Foundations of Quantum Gauge Time Theory I: Finite Access, Elementary Kinematics, and Returning Dynamics

Abstract

A conserved whole is taken as primitive and is represented by a conservative dynamics subject to finite non-injective access. The resulting observable/unread decomposition yields an exact memory kernel and self-energy, an exchange law between readable and unread sectors, and a dynamically defined distinction between a returning sector and a silent complement. Finite observations can identify invariants of the returning dynamics without uniquely reconstructing the physical internal partition. Inside a declared elementary category, the analysis then selects a reciprocal elementary kinematic type. Two explicit physical identifications connect this kinematics to a constrained hyperbolic pair action and to a cyclic unitary scalar readout. Bochner, Lanczos and Carleman reconstruction then determine a unique minimal essentially self-adjoint Jacobi generator on the cyclic returning sector. The paper distinguishes foundational premises, declared mathematical typing, theorem-level consequences, physical identifications and open physical gates. It does not determine the absolute physical scale, prove physical occupancy of the elementary category, fix the silent-sector completion, or derive Standard-Model and gravitational phenomenology.