The Geometry of the Aether Unit: Invariant Geometry, Time-Integrated Exposure, and the Geometric Origin of Subatomic Particle Structure

This monograph develops the mathematical foundation of the Aether Physics Model (APM) by deriving observable physical organization from invariant chronogeometric geometry. Beginning with the Aether Unit as the primitive invariant manifold, the work constructs a hierarchy of configuration geometry, differential geometry, chronogeometric evolution, observable projection, recursive compatibility, and invariant measurement. The development proceeds from mathematics toward physical interpretation. Observable particle structure is not postulated but emerges through variational selection, persistent time-integrated exposure, and recursive compatibility. Within this framework, the electron, proton, and neutron arise as distinguished stable chronogeometric configurations of a single invariant manifold. The monograph further develops the Quantum Measurement Unit (QMU) system as the natural measurement algebra of invariant chronogeometric organization. Primitive quantities including the quantum length, quantum frequency, magnetic charge, invariant area, and dynamic domain are shown to generate a closed system of measurement identities culminating in Ledger One. Physical constants, including the fine-structure constant and gravitational constant, are interpreted as invariant ratios within the completed measurement algebra. Throughout the work, mathematical rigor is emphasized through formal definitions, constructions, propositions, theorems, and proofs. Standard methods from topology, differential geometry, Riemannian geometry, variational calculus, and algebra are employed where appropriate while introducing new chronogeometric structures specific to the Aether Physics Model. This volume serves as the foundational mathematical reference for subsequent QADI publications concerning particle structure, magnetic charge, gravitation, chronovibration, temporal geometry, and Quantum Measurement Units.