The Universal Local de Sitter Anomaly Channel Is Uniquely Type A
Author-released preprint · Version 2.0 · 5 August 2026 · doi:10.5281/zenodo.21809544
De Sitter space, the idealised geometry of an empty universe with a positive cosmological constant, has two complementary round descriptions. One is the closed four-dimensional sphere used in the compact calculation. The other is the static patch visible to a single observer, bounded by a horizon.
Quantum fields can leave several distinct mathematical signatures on these geometries. This standalone paper proves that the protected local logarithmic anomaly response common to both descriptions has a one-dimensional image: the type-A Euler coefficient a. The horizon calculation contains genuine boundary effects absent on the closed sphere; after effects tied only to the temporary boundary are separated, the same microscopic coefficient survives.
a_SM = 1991/720 (leading free, unbroken minimal Standard Model census)
For the cosmological-constant paper, the significance is that a distinct de Sitter realisation independently selects the same type-A Euler coordinate that enters the compact construction. The cosmological-constant paper remains self-contained: it contains its own Euler extraction theorem, and its numerical chain does not depend on this standalone publication. The QCD premise, compact gravitational selections, cosmological source map and observed value of Λ remain separate questions.
Status - Standalone theorem publication - independent support, not a dependency of the cosmological-constant paper.
Abstract
We prove that the universal local logarithmic anomaly response of a four-dimensional quantum field theory on exact round de Sitter has a one-dimensional QFT image. Within the standard parity-even Weyl-anomaly sector, the only surviving microscopic coordinate is the type-A anomaly coefficient a. In four dimensions the local anomaly can also contain the type-B Weyl term, boundary charges and scheme-dependent total derivatives. We ask which of these data can be represented both on the closed round S⁴ saddle and in the n = 1 round-horizon response, while remaining invariant under finite counterterms and independent of the auxiliary regulating boundary. The answer is unique: the image is generated by the Euler/Wess–Zumino class. Bulk type-B data, boundary anomaly charges, particle masses and couplings do not enter as independent coordinates of this projected sector.
The static-patch representative provides a non-trivial boundary-sector test. The non-Euler invariant j2 is present and nonzero on the auxiliary worldtube. Its integrated geometrical coefficient depends singularly on the tube geometry as the horizon is approached, while its anomaly coefficient can depend on the imposed boundary condition. It is therefore genuine data of the specified smooth-boundary problem, but has no independent image in the original no-boundary round-horizon logarithm. The horizon leg is a stress test of the compact selection, not an independent derivation of the standard spherical 4a coefficient.
At a conformal fixed point the classification applies directly; away from one, beta-function and operator-mixing responses must first be separated by the local-RG projection. At one loop the result follows from the heat-kernel and local-counterterm classification; beyond one loop its structural content follows from Weyl cohomology and Wess–Zumino consistency. For the unbroken minimal Standard Model free-field census, aSM = 1991/720 ≃ 2.77.
Any observable whose microscopic dependence genuinely factors solely through this channel can depend on the QFT only through a. The theorem identifies the protected matter coordinate available to de Sitter anomaly-channel constructions; it does not determine the gravity-side scale-setting rule or the value of Λ.
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