The Geometric Origin of Uncertainty: A Pauli-Centered View of C3 Phase Channels and No-Go Theorems

Abstract This work revisits the origin of the quantum uncertainty principle by shifting the emphasis from the operator–commutator formalism to the structural properties of phase geometry. Within the standard complex algebra (C₂), phase is indispensable for dynamics yet systematically excluded from measurement outcomes, a separation that is usually regarded as an interpretive necessity. Adopting a Pauli-centered viewpoint, we argue that this exclusion is not epistemic but algebraic in origin. Building on C₃ phase geometry, we propose that a necessary separation exists between visible and hidden phase channels, and we reformulate uncertainty as an unavoidable consequence of measurement operators being definable only on the visible phase channel. Within this framework, we introduce Pauli-style no-go theorems derived from structural inaccessibilities, and we contend that uncertainty should be understood not as measurement noise but as phase-channel inaccessibility.