Space as a Substance: A Curvature-Coupled Superfluid

The glassy vacuum of S23 accounts for the propagation of light and gravitational waves, the hot Big Bang, the dark matter and a falsifiable siren offset, but gives the dark energy's history no carrier: the glass makes light modes only through a symmetry breaking of order 10⁻¹⁰⁴, far too weak for a note near H. This paper adds the carrier, a scalar mode χ of the glass that is massless in flat space and takes its mass from the curvature of the emergent metric, m² = ξ_R R. A Goldstone mode cannot couple this way, and a minimally coupled mode fits the distances no better than ΛCDM. The glass's known components are excluded one by one, and the mode is taken to be a remnant of the melt that never paired. Carrying the melt's conformal weight, it couples at ξ_R = 1/6 and never rings: aχ moves uniformly in conformal time, and the vacuum follows Q ∝ (τ − τ_b)/a, with one parameter, the conformal time τ_b at which the vacuum crosses zero. The mode is the vacuum's clock and not its fuel: its amplitude today lies below about 2×10⁻²³ of the Planck mass, and the vacuum's energy belongs to the glass, following the mode through a linear clock relation. No action with a propagating clock lets so slight a mode set the vacuum without being pushed back. A constrained clock, whose multiplier is the dark-matter density, sends that push to the dark matter: the vacuum then trades energy with the dark matter both ways along the dark matter's own four-velocity, the geodesic interacting vacuum, and the energy the falling vacuum releases returns to the dark matter with no separate carrier. In that construction the vacuum is a potential of the dark matter's proper time: the mode fixes the potential's one-parameter form and exerts no force, and that the potential copies the mode is assumed. Against DESI DR2, the Planck acoustic scale and the DES-Y5, Pantheon+ and Union3 supernovae the conformal breath gives Δχ² = −17.7, −11.9 and −13.6 relative to ΛCDM, and against the full Planck spectra and lensing with DESI DR2 and DES-Y5, with the perturbations solved, −17.1. The vacuum is born between z ≈ 7 and 8, where the series' Single Breath paper places it. The dark matter lends a few per cent of its energy while the vacuum rises and ends about a quarter denser than the microwave background implies, with S₈ ≈ 0.76; an estimate of cluster counts puts them within ten per cent of the ΛCDM fit to the same data. In the Single Breath model the mode reproduces the Euler rotation for z ≲ 2 at a rate that slows as the expansion accelerates, and removes the crunch at 88 Gyr; as the entropy clock's timekeeper it improves the Pantheon+ fit from −4.5 to −11.9 but loses that model's zero-parameter status, its released component, its excess growth and its positive neutrino mass. The fate is set by one number. Below ξ_R,c = 3 − 2√2 ≈ 0.172 the vacuum fades forever, returning its energy to the dark matter, with w → −2/3 at the conformal value; above it the vacuum turns negative and the Universe turns around and collapses, for couplings up to 0.28 no sooner than about 130 billion years from the start. The conformal value lies 2.9% below the threshold, so the fate turns on how far the setting broke the melt's conformal symmetry, a quantity the coming dark-energy surveys can bound. If the setting left the mode at rest, the breaking itself sets the mode in motion through the trace of the hot early Universe; the birth then requires a breaking of 10⁻¹⁸ or less, and the Universe fades forever.