Resolving the "Theory of Everything" Paradox via Constructive Immanence and the Boundedness of Physical Information: A Formal Proof of Physical Decidability

A recent proposal by Faizal et al. (2025) argues that because formal axiomatic systems describing quantum gravity are subject to Gödelian incompleteness, the physical universe must rely on "non-algorithmic" layers or an external "Meta-Theory of Everything" to ensure consistency. We demonstrate that this conclusion rests on a fundamental category error: the conflation of the syntactic limitations of a descriptive Formal Axiomatic System (FAS) with the semantic reality of the physical universe. We provide a formal proof that Gödel’s theorems, which apply strictly to systems capable of modeling Peano Arithmetic and Actual Infinity, are inapplicable to a physical universe constrained by the Bekenstein Bound. By formalizing the universe as a Measure-Many Quantum Finite Automaton (QFA) over a finite Hilbert space, we demonstrate an isomorphism to a Deterministic Finite Automaton (DFA) under unitary evolution. Unlike Turing Machines or Linear Bounded Automata, for which key logical properties are undecidable, the FSA class is strictly decidable. Consequently, we prove that the universe is logically self-consistent without the need for external axioms. Furthermore, we demonstrate that "singularities" are artifacts of the continuum limit ( ), representing a divergence between the information density required by the mathematical map and the capacity of the physical territory. We conclude that the universe operates on a principle of Constructive Immanence: consistency is not a theorem to be proved by a meta-system, but a state to be actualized by the system itself.