Black Hole Shadows as Realization Boundaries: A Jacobian Mechanism with Empirical Support from EHT M87*

Black hole images obtained by the Event Horizon Telescope (EHT) exhibit a striking coexistence of a geometrically stable shadow edge and a highly variable emission ring. In standard general-relativistic magnetohydrodynamic interpretations, both features arise within a unified dynamical framework, and their differing behavior is treated as an emergent outcome of complex plasma dynamics. In this work, we propose an alternative but complementary interpretation in which the black hole shadow is identified as a realization boundary: a structural limit beyond which physical realization, and therefore observable signal, fails. Within this framework, the dark interior of the shadow corresponds to the absence of a realizable image, while the surrounding bright ring emerges as a caustic-like enhancement caused by a degeneracy of the observational mapping. At the critical lensing boundary, a large number of distinct light paths collapse onto the same observed angle, naturally producing a stable ring structure. We formalize this mechanism using a realization-based observational mapping and show that shadow and ring formation arise generically from Jacobian degeneracy at the boundary of realizability, independent of any specific spacetime metric or plasma model. A minimal numerical model demonstrates the robustness of this mechanism and reproduces the qualitative phenomenology of black hole images. To test the central prediction of the framework, we perform a direct empirical analysis of publicly released EHT M87* 2018 interferometric visibility data. Using amplitude-based ring and ring-plus-asymmetry fits with robust statistical measures, we find that the geometric ring radius is stable at the ~1–2% level across observing days, frequency bands, and calibration pipelines, while emissive asymmetry varies by tens of percent. These results support a clear separation between geometric structure and emissive dynamics in black hole observations. The realization-boundary interpretation provides a structurally economical, empirically testable perspective that complements standard GR-based models and clarifies the observational meaning of black hole shadows and photon rings.