Transport Papers T09. The Twistor Correspondence

T09 of the Transport Papers. Version 1.0. 30 pages. Epistemic status: Tier A/B. The series' completion of the spacetime algebra is Cl(1,3) → Cl(2,4), forced by division by zero, and the spinor module of the completed algebra carries Penrose's twistor space as a chirality half. This paper proves the correspondence and applies it in both directions. The Chevalley construction realises complexified Cl(2,4) irreducibly on the Fock space of three fermionic ladder pairs, and the ambient vector space is recovered as Λ²T with the completion's null lines as the real slice of the Klein quadric: the null lines that resolve division by zero are lines of projective twistor space. The incidence relation ω = ixπ is proved to be the completion's chart, term by term: the (ω,π) splitting of a twistor is the Witt completion at spinor level, the Poincaré parabolic is the stabiliser of the infinity line, equivalently of the ray of n_∞, the factor i is the derived anti-Hermiticity of the real chart for the twistor form, and local twistor transport is the spinor square root of the tractor connection, up to one declared sign convention. On the palatial side: statistics refutes identifying quantised twistors with the completion's ladder pairs, and a two-storey picture is proved instead: twistors are the states of three ladder pairs, so(2,4) is the shared core of both storeys, and both quantisations incur a half-per-dimension ordering shift, the palatial half of which is the -2 in Penrose's homogeneity -2s-2. Unexpectedly, the ordering insensitivity the googly conjecture needs is a theorem. Sixty-nine exact checks verify every computation. Position in the series: Within the series it relies on T00, T01, T03, T06. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T09.py checks every computational identity in the paper in exact rational arithmetic (69 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_T09.py. Files: T09_twistor_correspondence.pdf; T09_twistor_correspondence.tex; verify_T09.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.