Geometric Activation and Spectral Gap: A Non-Newtonian Interpretation of Quadratic Energy Structure from Cyclic Symmetry

Position Statement All results are interpretive consequences of the spectral invariant derived from discrete cyclic lattice symmetry. No force laws, mass primitives, or velocity postulates are assumed. Physical quantities are mapped to spectral parameters through invariant-preserving correspondences. Abstract A quadratic spectral invariant derived from cyclic lattice eigenstructure is interpreted as a generalized energy relation. The invariant [\omega^2 - v_{\text{geom}}^2 \mu = \omega_0^2] admits a physically legible mapping in which frequency corresponds to activation rate, Laplacian eigenvalue corresponds to geometric curvature, and the spectral gap corresponds to resistance to coherent activation. The familiar quadratic energy structure commonly expressed as (E^2 = p^2 c^2 + m^2 c^4) emerges as a projection of a more primitive symmetry-derived invariant. Mass and propagation limits arise as derived quantities rather than primitives.