A Thought Experiment on a Model Particle (Continued) — The Fifth Frequency and the Composite Curvature Radius Seen from a Zero-Sum Condition

Observational paper (thought experiment; stealth draft v1). Sequel to the previous paper (model particle / admissibility of dimension). Taking the frequency ν as the basic metric, it observes that imposing a zero-sum conservation-type condition makes a fifth direction ν5 appear formally, giving ν1^2+ν2^2+ν3^2+ν4^2-ν5^2=0 (a (+,+,+,+,-) light-cone null condition, the same quadratic form as a mass shell, with no identification of ν5 with mass). It then formulates the central projection taking ν5 as radius (first stage) and the cut along another axis on the sphere (second stage), whose composite curvature radius is given by the closed form r_final^2 = R^2 - sum_{k in S} x_k'^2. Two-layer structure (established mathematics / correspondence hypothesis). No modification of standard quantum theory, general or special relativity; no new prediction.