SS-COS: Cosmological Geometry and Observational Diagnostics in Scale Space: Geodesic Optics, Clock–Ruler Tests and Conditional Confined Radiation

We present an exactly solvable kinematic benchmark for cosmological diagnostics in a five-dimensional Lorentzian clock-reading geometry. Geodesic observers and null rays yield conditional redshift, angular distance, expansion and clock–ruler consistency relations. Additional bounded calculations address the five-dimensional null-energy requirement, static finite-slab and sub-gap mode controls, receiver-dependent comoving waveguide flux, a flat vector-waveguide source, and synthetic-only parameter-identifiability comparisons. These calculations concern distinct restricted regimes and do not establish a calibrated cosmological luminosity-distance law or a fit to astronomical measurements. The background's physical gravitational support, retarded bulk radiation and calibrated observational inference remain open. A separate numerical supplement provides reproducibility scripts and representative data for the bounded waveguide and synthetic comparators.