Transport Papers T02. Projective Completes to Conformal: The Minimal Nondegenerate Completion of a Degenerate Clifford Algebra, and Where PGA's Missing Division Goes

T02 of the Transport Papers. Version 1.0. 8 pages. Epistemic status: Tier A. Projective geometric algebra Cl(3,0,1) and conformal geometric algebra Cl(4,1) are the two standard algebras of applied geometric computing, usually presented as independent modelling choices. This note proves that the second is the unique minimal nondegenerate completion of the first. For any real Clifford algebra Cl(p,q,r) of a degenerate form with nondegenerate part of signature (p,q) and radical of dimension r, the minimal nondegenerate Clifford completion exists, has signature exactly (p+r, q+r), and is unique up to an isometry fixing the original space pointwise: existence by adjoining the dual of the radical with the hyperbolic pairing, minimality because each radical direction must pair nontrivially into any completion, the signature forced by Witt splitting of the complement, and uniqueness by the Witt extension theorem. In particular Cl(3,0,1) completes minimally and uniquely to Cl(4,1). The completion converts the radical's nilpotent ideal into the unit ideal. No extension gives a radical element an inverse, since its square stays zero; what CGA supplies is a partner φ for each radical direction ρ with ρφ + φρ = 2, so the division PGA lacks becomes total at the level of ideals, through the pairing and not through inverses. The embedding carries PGA's translators to CGA's translators verbatim. Every result is proved in full; the note situates the theorem in the series' transport-rule taxonomy and delimits what minimality promises. All computational identities are verified in exact rational arithmetic in an accompanying script. Position in the series: Within the series it relies on T1, T4. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T02.py checks every computational identity in the paper in exact rational arithmetic (20 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_T02.py. Files: T02_projective_to_conformal.pdf; T02_projective_to_conformal.tex; verify_T02.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.