LFIS–19: Angular Burden and Dipole Matching Constraint

LFIS–19 formalizes the angular demand functional and the dipole matching constraint for the ℓ = 1 closure mode in Light Frame Cadence Geometry. Building on LFIS–18’s canonical radial scaling forms, the volume supplies the angular half of the dipole structure and combines it with the radial scaling into the scalar axial representative cos(θ)/r³. The volume treats the matching functional as a representability constraint surrogate, not as a full physical field or observable. It shows that the dipole angular form belongs to the first-order harmonic class and may be canonically represented by cos(θij), while the radial scaling follows from the ℓ = 1 closure-mode result Φ1(r) ∼ 1/r³. LFIS–19 supplies the canonical dipole matching form used downstream in LFIS treatments of directional closure demand, angular admissibility, and the dipole sector of representability matching.