Outer-Pedal Area Products in Elliptic Billiards

For a fixed confocal elliptic-caustic billiard family with least period congruent to two modulo four, we prove that the signed area of the outer tangent polygon times the signed area of its pedal polygon with respect to any fixed point is constant. Coprime star trajectories are included. The outer polygon is an explicit affine image of a half-step shift of the billiard orbit. After complexification, its area and the outer-pedal area have disjoint possible simple-pole sets. Central pairing separates the pedal map into two area traces, and two reversal symmetries provide the complementary zeros that make the product entire and elliptic. This establishes invariant k303,a under an explicitly stated least-period convention. Source record: AMR-050-0014 (raw ID 5100014, k303,a), Hugging Face dataset ulamai/UnsolvedMath. The arbitrary-point dependence is radial quadratic. For the six-periodic family with lambda=a^2*b^2/(a+b)^2, the invariant equals a*b*(a+2*b)*(2*a+b)*(1+|M|^2/(a+b)^2). Exact standard-library polynomial and quadratic-field controls verify the formulas and actual geometry. Two same-caustic triangles, each traversed twice, give a counterexample to the unrestricted six-entry-list interpretation; they do not refute the genuine least-period theorem. Hyperbolic and degenerate caustics are excluded. This is a self-audited, AI-assisted, unrefereed preprint, not an independently human-reviewed or formally verified proof. Prior confocal geometry, canonical Jacobi parametrization, adjacent tangent-pedal results and the established complex-pole method are credited. No first-proof or absolute priority claim is made.