Original Antipedal Centroids in Elliptic Billiards

We establish explicit, phase-independent vertex-centroid formulas for antipedals of the original polygon in elliptic billiards with a nondegenerate confocal elliptic caustic and even least period. The pole is the ellipse center or either focus, and all consecutive antipedal intersections are finite. The result covers admissible coprime star trajectories and repetitions of even primitive orbits; the circle is treated separately. A paired-chord identity and perimeter stationarity yield the focal coefficient in terms of semiaxes, caustic parameter and mean side length. An even number of listed vertices is not sufficient: exact twice-repeated primitive triangles show that the unrestricted even-list extension fails. This note gives a precisely scoped interpretation of invariant k405 in Reznik-Garcia-Koiller's Table 5, rather than declaring every interpretation of the abbreviated dataset record AMR-050-0023 resolved. Source record 5100023 belongs to the frozen Hugging Face dataset ulamai/UnsolvedMath v1.6.0. The construction is the original-polygon antipedal and its unweighted vertex mean, not an outer-polygon antipedal or an area centroid. No hyperbolic or degenerate-caustic extension is claimed. Portable exact symbolic and rational verification files accompany the analytic proof. This is an AI-assisted, self-audited, unrefereed preprint. Classical ingredients are credited; novelty remains undetermined, and no independent human review, proof-assistant verification or absolute-priority certification is asserted.