Transport Papers T07. Hawking Radiation from the Ledger

T07 of the Transport Papers. Version 1.0. 21 pages. Epistemic status: Tier A/B (itemised). This paper is a quantum companion to T05: it supplies the state, the continuum, and the four-dimensional lift between T05's single-mode core and the physical Hawking spectrum, each claim at its tier. Tier A: among the quasi-free states of the boundary modes' CAR algebra exactly one is KMS for the geometry's boost at the Hawking temperature, the I-state; existence is window-exact, carried to the full algebra by imported inductive-limit results; the KMS identity itself forces the pairing to vanish and the symbol to be Fermi-Dirac, all modes at once, extending T5's single-mode occupancy theorem; uniqueness beyond the class is the imported ideal-Fermi-gas theorem; and the statements carry to the continuum on a dense core. Tier B, the joints itemised: the helicity lift and greybody inheritance, whose only joint proved in this paper, the homogeneity -2s-2, is promoted to a stated result from inside the proof of the twistor paper's dictionary theorem; the exterior coincides with general relativity on the invertible region at Λ = 0, so the flux prediction equals Hawking's, filtering included. Tier A again: the finite mode space's deviations from the free-boson current algebra are edge-supported by an exact commutator identity; and, on the linear s-wave ladder of T5's premise (Q), an exact Planck factor with proven exponential window tails. The ℓ_P²/A scale of generic corrections is a dimensional reading at modelling level; the per-observable scaling is open. Open and named: axiomatic selection of the dynamics, the lift beyond assembly, the Kerr continuum. Exact-arithmetic checks verify the identities. Position in the series: Within the series it relies on T00, T01, T03, T05, T06, T09. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T07.py checks every computational identity in the paper in exact rational arithmetic (25 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_T07.py. Files: T07_hawking_radiation.pdf; T07_hawking_radiation.tex; verify_T07.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.