Recursive Symmetry Breaking Across Scales: Quantum Magnets, X-ray Mixing, and Cosmological Phase Transitions in KUTE Framework

We present a unified theoretical framework connecting recursive symmetry breaking in nested radical fields to quantum phase transitions incondensed matter and nonlinear optical systems. The central result is theDilip Mohanty Equation, a Lagrangian formulation that describes:LDM = |∂µS|2 −Λ(1−k2)|S|2 +λ|S|4 +ϵk(S3 +S†3)+gS(Sspin ×B) (1)where the recursion parameter k governs critical CPT violation at thethreshold |k| = 1. This work establishes three fundamental correspondences:* Spin-Radical Duality: Maps the anisotropy parameter ∆ in quantum easy-plane magnets to 1/k, with ⟨Sz⟩ ↔ QCP T* X-ray-Optical Mixing: Relates the cubic term ϵkS3to third-ordernonlinear susceptibility χ(3) in wave-mixing processes* Neutron Star Constraints: Uses observed mass-radius relations(e.g., PSR J1614−2230) to bound k = 1.2 ± 0.1 in the Λ = 9 sectorThe model predicts testable signatures across energy scales:* Discontinuous order parameters in quantum magnets (Rb2CuF4)* Threshold behavior in sum-frequency generation (LiNbO3 metasurfaces)* Gravitational waves (h0 ∼ 10−22) and axion couplings (gaγ ∼ 0.12GeV −1)from neutron starsA triple point at (Λ, ∆, χ(3)) = (9, 1, 1) emerges where CPT violation, magnetic ordering, and optical nonlinearity thresholds coincide. Thiswork provides a mathematical bridge between algebraic recursion relationsand observable phenomena in high-energy physics, condensed matter, andastrophysics.