Standalone theorem paper
Type-A Selection
The matter-side selection theorem, archived on Zenodo with its own DOI.
Why one protected Standard Model coefficient survives in de Sitter space
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 a closed four-dimensional sphere. The other is the region visible to a single observer, bounded by a horizon.
Quantum fields can leave several distinct mathematical signatures on these geometries. This paper proves that the protected local anomaly signature common to both descriptions is uniquely type A: the Euler coefficient \(a\), a number determined by the field content of the quantum theory. The horizon calculation matters because it contains genuine boundary effects that are absent on the closed sphere; the same coefficient survives after effects tied only to the temporary boundary used in the calculation are removed, so the result is robust across both descriptions.
For the free, unbroken minimal Standard Model field census,
\[a_{\rm SM}=\frac{1991}{720}.\]The implication for the cosmological-constant programme is precise: the first factor in its formula is supplied by a standalone matter-side theorem. The theorem fixes the matter coordinate only; the gravity-side selections and the observed value of \(\Lambda\) are separate questions, carried by the cosmological-constant paper’s own claim records (full scope in EXT-03).
Howard Lee, The Universal Local de Sitter Anomaly Channel Is Uniquely Type A, version 2.0 (2026). doi:10.5281/zenodo.21809544
Technical theorem, scope and boundary-sector test
The local anomaly space is \(\mathcal V_{\rm loc}=\mathrm{span}\{\mathcal E_4,\,C^2,\,j_1,\,j_2,\,\mathcal D\}\), with \(\mathcal E_4\) the Euler density with its boundary completion, \(C^2\) the Weyl-squared density, \(j_1,j_2\) the boundary anomaly invariants and \(\mathcal D\) the trivial (counterterm-removable) sector. The paired evaluation is \[\rho_{\rm dS}=\rho_{S^4}\oplus\rho_{\rm hor},\] into the closed-sphere and spherical-horizon response spaces. The theorem: \[\operatorname{Im}\!\left(\left.\Pi_{\rm dS}^{\rm univ}\circ\rho_{\rm dS}\right|_{\mathcal V_{\rm loc}}\right)=\operatorname{span}\{\mathbf e_A^{\rm dS}\},\] with \(\mathbf e_A^{\rm dS}\) the unit-normalised generator of the Euler/Wess–Zumino quotient line; a QFT \(Q\) has projected local response \(4a(Q)\,\mathbf e_A^{\rm dS}\) and the transmitted coordinate is \(\mathfrak a_{\rm dS}(Q)=a(Q)\).
Sector by sector: \(C^2\) and \(j_1\) vanish by conformal flatness; the trivial sector is removed by finite-counterterm invariance; and the \(j_2\) sector is nonzero but auxiliary. The paper computes \[\int\sqrt h\,\operatorname{Tr}\widehat K^3=-\frac{16\pi^2}{9Hr_0f_0},\qquad -\frac{16\pi^2}{9H^2\delta^2}+O(\delta^0)\ \text{near the horizon},\] so the exclusion of \(j_2\) from the common channel is substantive: that sector has no closed-\(S^4\) representative, depends on the auxiliary worldtube geometry and boundary condition, and is not an independent datum of the no-boundary spherical-horizon logarithm. That is the cross-realisation robustness result.
Scope. The theorem concerns the defined local fixed-point anomaly channel. The full matter determinant, the full static-patch partition function, the edge algebra and the gravitational scale-setting dynamics are separate objects outside its statement.