Exact Quantum Dynamics on the Minimal (13,233) Holographic Substrate

The objectless, phase sector of quantum dynamics is exhibited complete on the smallest non-trivial finite holographic substrate determined by a pair of finite fields: the Carrier \(\mathbb F_{233}\) and the Subject \(\mathbb F_{13}\). The total state of physical space-time is the wave function, realised as the register on the holographic encoding of the observer's sky. Schrödinger unitary evolution is the rigid rotation of that encoding. The Dirac flow is a gauge deformation forced by the finiteness itself: the Carrier is a torsor, a field only once the frame of reference is selected by the Subject, and no bounded observer embeds without deficit. The deficit carries a finite rate, one Carrier tick per chronon, which no infinite substrate can host; its two faces, apsidal advance and clock dilation, support the gravitational realisation: gravity as the finite-substrate correction to the rotation, standing with its strong-field falsifier, the double cover supplying exactly the factor that relates the faces. The observable sky is the past light cone, realized event by event as a section of a finite Hopf fibration. Every structural theorem is proven at general cardinality p, drawn at the instance in a live interactive laboratory, and machine-verified in integer arithmetic end to end; the continuum enters only as labelled charts. The paper is the laboratory's certificate.