Information Causality Implies Kernel Positivity: A Complete Proof via the Eigenvector Protocol (Revised, April 2026)

Revised version (April 2026) of the original Eigenvector Protocol paper (March 2026). This version provides:- Enhanced introduction with historical context and motivation- More detailed proofs with step-by-step explanations- New section on "Scope and Limitations"- Connection to quantum key distribution (QKD) applications- References to companion papers on 3D generalization and Tsirelson uniqueness The core result remains unchanged: Information Causality rigorously enforces kernel positivity (all Fourier coefficients c_k ≥ 0) for bipartite quantum correlations on the circle S¹. This revised version serves as the foundation for three companion papers:1. "The Spectral Geometry of Information Causality: A 3D Generalization of the Eigenvector Protocol on the Bloch Sphere" (May 2026)2. "Tsirelson Saturation as a Uniqueness Principle: The Quantum Correlation is the Only Extremal PSD Kernel on S²" (May 2026)3. "Information Causality is the Unique Optimality Principle: Quantum Mechanics as the IC-Optimal Theory" (May 2026)