We formulate the Swirl Holographic Principle (SHP) as a foundational postulate of Swirl-String Theory (SST). SHP states that, for incompressible and inviscid swirl dynamics with conserved topological sector, the bulk state within a bounded domain is uniquely determined by tangential boundary swirl data together with discrete sector labels. We prove this claim at theorem level in the classical Euler regime using Hodge decomposition and vorticity flux constraints, establishing a well-defined reconstruction map from boundary data to bulk fields.We show that General Relativity arises as a geometric specialization of the same constraint-holographic structure when the dynamical variables are replaced by metric data and the Euler constraints by the ADM constraint system. Likewise, AdS/CFT is shown to be a functional, quantum-field-theoretic specialization in which bulk solutions are reconstructed from boundary sources via the on-shell action.Within SST, SHP implies clock holography: local time-dilation fields are boundary-encoded through their dependence on vorticity. The principle further predicts topologically protected bulk information and a controlled, observable breakdown of holography under reconnection, dissipation, or compressibility. These features distinguish SST sharply from purely metric or quantum-field holographic frameworks and render SHP experimentally falsifiable in principle.