Transport Papers T04. Clifford Sheaves over Degenerate Metrics

T04 of the Transport Papers. Version 1.0. 50 pages. Epistemic status: Tier A. Let M be a smooth manifold with a cometric G on T^*M, degenerating tamely to corank one on a hypersurface Σ. The Clifford sheaf of the pair meets an apparent contradiction: locally free fibre dimension cannot jump, yet the series' transport principle demands Cl(p,q) off Σ and Cl(p+1,q+1) over it. The jump goes into structure, twice over. The degeneration sheaf has constant rank 2^n; over Σ its fibres acquire a canonical square-zero ideal, generated by the radical line, that any nondegenerate completion converts into the unit ideal. The ambient sheaf has constant rank 2^(n+2) and signature (p+1,q+1) on the closed physical side; what fails on Σ is a splitting, the adjoined ladder pair supported exactly there. A conservation law follows: no completion standard off the wall is nondegenerate on both sides; the degeneracy reappears on a displaced shadow wall, tame for good couplings, and the construction iterates. The normal cone carries an exceptional algebra, and the metric's residue makes the dying line a canonical square root of the conormal bundle. The completion is canonically independent of the collar transversal, yet the wall admits no equivariant value and no canonical ladder partner: the no-repair theorem's analogue at the wall itself. Blown up and Kasner-weighted, the Schwarzschild singularity becomes a boundary-tame wall receiving the same completion, no shadow wall, the weights forced to the Kasner exponents; the weighted module is the unique rain-bounded boundary-tame extension, and the theory extends, stably, to position-dependent exponents. Complete proofs; imports stated as facts with provenance. Position in the series: Within the series it relies on T00, T01. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T04.py checks every computational identity in the paper in exact rational arithmetic (296 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_T04.py. Files: T04_clifford_sheaves.pdf; T04_clifford_sheaves.tex; verify_T04.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.