Critical Demixing as a False Gravity: the Relative Sector of a Two-Component Logarithmic Superfluid Vacuum

Two earlier no-go theorems in this program showed a single-component logarithmic superfluid vacuum sources electromagnetism but not gravity, and that no linearly coupled scalar companion repairs this. Here I take the next minimal step inward: an internal doublet. At the SU(2)-symmetric point, a U(2) two-component condensate contains exactly the object the first theorem demanded — a gapless, divergence-capable relative-density channel with unscreened 1/r response. This channel mediates a genuine, mechanically generated, universal long-range attraction between like-polarized matter — the first in this class of theories, exactly solvable and confirmed by 3D GPU minimization (11/11 signs, the 1/d law to 0.6%). But it is not gravity: it is the critical precursor of phase separation, its charge is a number-and-size quantity rather than energy, and MICROSCOPE excludes it at gravitational strength by ~14 orders of magnitude. What survives is a falsifiable sub-gravitational fifth-force window.