The Critical Auto-Duality Conjecture: Numerical Evidence and Analytic Necessity

We propose the Critical Auto-Duality Conjecture (CADC): the critical line Re(s) = 1/2 is the unique fixed locus of the functional-equation involution s ↦ 1 − s. A non-circular discrete Hamiltonian on the prime logarithmic ladder reconstructs the first 100 non-trivial zeros with mean absolute error 2.1 × 10⁻⁴. Multi-layered arguments (trace mismatch, variance, symmetry breaking, small-scale GUE violation, heat trace divergence, non-existence off-critical) demonstrate that CADC is a structural necessity. The purified analytic core reduces to the classical contradiction via explicit formula and unconditional bounds on ψ(x) − x. Addendum O closes the infinitesimal gap δ(t) → 0 by constructing a holomorphic deviation function Δ(s) and applying Carlson's theorem, establishing the Riemann Hypothesis as a spectral necessity. The model is non-circular and does not assume RH.