Observational Evidence for Physical Boundaries in Black Holes: Resolving the Singularity through M87* and GSN 069

The classical vacuum Schwarzschild-Kerr paradigm predicts a black hole shadow diameter of approximately 5.2 Rs. However, high-precision VLBI observations of M87* by the Event Horizon Telescope reveal a persistent 10.5% geometric redundancy (5.5 Rs). This paper demonstrates that this surplus is not an observational error but a deterministic consequence of a physical boundary (Rp) existing slightly outside the mathematical event horizon. Utilizing the (LSG/LIEG) framework, we prove that the presence of a non-singular physical shell induces an outward migration of the effective photon sphere. Our model provides a unified explanation for the geometric expansion of M87* and the unexpected 9-hour phase coherence of quasi-periodic eruptions (QPEs) in GSN 069. These findings signal a paradigm shift from mathematical singularities to finite-volume physical entities, offering a robust resolution to the black hole information paradox.

• The 10.5% Redundancy: First quantitative derivation of the shadow surplus using the Boundary Displacement Scaling: Dobs = Dvac ⋅ √(1 + ξ).

• Theorem: Formal proof that physical boundaries (Rp > Rs) inevitably lead to the outward displacement of the critical impact parameter.

• GSN 069 Coherence: Attribution of QPE stability to the "stiffness" of a physical boundary rather than vacuum accretion dynamics.

• GW Signature: Prediction of a ~0.02s discrete periodicity in gravitational wave residuals as a direct probe of the physical shell's heartbeat.