Why a rank cross-correlation with a spherical template cannot test dark matter: a corrected Gaia x Fermi gamma-ray halo-residual analysis

THIS VERSION WITHDRAWS AND REPLACES ALL FIVE EARLIER VERSIONS OF THIS RECORD (v1.0 through v5.0). Earlier versions reported a positive spatial cross-correlation between a Gaia DR3 proper-motion-selected stellar map and the Fermi gamma-ray halo residual of Totani (2025) and presented it as support for a dark-matter interpretation. Version 5.0 reported three correlated messenger pairs, a frozen-pipeline significance of 6.1 sigma, a Bayes factor of 2e34 for the spectral shape, and a non-negative-least-squares unmixing giving 100 percent dark matter. All of it is withdrawn. Two defects account for them. First, the spatial support was conditioned on the target: the region of interest was described by a coordinate rule containing 7596 HEALPix pixels, but the mask actually used contained 5808, and all 1782 pixels at which the target flux is negative had been excluded. The retained support contained no negative-target pixels. Pixel inclusion was therefore conditioned on the sign of the map being correlated, so the quoted significances are not calibrated inference. Second, on the corrected coordinate-defined support the latitude-controlled partial rank correlation is +0.182, and controlling additionally for the angular distance from the Galactic Centre reduces it to +0.016, consistent with zero under a null model whose type-I error is measured (p = 0.44). The same collapse occurs for every independent stellar tracer tested. What replaces the withdrawn claim is a structural result that holds independently of these data. For a spherically symmetric halo the line-of-sight annihilation morphology depends on direction only through the angle from the Galactic Centre and decreases monotonically with it; rank statistics are invariant under monotone transformation; a computed NFW-squared J-factor map has Spearman correlation -1.000000 with that angle. A rank cross-correlation between any tracer and a spherically symmetric gamma-ray template is therefore mathematically a test of central concentration, and cannot in principle isolate dark-matter-specific morphology. The reanalysis further establishes that the energy axis, which geometry cannot fake, returns nothing: across all nine per-energy maps no bin is significant after controlling the Galactocentric angle, and the 21 GeV value is the closest to zero of the nine. It also shows that a spherical template accounts for only about a tenth of the target map's variance, that the remainder matches none of fifteen templates tested, and that a control built from the target can inflate a correlation as readily as null it — from a baseline of +0.182, the target's own residual as a control gives +0.534. This record contains the corrected paper, the analysis code, the input maps, a clean-room reproduction harness, and a full response to the external audits that found the defects. No detection is claimed. No annihilation cross-section limits are placed. Nothing here bears on whether the Totani excess is real; it has since been independently reproduced at pixel level (arXiv:2607.08552).