The Compact Fiber as the Canonical Admissibility Structure for Discrete Scalar Motion

The Compact Fiber as the Canonical Admissibility Structure for Discrete Scalar Motion: A Necessity Result for the Reciprocal System. This paper derives the compact admissibility structure appropriate to the stable local material regime of discrete scalar motion. Its central claim is a necessity claim rather than a phenomenological fit claim: once the relevant closure, covering, and stability conditions of the stable local regime are imposed, the compact fiber is not a convenient model choice but the canonical admissibility structure. The result is intended as a foundational paper for later atomic and effective-quantum developments within the stable local regime. It does not claim that all scalar-motion regimes, including earlier or less structured regimes such as radiation, must instantiate the same full compact local carrier in the same way.