CVFT - Technical Document And Mathematics

This work develops the rigorous mathematical framework underlying Correlational Variational FieldTheory (CVFT). We formalize the functional-analytic structure of the kernel space, establish coercivity conditions for the structural functional, and define the gradient flow governing connectivityevolution.We prove well-posedness of the flow under minimal regularity assumptions and introduce intrinsic refinement as a strongly continuous contractive semigroup acting on the admissible kernelspace. The interplay between variational dynamics and refinement yields compactness propertiesin the infrared regime.Under suitable spectral boundedness and non-pathology conditions, we establish the existenceof invariant sets and characterize the structure of potential attractors. Conditional spectral compression theorems are formulated, showing how multiscale contraction suppresses unstable modesand stabilizes finite-dimensional infrared sectors.These results provide the mathematical backbone required for structural selection, universalityclass formation, and effective field emergence within CVFT.