SomaNoesis - A Mathematical Theory of Admissible Structural Evolution

This monograph introduces the Soma–Noēsis (SN) framework, a mathematical theory for analysing structural evolution under admissible transformations. The framework is developed in three stages. The first constructs the benchmark-dependent mathematical objects required for admissible structural comparison, including benchmark families, observable maps, admissible operator classes, residual representations, residual optimisation, and structural classification. The second develops the associated analytical theory through structural persistence, variational formulations, residual geometry, structural rigidity, persistence laws, admissible equivalence, global persistence, and asymptotic classification. The final part presents a complementary mathematical formulation based on possibility spaces, constraint objects, organised constraint systems, and organisation theory. Throughout, the theory is formulated independently of any particular scientific application. Applications arise only through the specification of benchmark families and admissible transformations, while the underlying mathematical framework remains unchanged. This preprint presents the current mathematical formulation of the SN framework and is intended to support scholarly discussion, independent analysis, and future mathematical development.