Universal Dimensional Collapse for Incompatible Observables in Quantum Dynamics

This repository contains the full Supplemental Material for the manuscript “Universal Dimensional Collapse for Incompatible Observables in Quantum Dynamics.”

It provides the extended mathematical and conceptual foundations underlying the main theorem, including:

the geometric formulation of observable-space projections,

rigorous curvature and bandwidth bounds,

the proof of the finite-time collapse of two-dimensional expectation-value dynamics onto a smooth one-dimensional manifold,

detailed discussion of effective generators and finite-bandwidth constraints in realistic (possibly open) systems,

treatment of unbounded observables through operational energy windows,

examples from qubit systems, trapped-ion effective spins, and rotor models,

comparison with quantum speed limits,

analysis of saturation behavior, attractor structure, and universality of the collapsed manifold,

clarification of conceptual issues related to projection dimensionality, normalization dependence, and experimental observability.