Transport Papers T05. Division by Zero at the Gravitational Singularity

T05 of the Transport Papers. Version 1.0. 77 pages. Epistemic status: Tier B (with named premises). In gauge theory gravity the Schwarzschild solution is carried by an invertibility-demanding linear map, and the singularity is where the theory divides by zero. The series' transport algorithm is run on that division. The gauge field is a unipotent ray at every radius, so the divergence lies in the connection bivector; at the centre the light cones fold onto a null direction, a type-N obstruction whose forced repair is the Witt completion Cl(1,3) → Cl(2,4). No classical value repairs the dying directions, by two no-go theorems; the completion installs canonical anticommutation relations, one fermionic mode per boundary point, and the curvature factorises exactly into -M/r³ times a fixed shape operator, selecting the boost plane. Descent to the metric level is, mode by mode, the fermion parity average, so every physical state has thermal single-mode marginals, and one named premise, KMS at the Euclidean section's period, sets their temperature at Hawking's and leaves the joint state free. Bosonisation at s-wave scope gives the Planck sector from a named quasi-freeness premise. The descent's multi-mode cost is a relative entropy carried by inter-quanta correlations: on the pointwise-descent reading, information is lost in Cl(1,3) and preserved in Cl(2,4), a category error between levels. In a rate model with boundary-mode locality the radiation entropy is exactly the window's thermal content, giving the Page envelope without typicality. Inside, the modular flow is the t-line holonomy of the collar, at Hubble-normalised rate 1/3; the premised locality's pairing part is the tangent of the vacuum orbit. Position in the series: Within the series it relies on T01, T03, T04, T06. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T05.py checks every computational identity in the paper in exact rational arithmetic (233 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_T05.py. Files: T05_gravitational_singularity.pdf; T05_gravitational_singularity.tex; verify_T05.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.