Transport Papers T06. The Geometry of the Black-Hole Interior

T06 of the Transport Papers. Version 1.0. 31 pages. Epistemic status: Tier B. This paper is the mathematical-relativity companion to T5: the geometry of the ascent Cl(1,3) → Cl(2,4) at the black-hole singularity, in three parts. Part one, where division fails: the Schwarzschild gauge field is a ray in a one-parameter unipotent group, and the curvature factorises exactly, at every radius, into a divergent conformal scale times a fixed shape operator S satisfying S² + S = 2. Part two, the covariant form: the vacuum field equations are exactly equivalent to the covariant constancy of the null scale section of the rank-six tractor bundle, a parallel ideal point; for Λ ≠ 0 the point leaves the cone with squared norm Λ/3, and its stabiliser rotates from parabolic Poincaré to reductive (anti-)de Sitter. Part three, the approach and the tests: under a blow-up weighted by the Kasner exponents (-1/3, 2/3, 2/3) the tractor formulation extends to the singular locus for the Einstein velocity-dominated class, with values-level boundary holonomy exactly so(1,3), for Λ = 0 the Levi factor of the frozen point's parabolic stabiliser, and transport-level convergence along tangential curves of fixed Hubble-normalised length; and Kerr passes three tests: unipotency on a null shear, a complex factorisation locating the ring and leaving the disc regular, and the conformal scale as the inverse cube of the Walker-Penrose Killing spinor. At the perturbed Cauchy horizon point-level structure extends continuously while connection-level structure generically fails, proved in spherical symmetry and expected for Kerr; the conformal-over-metric separation is the sharpest open problem. Eighty-two checks verify the computational identities. Position in the series: Within the series it relies on T00, T01, T04, T05. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T06.py checks every computational identity in the paper in exact rational arithmetic (82 checks, all passing at deposit). It imports GA.py, the series' shared exact-arithmetic library, deposited alongside so the record is self-contained. Run with a bare Python 3: python verify_T06.py. One control check uses numpy/scipy and is reported as skipped when they are absent; the 81 exact checks are unaffected. Files: T06_blackhole_interior.pdf; T06_blackhole_interior.tex; verify_T06.py; GA.py; LICENSE-CODE.txt. Licence: the paper (PDF and LaTeX source) is CC BY 4.0. The code files in this record are additionally released under the MIT licence; see LICENSE-CODE.txt. Authorship and disclosure. The founding idea of the series is the author's: that division by zero in a Clifford algebra should be read not as a prohibition but as a transport into a higher-dimensional algebra, and that the transported division need not be accompanied by an inverse operation. The direction of investigation and the critical review of the results are likewise the author's. The mathematical development and the drafting of the text were carried out in extended collaboration with Claude Fable 5 (Anthropic), an AI system.