The GTE-Möbius Substrate: Arithmetic Unification of Computation and Transputation in the Universal Generative Principle

The Universal Generative Principle requires a physical substrate capable of two operationally distinct but inseparable modes: computation (deterministic evolution under ) and transputation (PSC-forced, non-computable selection among undecidable alternatives). We formalize this as the Generative Triple Evolution (GTE)-Möbius substrate—the triple (A, e, ), where A is the GTE arithmetic carrier ( winding dynamics), e is the self-encoding map conferring Turing completeness, and is the class of PSC-consistent coherence measures constrained by D1–D5. The Möbius name reflects a single-surface architecture: computation and transputation share a common substrate without a sharp syntactic boundary; the Gödel–Turing boundary of (A,e) is the computation/transputation boundary of the physics. We prove that the T(2,3) torus knot has both parameters GTE-derived (, zero sorry), define the Turing–PSC (TPC) computability class as strictly intermediate between Turing-decidable and hypercomputation (13 Lean theorems, ), and show its three-level hierarchy depth equals = 3 (). Conjecture C1 (GTE as the final F_PSC-coalgebra) is fully proved (, zero axiom); four consistency conjectures (C2–C5) remain open, with C3 and C4 the most tractable. The abstract carrier A realizes as the PSC-admissible kink sector of the Phi_MDL Klein–Gordon field; binary coarse-graining recovers in the continuum limit. Three Lean-certified lifting theorems connect beable, discrete, and physical scales (); the GTE equivalence principle and geodesic theorem () connect emergent gravity to -weighted trajectories. Quantum field-theoretic and completeness consequences are developed in companion papers .