Temporal Phase Encoding (TPE) : A Theoretical Framework for Phase-Coherent Artificial Intelligence

Temporal Phase Encoding (TPE) v1.2 specifies a minimal method for injecting a cyclic phase coordinate into AI systems so they can reason and act in coordination with periodic processes and phase-window scheduling stacks (Human–AI–Quantum). TPE represents time by a canonical normalized phase \(\phi(t)\in[0,1)\cong \mathbb{S}^1\) derived from protocol conventions \((t_0, T_{\mathrm{cycle}})\), and embeds this phase using Fourier features \([\sin(2\pi k\phi), \cos(2\pi k\phi)]_{k=1}^K\). This release aligns TPE with the series-wide Phase-Coordination conventions (cycle index \(n(t)\), wrap-around-safe circular distance, half-width window tolerance \(\Delta\Phi\)) and makes explicit how a phase-aware AI component can select cycle-anchored phase windows compatible with macro-window/micro-slot coordination (Q-Address style). TPE is a representational and decision-layer tool: coordination guarantees depend on external bootstrapping and execution layers (e.g., phase estimation error, oscillator stability, and system latency), and are not implied by the encoding alone. This is an interoperability-focused update intended to make TPE consistent with the broader coordination stack (Human UI, AI scheduling, and distributed quantum/hardware control) without requiring absolute timestamp targeting. Previous version: TPE v1.0 (Zenodo: 10.5281/zenodo.18001065) This release: v1.2 (Zenodo: 10.5281/zenodo.18064354) Keywords: phase coordination, cyclic phase, Fourier features, temporal encoding, AI scheduling, interoperability, Human–AI–Quantum.