The Boundary-Induced Collapse Ontological Theorem (BIC Theorem)

We formalize the Boundary-Induced Collapse (BIC) Ontological Theorem, providing a structural derivation of quantum state reduction that replaces stochastic postulates with physical necessity. We demonstrate that the interaction between a quantum system and its physical boundary—environment, apparatus, or constraints—induces a self-adjoint operator hatB whose spectral decomposition defines a set of structurally stable modes, or Ontological Deltas (|deltaᵢ). The theorem proves that collapse is not a probabilistic miracle but an objective transition determined by the microscopic configuration of the boundary, which "forbids" alternatives through spectral selection. By establishing that decoherence is the mechanism and BIC is the ontology, we unify quantum measurement with the stability of linear systems. This theorem restores quantum mechanics to the domain of structural physics, asserting that reality does not "choose" outcomes; rather, boundaries enforce them through spectral necessity. Diagram https: //drive. google. com/file/d/1TxZtBJpwCAzkOGBU3sEpLwhV7DoC3tFA/view? usp=driveₗink