Vacuum Rigidity as a Negentropic Force

The vacuum of established physics is twice ordered, and both orders have a measured stiffness. This paper states the premise that space is a rigid frame, an ordered medium whose stiffness is a restoring force of energetic rather than entropic origin, makes the premise precise, and tests it against the record. A rigidity is defined as the stiffness that follows from a spontaneously broken continuous symmetry, and a negentropic force as a restoring force that originates in the energy of an ordered configuration, is carried by a component of zero entropy, and vanishes with the order at the transition. So defined, and with space meaning the vacuum state of the Standard Model, the premise is established physics with measured numbers at every clause: the energetic fraction of a restoring force is 0.12 ± 0.02 for rubber and 1 for the superfluid component of helium; the vanishing of rigidity at the transition is computed in finite-temperature field theory and confirmed on the lattice for both vacua, and in the laboratory its universal law is computed from first principles and the measured rigidity exponent agrees with it to four decimals; the strong vacuum has a stiffness of 92.1 MeV whose Goldstone modes obey the soft-pion predictions to one or two percent and whose ordered phase supplies more than 90% of the mass of ordinary matter; and the electroweak vacuum has a stiffness of 246.22 GeV whose amplitude mode has been produced and weighed, and whose influence on low-energy physics is screened by theorem. The frame introduces no preferred frame: a scalar condensate has no velocity, and every null result that a medium must reproduce, from the anisotropy of the speed of light at a part in $10^{18}$ to the equality of the speeds of light and gravity at a part in $10^{15}$, is reproduced for a stated reason. The premise goes beyond the record in one place, the dark sector, where the paper makes a single postulate: the cold dark matter is the Goldstone condensate of a third, ungauged rigidity. Its coldness, darkness, stability, quantized circulation and quantum pressure then follow, and so does a result on the standing of the amplitude register: it is locked to the dark-matter mass with a coupling of magnitude $10^{3}$ or larger, four orders of magnitude above the measured bound on any rolling dark-sector coupling, so it cannot thaw, and any thawing dark-energy field is a separate and secondary scalar. The theory differs from cold dark matter in one named observable, a deficit of spin among black holes of a few hundred to fifty thousand solar masses, and a first intermediate-mass spin measurement has already narrowed the allowed mass window to roughly $10^{-15}$ to $7\times10^{-14}$ eV. The theory owes one number, the explicit-breaking susceptibility of the dark condensate; if the breaking is gravitational and protected by a discrete symmetry, that number is an integer, and the allowed masses form a discrete set. Keywords: vacuum rigidity; generalized rigidity; spontaneous symmetry breaking; Goldstone bosons; superfluidity; negentropy; chiral condensate; electroweak vacuum; ultralight dark matter; black-hole superradiance