Matter Maps to Geometry in Gravitational Collapse

We establish an exact bidirectional map between the effective homogeneous interior density of a collapsing star and the exterior metric function in generalized Oppenheimer–Snyder collapse. The Darmois–Israel junction conditions reduce this relation to a purely algebraic form, providing a direct way to reconstruct candidate static geometries and their surface dynamics without solving the corresponding differential field equations separately. Correction powers diagnose models: integer exponents signal ultraviolet completions, while fractional powers identify phenomenological ones. Our framework not only simplifies the construction of regular black holes but also provides a universal benchmark for testing singularity resolution and cosmic censorship in quantum gravity phenomenology.