Coordinate Slicing Theory (CST): A Single-Reality Framework for Quantum Mechanics with an Ontic Probability Manifold

We propose Coordinate Slicing Theory (CST), an interpretive framework for quantum mechanics that maintains a single realized reality without hidden variables, branching worlds, or observer-dependent collapse. CST posits that physical systems extend not only through spacetime but also through an ontic probability manifold P — a real, observer-independent structure encoding unresolved potential for definiteness, rather than a catalogue of pre-existing outcomes or mere epistemic uncertainty. Definite facts are created through interaction via "slicing": a localized interaction that produces stable relational records by localizing a system's extension in P. Which outcome a slicing event creates is irreducibly chancy: CST relocates and reframes the selection problem rather than solving it, contributing an ontology of the pre-outcome situation and a covariant account of when and where facts are created. Classical definiteness arises from continual environmental slicing, while quantum phenomena appear when extension in P persists until interaction. Entanglement is reinterpreted geometrically as shared probability structure: entangled systems occupy a common structure in P, so a single slicing event jointly creates correlated outcomes without signaling, temporal ordering, or pre-existing values. CST is an interpretation, not a modification of quantum dynamics, and is empirically equivalent to standard quantum mechanics. We construct explicit toy models in which quantum states arise as projections of densities on probability manifolds (S² for qubits, CP³ for qubit pairs), with unitary dynamics lifted to a flow on the manifold. A no-go lemma shows that deterministic responses cannot reproduce the Born rule for pure states; the models therefore employ stochastic likelihood responses, which reproduce Born statistics exactly for all preparations, recover projective collapse and repeatability, satisfy no-signaling, reproduce Bell correlations, and yield a foliation-independent update scheme for spacelike-separated interactions.