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We study supercooled first-order phase transitions above the QCD scale in a wide class of conformal Majoron-like U(1)′ models that explain the totality of active neutrino oscillation data and produce a detectable stochastic gravitational wave background (SGWB) at LIGO, LISA and ET. We place constraints on the U(1)′ breaking scale and gauge coupling using current LIGO-Virgo-Kagra data. We find that
