From Harmonic Divergence to Dimensional Closure Atomic Continuum Ontology and the s = 2 Transition

Quantum theory has long combined extraordinary formal success with persistent ontological instability. This paper argues that the underlying difficulty lies not primarily in the irrationality of the quantum domain, but in the absence of an adequate ontology for an intermediate regime of closure. That regime can be illuminated mathematically through the Euler-zeta transition from the divergent harmonic boundary at s = 1 to the first stable convergent condition at s = 2. The paper proposes that the interval 1 < s < 2 should be interpreted as a regime of partial closure, designated here as Atomic Continuum Ontology (ACO). Within this framework, s = 1 marks unresolved harmonic openness, 1 < s < 2 marks increasing but incomplete closure, and s = 2 marks the first stable threshold of dimensional admissibility. This framework reclassifies the central paradoxes of quantum theory. Wave-particle duality becomes dualaspect expression, superposition becomes partial-closure multiplicity, entanglement becomes relational persistence, collapse becomes closure deepening, and measurement becomes closure selection culminating in AO Atomic Ontology stabilization.