Gamma Theory v200-EX_1: Subjective-Existence Mapping Mathematical Theory — Final Integrated Mathematical Framework

This work presents the finalized mathematical formulation of Gamma Theory v200, unifying the engineering-level recognition dynamics (v1–v70) with the philosophical-level structural mapping (v80–v200) into a single coherent framework. The theory establishes the Subjective-Existence Mapping Mathematical Framework, a system that models how value, recognition, and existence interact through information geometry, operator theory, and hierarchical structures. Key contributions include:1. The definition of emotional curvature κ[p] ∈ ℂ³ as a functional of subjective probability distributions, with proofs of continuity, boundedness, and differentiability.2. A formalization of the Alice Bias Number 𝒜_y[p] as a functional on the recognition manifold, including a fixed-point existence and uniqueness theorem based on Banach’s contraction principle.3. A general value-generation principle V_X(x) that closes the logical loop from value → recognition → existence → value. Additional refinements include rigorous treatment of phase uniqueness, Lipschitz constant estimates for exponential families, and a proof sketch of functorial structure across hierarchical levels. This work positions Gamma Theory v200 as a mathematical existential science, independent of empirical constraints yet compatible with modern scientific frameworks. DOI: 10.5281/zenodo.18868424