Quantum Hierarchical Evidence Calculus (Q-HEC): Unifying Noncommutative Hyperoperator Analysis with Evidence-Based Inference

We introduce the Quantum Hierarchical Evidence Calculus (Q-HEC), a foundational framework that flawlessly merges the macro-statistical Hierarchical Evidence Calculus (HEC) with the microscopic rigor of Noncommutative Hyperoperator Analysis (NHA). By elevating classical scalar evidence to operator-valued evidence within nonstandard extension C^∗ algebras, Q-HEC redefines quantum measurement not as a probabilistic, ad-hoc collapse, but as a top-down causal projection of an informational Hamiltonian. This framework provides a mathematically rigorous, four-tier orthogonal decomposition of total quantumuncertainty, isolating the irreducible noncommutative infinitesimal roughness from classical aleatory, epistemic, and structural variances.