LFIS–05: Representability, Horizons, and Beyond-Phase Structure — Derivational Form

LFIS–05 derives the representability and boundary structure of Light Frame Cadence Geometry in the balanced-contract regime. The volume defines a representable frame by its mode-plane state, radial magnitude, angular orientation, and capacity headroom, with representability governed by the finite capacity condition ρ ≤ LFC. At the saturation boundary ρ = LFC, LFIS–05 replaces informal horizon language with a precise vector-increment admissibility law: incoming increments remain admissible only when they move the state back inside the capacity boundary. This produces source-vs-receiver asymmetry and yields three canonical horizon-like limits: TS-dominant, TD-dominant, and balanced saturation. The volume also clarifies beyond-phase as a failed two-mode continuation marker rather than an ordinary external region with its own ontology. LFIS–05 supplies the boundary and horizon infrastructure used by LFIS–06’s transition kinematics, LFIS–09’s photon propagation rules, LFIS–10’s measurement limits, and the later full three-mode horizon structure developed in the Light Frame Infrastructure Series.