Optical Reconstruction in Constrained Null Geometry: From Null Boundary Relations to Geometric and Modal Optics

This work reconstructs optical phenomena within Constrained Null Geometry (CNG) without treating light as a primitive particle, a material wave, a force carrier, or an object following a microscopic trajectory through pre-existing spacetime. It first establishes that the term “light” refers to several mathematically distinct structures: primitive null-channel data, protected phase transport, source-boundary reorganization, null endpoint relations, coherent channel sections, materially dressed realizations, and timelike detector records. The Lorentzian null cone is derived from the positive rank-one boundary of a completed two-complex-dimensional reconstruction record rather than assumed in advance. The associated determinant supplies the Lorentz form, while the Cauchy–Binet identity identifies timelike mass with positive projective non-collinearity of the same underlying records. Null direction, straightness, and the invariant role of c are consequently formulated as closure relations rather than properties of a traveling object. From this structure, the paper derives reflection, refraction, total internal continuation loss, thin-lens focusing, interference, diffraction, gratings, cavity modes, coherence, polarization, Doppler shift, inverse-square dilution, Compton kinematics, gravitational redshift, weak-field lensing, horizon behavior, Planck’s law, the Stefan–Boltzmann law, and the vacuum Maxwell-form curvature equations. Material optics is expressed through a protected spectral resolvent and a conormal Dirichlet-to-Neumann interface operator, clearly separating universal optical geometry from material-specific calculations. A complete hydrogen Lyman-alpha source calculation derives the normalized 2p-to-1s carrier overlap, the rate-bearing conormal boundary operator, angular current, absolute transition rate, natural linewidth, and resolved doublet currents without using an empirical lifetime as an input. The accompanying reproducibility supplement contains the manuscript source, a Zenodo DOI manifest, integrity checks, and independent computational tests of the principal finite-dimensional and numerical results. All 91 included checks pass.