In-medium hyperon potentials and the quarkyonic hyperon onset: charged 's in beta-equilibrium and the neutrino connection

Quarkyonic matter resolves the neutron-star hyperon puzzle statistically: neutrons fill low-momentum d-quark phase space, shifting the S=-1 threshold from =M Y to 2M Y-M N and suppressing residual softening by 1/ cubed in the Fujimoto--Kojo--McLerran (FKM) mechanism. We dress FKM's IdylliQ model with in-medium potentials, constrained by hypernuclear data and neutrino-induced hyperon FSI, and find: (i) the dressed onset, onset=(2M Y - M N)+2U Y-, carries U Y at weight 2, with dn onset/dU Y 0.3, per 10, twice the leverage. (ii) A self-consistent neutron potential enters at weight-2, so protection needs (n onset) +96. (iii) With leptons in beta equilibrium, the- (dds) onset becomes 258 + -, never reached inside a 2, core:- switches from first hyperon to forbidden and the ordering inverts. (iv) The continuation gives TOV softening below 0.05, in the FKM ansatz family and below 0.025, for the realistic interacting star, 4 -- 8 below hadronic models. In the family this is a ceiling; generally it is a floor, since hyperons above are omitted. (v) In an interacting low-density sector calibrated to =2.12,, core strangeness is controlled by (,c): at =-28, the maximum-mass star is hyperon-free once the supra-saturation YNN turn-over exceeds a few-MeV threshold c*. Projected SBND+DUNE FSI precision pins but leaves c -- to which neutrino data are blind -- decisive: with the heavy-ion prior, P(hyperon-free core)=0.90, versus 0.89 from priors alone, prior-dominated rather than measured. The sharpest observable is differential: d /dU Y is an order of magnitude smaller than in mean-field models, discriminating the two resolutions.