Layered τ₀ Theory: Universal Causal Response and Discrete Computation

This paper proposes the Layered τ₀ Theory, a foundational framework establishing that all physical systems evolve through discrete causal steps of minimal duration τ₀ > 0. The theory is constructed via five axiomatic modules:τ₀-Computational Equivalence: Physical systems are computationally equivalent to universal Turing machines under τ₀ constraints.Upper Bound on Computational Speed: No system exceeds the operation rate 1/τ₀.Complexity Hierarchy: System couplings respect τ₀-induced layered constraints.Quantum-Classical Transition: Classicality emerges when decoherence timescales T₂ ≪ τ₀.Generalized Cellular Automaton: Continuous spacetime maps to discrete causal updates.All derivations rely solely on reductio ad absurdum proofs from first principles, requiring no experimental input. The theory unifies computation, quantum dynamics, and emergent complexity under a single τ₀-constrained framework.