The Triple-Axiom Foundation of Empirical Science Deduction of the Minimal Necessary Architectural Class for Physical Execution

Structural Execution Sequence (The Deductive Itinerary): This manuscript does not propose a continuous physical theory; it executes a formal mathematical theorem. By strictly bounding the scientific enterprise to the thermodynamic limits of finite computation, it outlines the exact deductive sequence that isolates the minimal necessary architectural class capable of compiling empirical reality. The theorem unrolls across four sequential proofs: 1. The Ontological Anchor (Axiom I: The Embedded Observer): The observer is formally defined as a finite physical sub-system. Scientific prediction evaluates strictly as the act of physical computation. It is governed by the Universal Cost Ledger (C_univ), which algorithmically penalizes static memory allocation (S) and dynamic execution trace (T). 2. The Syntactic Anchor (Axiom II: The Computable Boundary): Because the embedded agent is finite, any valid generative framework must execute safely on finite hardware. Empirical science evaluates exclusively as a formal closed system operating within the Computable Domain (M_TTG): the strict mathematical intersection of computability (Turing 1936), semantic exteriority (Tarski 1936), and bounded scope (Gödel 1931). 3. The Semantic Anchor (Axiom III: Data Supremacy): The raw observational array (D), extracted via thermodynamic collision with the environment, evaluates as the absolute ground truth. The syntactic injection of uncomputable continuous parameters or infinite-precision fields (Δθ) triggers a catastrophic memory leak (C_univ -> ∞) and is structurally forbidden by the Zero-Patch Standard. 4. The Hardware Compilation (m*): By enforcing these three axioms against the macroscopic Evidence Vector (E), we algorithmically deduce the exact hardware interface of reality. The minimal necessary architectural class (m*) compiles strictly as a discrete, local, deterministic Base-72 symplectic state-machine. The Checksum Protocol: We dynamically unroll this architectural class to verify that emergent Lorentz invariance, quantum measurement bounds, fractal self-similarity, objective causality, and thermodynamic irreversibility execute natively as the deterministic compiler artifacts of the discrete hardware itself.