Transport Papers T10. Dark Energy and the Action of Gravity

T10 of the Transport Papers. Version 1.0. 36 pages. Epistemic status: Tier B (with declared levels). Gravity's MacDowell-Mansouri action needs a fixed-norm internal vector whose covariant derivative is the tetrad, and the framework supplies it from the frozen point, the parallel scale tractor of the geometry paper whose squared norm is the cosmological constant. The frozen point is parallel, so it is not the Stelle-West vector; it makes that vector: the canonical tractor projected orthogonally to it has squared norm -3/Λ and covariant derivative exactly the soldering form; the action is the curvature squared of the ambient connection contracted with the two vectors, with the frozen point's inverse norm as prefactor. Consequences, at declared levels: the functional is polynomial and defined across the singular locus; its curvature-squared presentation exists precisely when Λ ≠ 0, the Λ → 0 limit being the Einstein-Cartan functional after a topological subtraction; at a wall of the soldering form the equations never propagate a symmetric form on the wall, which on the flat model they constrain by exactly one scalar relation, while at the Schwarzschild wall the datum's connection has a simple pole whose residues, fixed by the field equations, are the weights the completion is built from; dark energy cannot evolve on the vacuum region (w = -1), registered against DESI and conditional off it; the forces are conformal-level while gravity alone is pre-metric; and in the neutral thermal sector of the s-wave current algebra nothing couples to the metric-forming correlations at first order except the stress-energy sector, with the (I,V)-sector pure gauge. Exact-arithmetic checks accompany it. Position in the series: Within the series it relies on T00, T01, T04, T05, T06, T07, T08, T12. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T10.py checks every computational identity in the paper in exact rational arithmetic (90 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_T10.py. Files: T10_dark_energy.pdf; T10_dark_energy.tex; verify_T10.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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-12
DOI
https://doi.org/10.5281/zenodo.22722496
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Transport Papers T10. Dark Energy and the Action of Gravity

Leon Butler
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Transport Papers T10. Dark Energy and the Action of Gravity

Leon Butler
preprint en

Abstract

T10 of the Transport Papers. Version 1.0. 36 pages. Epistemic status: Tier B (with declared levels). Gravity's MacDowell-Mansouri action needs a fixed-norm internal vector whose covariant derivative is the tetrad, and the framework supplies it from the frozen point, the parallel scale tractor of the geometry paper whose squared norm is the cosmological constant. The frozen point is parallel, so it is not the Stelle-West vector; it makes that vector: the canonical tractor projected orthogonally to it has squared norm -3/Λ and covariant derivative exactly the soldering form; the action is the curvature squared of the ambient connection contracted with the two vectors, with the frozen point's inverse norm as prefactor. Consequences, at declared levels: the functional is polynomial and defined across the singular locus; its curvature-squared presentation exists precisely when Λ ≠ 0, the Λ → 0 limit being the Einstein-Cartan functional after a topological subtraction; at a wall of the soldering form the equations never propagate a symmetric form on the wall, which on the flat model they constrain by exactly one scalar relation, while at the Schwarzschild wall the datum's connection has a simple pole whose residues, fixed by the field equations, are the weights the completion is built from; dark energy cannot evolve on the vacuum region (w = -1), registered against DESI and conditional off it; the forces are conformal-level while gravity alone is pre-metric; and in the neutral thermal sector of the s-wave current algebra nothing couples to the metric-forming correlations at first order except the stress-energy sector, with the (I,V)-sector pure gauge. Exact-arithmetic checks accompany it. Position in the series: Within the series it relies on T00, T01, T04, T05, T06, T07, T08, T12. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T10.py checks every computational identity in the paper in exact rational arithmetic (90 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_T10.py. Files: T10_dark_energy.pdf; T10_dark_energy.tex; verify_T10.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.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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