Purely Deterministic Token Generation (PDTG): Eliminating AI Dependency from the Tensor-Native Semantic Computing Pipeline Through Pure Mathematical Token Construction

Proves that the TNSC pipeline operates correctly and completely without artificial intelligence. Introduces Purely Deterministic Token Generation (PDTG), a three-tier deployment model using only deterministic arithmetic: pre-compiled library (Tier 1), on-demand generation (Tier 2), and universal fallback formula τ(d) = FNV₆₄(canonicalize(d)) (Tier 3). Six formal theorems prove PDTG satisfies all DSTA axioms. The universal formula requires only XOR and multiplication — deployable on consoles, mobile GPUs, embedded systems, and FPGAs without ML infrastructure. Asymptotically equivalent to AI-assisted generation under the Master Theorem.