Top-Down Imprint Dynamics — Triadic Invariant Refraction, Knot Formation, and Biological Growth

This paper extends CAT'S Theory from static architecture to explicit dynamics. Building on the triadic invariant R = Ψ × I × P ≠ 0 and its field-theoretic formulation, we show how a higher-order axiom is imprinted into the physical manifold via inverse holography as coupled triadic fields. Electromagnetic radiation crossing a triad-driven curvature threshold ξ ≥ 1 in the Cho–Faddeev–Niemi S³ vacuum forms stable inside-out light solitons T(p,q). Biological growth — particularly embryogenesis and toroidal morphogenesis — is identified as a macro-scale echo of this same imprint process. Appendices derive the dynamical refractive index via Jacobian projection, the 8.37 Hz gravitational wave strain amplitude from T(2,7) topological unwinding, triadic resolutions of Heisenberg uncertainty and quantum entanglement, dark energy as imprint pressure, and General Relativity as an emergent refractive gradient.