Transport Papers T14a: One Dimension at a Time: The Odd Extensions of the Oriented Towers

T14a of the Transport Papers, a companion note to T14 (Dark Matter and the Arrow of Time). Version 1.0. 23 pages. Epistemic status: Tier C. Position in the series: Within the series it relies on T1, T2, T3, T4, T9, T10, T12 and T14, and is a companion to T14. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T14a.py checks every computational identity in the note in exact rational arithmetic (86 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_T14a.py. Files: T14a_odd_extensions.pdf; T14a_odd_extensions.tex; verify_T14a.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.