Four-Dimensional Completion Dependence of a Minkowski-Core Geometry

Version 4.1 is a corrected revision of version 4.0. It corrects the Weyl-invariant identity in Section 11 and updates the associated geometric interpretation, radius figure, symbolic reproduction script, claims table, discussion, and conclusion. The branch-turning/mass-noninvertibility result, the exact NLED and mimetic embeddings, the mimetic odd-parity degeneracy, and the central four-dimensional completion-dependence conclusion are unchanged.

The corrected scaling-class identity is C^2 = 3 ell^-4 [2 x Phi'(x) + 3 x^2 Phi''(x)]^2. Consequently, branch turning and conformal flatness are generically distinct. For the target Minkowski-core geometry, the branch-turning surface remains x^(10/3)=3/2, while two distinct Weyl-flat shells occur at x^(10/3)=(21 +/- 5 sqrt(17))/4. The mimetic branch transition and loss of odd-parity hyperbolicity remain tied to the branch-turning surface rather than to Weyl flatness.

The paper compares inequivalent four-dimensional covariant completions of the same exact spherical geometry. A restricted magnetic Einstein-NLED embedding reproduces the target exactly but develops a finite-radius constitutive degeneracy and, on the sampled branch where the inner horizon is reached first, a nonzero regularity mismatch. A parity-even P^2 completion changes the slow-rotation sector without changing the static background, demonstrating that the stationary obstruction is not fixed by the spherical geometry alone. An exact extended-mimetic embedding admits regular stationary frame dragging but its local odd-parity principal cone degenerates at the branch-turning surface and becomes non-hyperbolic on the core side. These pathologies are treated as physical viability problems of the respective completions as written, not as coordinate artifacts.

The chronology-protection relevance is limited but concrete: regularizing the spherical core does not by itself determine whether a four-dimensional rotating extension is regular, singular, or hyperbolic. No proof or violation of Hawking's chronology protection conjecture, UV-complete theory, finite-spin regular rotating black hole, or nonlinear stability theorem is claimed. The reproduction package includes symbolic checks, numerical scans, independent DOP853/RK45 cross-checks, figures, tables, and complete source code.