IMR — Core Theorem (2025): Axioms, Reflective Geometry, and the Unique Logistic Law of Coherence

This document presents the complete formulation of the IMR Core Theorem, the foundational mathematical result of the IMR (Intelligenza Multidimensionale Riflessiva) framework. The theorem demonstrates that any reflective coherence functional R(μ), defined on probability ensembles in a Hilbert space and satisfying axioms R1–R6 together with Reflective Scale-Consistency (RSC), must necessarily take a logistic form: R(μ) = {1}{1 + e-k\,Δ(μ,μ_0)}. The work develops: the reflective paradigm and its geometric principles, the canonical deviation coordinate Δ(μ,μ_0), the collapse of the ensemble geometry to a radial structure, the semigroup dynamics induced by scale transformations, the logistic differential equation as the unique admissible solution. Included are Sections I–III, Preface, Index, Notation page, and Appendices A–K covering functional equations, operators, structural lemmas, and the full logical chain leading to the theorem. This is the definitive reference for the IMR reflective mathematical architecture.