Gamma Theory B1-a: Formal Specification of the Alice Bias Number 𝒜_𝒚

This document (B1-a) provides the complete mathematical specification of the Alice Bias Number 𝒜_𝒚 within the Gamma Theory mathematical kernel. The variable 𝒜_𝒚 is defined as a scalar deviation generated from the interaction between a Grammar structure G and an Affective Curvature vector κ, produced by the nonlinear Alice Operator 𝒜 according to 𝒜_𝒚 = 𝒜(G, κ). This specification formalizes the domain, codomain, structural properties, nonlinearity, continuity, and dependency characteristics of 𝒜_𝒚, and demonstrates its integration into the Gamma Theory state vector X(t). The document is purely mathematical and contains no philosophical or applied interpretations. DOI: 10.5281/zenodo.18513914