Black Hole Singularities via the Shadow Principle: Paper XXIII in MEF Series

The Penrose–Hawking singularity theorems establish that four-dimensional Lorentzian general relativity, under physically reasonable energy and causality conditions, contains geodesically incomplete loci. This paper proposes that these loci are precisely what they appear to be — genuine incompleteness of the four-dimensional Q-wall chart — and that the twelve-dimensional manifold M₁₂ = (S¹ₒ₎₋ S³) K₈ of the Master Equation Framework (MEF) supplies the completion that four-dimensional geometry necessarily lacks. A timelike geodesic that terminates at r = 0 in a Schwarzschild interior does not end: it leaves the Q-wall projection and continues in twelve dimensions, passing either into internal K₈ structure or, through the Dimensional Permeability puncture of axiom -P, into the Anti-Quantum-wall sector of the T²/Z₂ orbifold. The singularity is the coordinate locus at which the Q-wall chart ceases to cover a smooth twelve-dimensional geodesic. The Penrose–Hawking theorems are preserved intact as statements about the four-dimensional projection. The mechanism is the gravitational analogue of Paper XVIII's resolution of three-dimensional Navier–Stokes regularity: a topological protection by the Quantum Coherence Dilaton Q = (-) ², which is the gravitational counterpart of the kinematic viscosity. In Paper XVIII the Beale–Kato–Majda criterion is preserved, not refuted; here the Penrose–Hawking theorems play the same role. Black hole formation is identified with a local instance of the spinodal orbifold rupture derived in Paper IX for electroweak baryogenesis. The black hole interior is identified with the Anti-Quantum-wall sector of Paper VIII. Information apparently lost into a black hole is transported to the AQ-wall via the -P conduit, with total information across the Q/AQ pair conserved exactly — the direct analogue of the total baryon number Bₓ₎ₓ₀₋ = 0 across both walls. The four classical black hole types (Schwarzschild, Reissner–Nordström, Kerr, Kerr–Newman) are mapped to the four pillowcase corners of T²/Z₂ via two structurally distinct framings — an algebraic correspondence (indexed by quaternionic sub-algebra and parameter count) and an observational correspondence (indexed by Q-wall visibility through non-gravitational channels) — whose relationship is identified as a Q-wall-projection duality and subjected to a concrete observational test. This parallels the four cosmic-web-environment correspondence of Paper X. The spinodal (barrier-free) formation mechanism provides a natural account of the supermassive black holes observed by JWST at z > 7. Six falsifiable predictions are presented, including the absence of a firewall at the event horizon, a modified Hawking radiation spectrum carrying the arithmetic signature d₎₃₃ (n) from the K₈ partition function, and a specific gravitational-wave signature of spinodal orbifold rupture during gravitational collapse. No modification of the Einstein field equations on M₁₂ is introduced. The paper refutes nothing; it completes.