Admissibility and Invariance: Constraint Structures in Lorentz Symmetry, General Covariance, and Quantum Field Theory

Abstract This paper offers a register-disciplined alignment between a constraint-based ontology and several foundational principles of modern physics. The motivating problem is that Lorentz invariance, general covariance, and quantum field theory are frequently treated as ontological disclosures, which invites category errors such as reifying fields as substances, treating the physical vacuum as “nothingness”, or elevating invariance principles into metaphysical primitives. We argue that much of the perceived tension dissolves once explanatory direction is held fixed: Ontology to Constraint to Structure to Physics. Ontologically, the Categorical Absence of Being (CAB) is defined as absolute non-being and is treated as incoherent as a possible state. From this follows the Primitive Principle, Intention-to-Exist (ItoE), understood as a primitive constraint of admissibility excluding null-equivalent configurations without invoking causation, teleology, or agency. Admissible existence is then structurally articulated by the Triaxial Existential Field (TEF): Coherence (C) as determinate identity persistence, Reflexivity (R) as consciousness per se in the sense of interior state-availability, and Participation (P) as influence per se through relational actualisation across boundaries. Within this interface, Lorentz invariance and general covariance are treated as Whole-level constraint regularities (R₍Whole₎) governing admissible coordinatisation of participation, while QFT is treated as a calculus of participation patterns whose “vacuum” is non-null and therefore not CAB. An optional subsection locates the Second Law as a constraint on typical P-trajectories for C-stabilised entities under R₍Whole₎, without elevating entropy into a metaphysical arrow. The result is a non-reductive synthesis in which these physical principles remain intact, do not compete for ontological primacy, and are conceptually coherent when read as constraint structures operating within admissible existence.