Center-Pedal Area Products in Elliptic Billiards

We prove constancy of the product of the signed area of an elliptic billiard orbit and the signed area of its pedal polygon at the common center, for a fixed nondegenerate confocal elliptic caustic and least period odd or divisible by four. Primitive star trajectories are included. A reflection-coordinate telescope expresses the centered pedal area as a fixed multiple of a Jacobi trace. After complexifying the billiard parameter, the original area and this trace have complementary simple-pole sets; odd pairing and reversed-edge pairing remove every pole of their product. This establishes invariant k203,b under an explicitly stated genuine-period convention. Source record: AMR-050-0012 (raw ID 5100012, k203,b), Hugging Face dataset ulamai/UnsolvedMath. Exact standard-library controls verify the centered-pedal prefactor and actual low-period geometry. Primitive six-periodic controls show why an unrestricted repeated-list interpretation would be false. Hyperbolic and degenerate caustics are excluded. This is a self-audited, AI-assisted, unrefereed preprint; no independent human review, formal proof-assistant verification or absolute priority claim is made. Prior geometry, Jacobi parametrization and the established complex-pole method are credited, and novelty remains undetermined after a bounded primary-literature search.