The Qubit as a Topological Intersection of Infinite Constraints: A Simplicial Interpretation of Quantum States by Rollo Dicks

Standard formulations of quantum mechanics treat the qubit as a fundamental, point-like vector in complex Hilbert space, a formalism that generates interpretational paradoxes regarding non-locality and the mechanism of wavefunction collapse. This paper proposes a novel Simplicial Interpretation, positing that finite quantum states are not primitive objects, but are derived topologically from the intersection of infinite global boundary constraints. By formalizing the Collision Space:= a region of constructive interference generated by overlapping affine half-spaces; we establish a minimal topological condition for boundedness in -dimensions. Furthermore, we demonstrate that the linear inversion of a generating ray creates a disjoint negative interval, an anomaly that necessitates an expansion into an orthogonal degree of freedom. We argue this topological inversion provides a geometric origin for the complex phase in quantum mechanics. This framework reframes superposition as a deterministic boundary-value resonance and collapse as a topological transition resulting from constraint damping.