The Spectral Geometry of Information Causality: A 3D Generalization of the Eigenvector Protocol on the Bloch Sphere

We generalize the Eigenvector Protocol to the full Bloch sphere S². Using a dimensionally corrected IC-sum and multiple SO(3)-symmetric measurement ensembles, we prove that Information Causality (IC) rigorously enforces kernel positivity (aₗ ≥ 0) for all Legendre coefficients of the correlation function. For even l ≥ 2, a strictly stronger analytical bound holds: the maximum CHSH value satisfies Mₗ ≤ 2√2 − 2(√2−1)cₗ,₀ < 2√2, where cₗ,₀ > 0 is the constant Chebyshev term of Pₗ. For odd l ≥ 3, higher multipoles are strongly suppressed by rotational geometry and numerically confirmed to satisfy Mₗ < 2√2. A residual space for weakly positive Almost Quantum correlations remains, identifying a structural gap whose closure requires an additional extremality principle — developed in a companion paper. This paper extends the original Eigenvector Protocol from the circle S¹ to the full Bloch sphere S².