A Monster-Symmetric Admissibility Formulation of the SEXA Unified Field Theory: Operator-Glyph Closure, Σ₆₀ Exciternion Logic, and Falsifiable Reduction to General Relativity, Quantum Field Theory, and Yukawa Interaction Regimes

Related work and extensions: https://BabyMonsterMath.com Published journal article from the Journal of Advances in Mathematics (JAM). This paper presents an operator-level admissibility formulation of the SEXA Unified Field Theory in which physical configurations are governed by a structured glyph operator chain acting on a unified energy functional. The framework introduces Γ as a six-operator admissibility chain, with Σ₆₀ exciternion logic and Monster/Baby Monster symmetry constraining admissible configurations, while requiring falsifiable reduction to General Relativity, Quantum Field Theory, and Yukawa interaction regimes. Original journal DOI: 10.24297/jam.v25i.9887. ABSTRACT This paper presents an operator-level admissibility formulation of the SEXA Unified Field Theory in which physical configurations are governed by a structured glyph operator chain acting on a unified energy functional. The formulation extends recursive closure frameworks by introducing a six-operator admissibility chain, Γ, that enforces existence conditions prior to physical interpretation. Each operator corresponds to a non-reducible constraint governing energy admissibility, propagation consistency, manifold, symmetry invariance, mass-memory persistence, and observational registration. A configuration is phcompatibilityysically admissible if and only if it survives ordered evaluation under Γ. The Σ₆₀ logical system defines the higher-order admissibility algebra, while Monster and Baby Monster symmetry constrain admissible configurations through invariant orbit classification. The framework is explicitly falsifiable. Failure of operator closure, recursive convergence, symmetry classification, or recovery of established limits in General Relativity, Quantum Field Theory, or Yukawa-type interaction regimes results in immediate rejection. This establishes admissibility as a primary condition, defining a constrained and testable pathway toward unified field consistency. INTRODUCTION The development of unified field theories has traditionally proceeded through extension, introducing additional fields, symmetries, or higher-dimensional embeddings to reconcile known physical interactions. While these approaches have produced powerful models, they do not impose a prior condition governing which configurations are admissible before unification is attempted. The SEXA Unified Field Theory introduces a closure-based formulation in which condensed and perpetual energy regimes are unified through a single invariant action defined on a five-dimensional exciter manifold with recursive extension into higher-dimensional structure. Within this framework, physical configurations are not unrestricted but must satisfy recursive closure across dimensional embeddings in order to remain consistent. Closure alone, however, does not determine admissibility. A configuration may satisfy closure conditions while failing under recursive evaluation, dimensional projection, or invariant preservation. This reveals the necessity of a pre-interpretive admissibility mechanism capable of determining whether a configuration is permitted to exist prior to physical interpretation. The Recursive Closure Criterion and Prime Atom of Logic framework establish this mechanism through the Exciternion, which defines admissibility as a structural condition independent of domain. Within that formulation, energy, fields, and physical expressions are not primary objects but emerge as admissible configurations within a recursively constrained logical space. The present work introduces the operational realization of this admissibility structure within the SEXA Unified Field Theory. The six-glyph system, previously introduced as a compact structural representation of the unified energy equation, is reformulated here as an ordered operator chain acting directly on the energy functional. Each glyph functions as an operator rather than a symbolic label. The ordered application of these operators defines a strict admissibility sequence such that physical configurations exist only if they survive sequential evaluation under the complete glyph chain Γ. The unified equation therefore, specifies the space of evaluable configurations, while admissibility determines the subset that can exist. This formulation is further constrained through invariant orbit classification under Monster and Baby Monster symmetry, restricting admissible configurations to discrete classes consistent with symmetry-preserving structure. The Σ60 logical system operates as the governing admissibility algebra, enforcing recursive consistency across all levels of the formulation. The framework is explicitly constructed to be falsifiable. Failure of operator closure, failure of recursive convergence, failure of invariant classification, or failure to recover known physical limits results in immediate rejection without parameter adjustment or interpretive modification. Admissibility is therefore treated as a primary condition, and all physical structure emerges as a consequence of satisfying this condition.