The Boundary of the Azimuthal Family: Which Quadrupole-Octopole Profiles About the CMB Axis the Planck Sky Still Permits, and the Falsifier the Boundary Selects
Year: 2026
Type: preprint
Abstract: The registered azimuthal-average test of the founding profile about the cosmic microwave background axis (l, b) = (-100, 60) degrees has returned its verdict: the fitted amplitude of the fixed profile f = P2 + 2.1376 P3 is consistent with zero on all four Planck PR3 component-separated maps (DOI 10.5281/zenodo.24115737), and falsifier F-CS1 (DOI 10.5281/zenodo.24053823) had already failed the same branch on its own pre-registered clauses. A verdict on one profile leaves open the question the verdict itself cannot answer: what of the rest of the family? This paper computes the boundary. Freeing both amplitudes of the same two multipoles, dT = -A2 P2(cos) - A3 P3(cos), and re-running the verdict run's machinery unchanged - validated against its deposited results exactly - produces no detection at any ratio: the best two-amplitude fits are ordinary draws of the rotated-axis null (on the primary map, 46% of null axes improve the fit by more than the true axis does). The set of profiles not excluded at any single annulus at 95% is a fifteen-vertex region of the (A2, A3) plane with the origin in its interior: no ratio in the family is excluded, and the boundary is an amplitude bound, nearly blind to the ratio - the permitted interval along the registered ray, A2 in [-14.7, +14.9] microkelvin, is nearly identical to that along the ray of opposite octopole sign. The bound nevertheless bites where the registration lived: the registered profile at its no-cancellation cap (B2 = 21.69 microkelvin) lies outside the region, breaching eight annulus bands, and the largest amplitude the sky permits along the registered ray is 14.93 microkelvin. At the Cold Spot's latitude the largest point value any permitted profile can take is 17.7 microkelvin, twelve per cent of the spot's approximately -150 microkelvin central decrement, so no profile of this family, at any permitted amplitude or ratio, can be the spot's cause; a surviving account of the Cold Spot must be predominantly localised on the sky or carried by its line of sight. That consequence selects the next test. F-CS2 - the series' own ungraded falsifier, on the lensing and density fields of the spot's line of sight at standard amplitude - is registered in this paper, with frozen thresholds, and is deposited with it (NEXT-TEST.md).
Author: Aldred, William Alexander
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225811434