ACORN Booklet 12: Quantum Mechanics — Deterministic Curvature Closure and the Origin of Quantum Behaviour

ACORN Framework Booklet Series The ACORN framework is a geometric curvature–closure approach to fundamental physics in which mass, quantisation, and dynamical behaviour arise from closed circulation of intrinsic curvature channels governed by a compact canonical operator structure. From these canonical relations emerge invariant closure norms, quantised loop actions, and universal recurrence relations organising stable physical structure. The ACORN booklet series develops the consequences of this canonical framework across multiple domains of physics. Each booklet begins from the frozen Canon and explores how familiar physical phenomena arise as projections or consequences of curvature closure dynamics. This booklet examines the relationship between the ACORN framework and quantum mechanics. Within ACORN, quantisation arises naturally from integer loop closure of intrinsic curvature circulation rather than from probabilistic axioms. The universal recurrence law mc2T0=Nhmc^2 T_0 = Nhmc2T0=Nh establishes the Planck constant hhh as the minimal closed-loop action of curvature dynamics. Quantum behaviour therefore appears as a manifestation of discrete closure states within the curvature–closure framework. Observable probabilistic behaviour emerges when intrinsic curvature recurrence is projected into observable spacetime coordinates and phase information is partially averaged or unresolved. Wavefunctions therefore represent projection-level descriptions of underlying deterministic curvature dynamics. Within this interpretation several characteristic features of quantum mechanics acquire geometric meaning, including: • quantised energy levels as closure eigenmodes,• wave–particle duality as projection behaviour of curvature circulation,• interference as phase interaction of closure modes,• and probabilistic measurement as statistical description of unresolved curvature phase. ACORN: Quantum Mechanics therefore proposes that quantum phenomena do not require fundamentally indeterministic laws, but instead reflect the projection-level behaviour of deterministic curvature closure governed by the ACORN Canon. This booklet situates quantum mechanics within the broader curvature–closure framework and prepares the ground for the subsequent interpretation of the Standard Model and particle phenomenology.