The Born Rule as a Forced Theorem of Event Density: A Gleason–Busch Reconstruction from First Principles

We derive the Born rule of quantum mechanics as a forced structural consequence of the Event-Density (ED) primitive stack, via the Gleason–Busch route. Standard formulations of quantum mechanics treat the Born rule as an independent postulate, and Gleason’s 1957 theorem reduces it to a non-contextuality assumption that is itself postulated. We show that ED’s channels as primitive ontological sub-structures of the participation graph (Primitive 07) and bandwidth as an edge-weight on those sub-structures (Primitive 04) - forces the non-contextuality assumption rather than postulating it. Combined with the σ-additivity and dimensional admissibility checks and with Busch’s 2003 POVM extension, we establish Theorem 10.