Dark Matter via Quantum σ-Flip: Freeze-In at the QCD Transition and the Role of Gravitational Collapse

ABSTRACT We propose a mechanism for dark matter (DM) production via stellar gravitational collapse based on a gauge quantum number σ = ±1 associated with a local U (1) _σ symmetry, mediated by a dark photon Z' of mass m_φ ~ 10 MeV. The symmetry is broken spontaneously at supernuclear densities (ρ ≥ ρₙuclear ≈ 2. 3 × 10¹7 kg/m³, Tc ~ 10¹2 K), triggering a σ-flip transition that converts visible-sector particles (σ = +1) into dark-sector fermions (σ = −1) of mass m_χ ~ MeV. This mass scale is cold enough to form structure consistent with observations, while the self-interaction cross-section σ/m ≈ 2. 8 cm²/g (in the heavy-mediator Born limit) naturally resolves the core-cusp problem through Core+NFW halo profiles. The energy budget per supernova (ESN ~ 3 × 10⁴6 J) supports MDM ~ 1. 5 × 10^−4 M_☉ per event for efficiency ε_σ ~ 10^−3, consistent with conservation laws. BBN compatibility is guaranteed since Tc ~ 10¹2 K >> TBBN ~ 10⁹ K. Black holes are further proposed as informational transducers: at supercritical informational densities, photon-neutrino condensates undergo σ-flip, generating a linear MBH–MDM correlation testable by JWST and Euclid. Seven falsifiable predictions are derived for DUNE, Rubin LSST, Belle II, and gravitational wave observatories. Keywords: dark matter, stellar collapse, sigma-flip, self-interacting dark matter, U (1) gauge symmetry, Cosmic Information Theory, non-thermal production, core-cusp problem