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.
