The Zeta Zoo: The Mathematical Side of Functional Stability Theory

Functional Stability Theory (FST) identifies a single structural pattern — functional positivity under a gauge constraint — as the common substrate of open problems in number theory, mathematical physics, and cosmology. This paper is the mathematical classification side of FST. DRAFT version. This preprint is subject to revisions. Version 2.1 is a guardrail release: it sharpens the status language after strict review, separates self-adjoint YES cases from resonance YES cases, and makes the Riemann, Dedekind, Ihara, CRM, and companion-program claims more explicit. We formalise the trinity of meta-principles governing the zeta-type branch: the Universal Convexity Uniqueness (UCU) lemma, the Semigroup-Group…