TNA as a Structural Framework for Transcendence, Sacramentality, and Non-Closure

This paper explores the structural convergence between the Theory of Axiomatic Necessity (TNA) and classical theological ontology, mapping theological concepts without reducing them to physics or mathematics. Distinguishing between local observable dynamics (N₀) and the non-local domain of external selection and realizability constraints (N₁), the author demonstrates that complex realizable systems exhibit a Failure of Local Closure, generating multiple admissible trajectories (> 1) that cannot self-stabilize. Within this framework, foundational Christian tenets—including the Johannine Logos, creatio continua, sacramentality, and Eucharistic participation—are reinterpreted structurally as interface mechanisms that bridge local dynamics with non-local closure. Ultimately, the paper posits that mathematical intelligibility does not eliminate theological mystery, but rather formalizes exactly why complete materialist closure remains structurally impossible.