math-021-disprove: Disprove The Perfect Cuboid Problem

[IndieMath:math-021:disprove] Disprove the The Perfect Cuboid Problem conjecture through an IndieMath AI research attempt. Canonical statement: There is no rectangular box with all of: integer edge lengths a, b, c; integer face diagonals √(a²+b²), √(b²+c²), √(a²+c²); and integer space diagonal √(a²+b²+c²). Contributions fund model usage and related compute for this direction.