Unrefereed candidate with a complete prose proof of a sparse upper bound for regular, unobstructed images in positive multiplane point-mass lenses. The arbitrary-plane nearest-neighbor support yields an exact mixed-volume transfer recurrence, giving 33 for two binary planes and 213 for three. The sharp product conjecture and physical attainment remain unresolved.Version 0.2.0 addresses the supplied AI-assisted minor-revision review. Exact finite checks, known-example interval certification and separately written review checks are included. These are not formal proof, authenticated human peer review, independent external reproduction or a novelty certificate. The relevant 2022 Perry dissertation remains unread. Original prose/data: CC0; original code: MIT; supplied audit: NOASSERTION, preserved without relicensing.