CPT Violation Thresholds and Vacuum Phase Transitions in Dynamical Nested Radical System

We establish a novel connection between nested radical dynamical systems and quantum field theoretic phenomena through the identification of critical CPTviolating thresholds. The system S = √Λ+kS exhibits phase transitions at |k| = 1, demarcating symmetric (QCPT = 0) and symmetry-broken (QCPT= 0) regimes. Through canonical quantization of Noether currents, we demonstrate how the operator ˆ QCPT = R d3x(ˆ S†∂0 ˆ S− ˆ S∂0 ˆ S†) measures vacuum asymmetry, with graphical evidence showing potential tilting at k ≥ 1. The effective potential V (S,S†) = m2S†S +λ(S†S)2 +ϵ(kS2 +k∗S†2) yields testable predictions for axion-photon coupling (gaγ ∼ 0.1k/GeV −1) and gravitational wave spectra (h0 ∼ 10−22(k−1)3/2). This work unifies mathematical recursion relations with high-energy phenomenology, suggesting observable signatures in neutron star mergers (LIGO-Virgo) and dark matter detection (ADMX).