all effective computation.