Dark Matter as Planck Core Remnants in the Quantum Core Framework

This paper provides a systematic and exhaustive investigation of dark matter candidates within the Quantum Core Framework. Three possible candidates naturally arise from the underlying Kitaev ν=6ν=6 topological order: Ising anyons (σσ particles), stable heavy fermions with winding number ν≥4ν≥4, and Planck core remnants from primordial black hole evaporation. Through rigorous quantitative calculation, Ising anyons are shown to be excluded by overwhelming overproduction under every known production mechanism—thermal freeze-out exceeds the observed dark matter abundance by a factor of ∼1023∼1023, and Kibble–Zurek production at the grand unified phase transition exceeds it by ∼1011∼1011. Heavy fermions are excluded by collider constraints and direct detection limits. Planck core remnants emerge as the unique surviving candidate. The precise cosmological conditions required for them to constitute the observed dark matter density ΩDM≈0.26ΩDM≈0.26 are derived: a primordial black hole mass window M≲8.5×1010 kgM≲8.5×1010kg, an abundance at formation β∼0.05−0.1β∼0.05−0.1, and a corresponding enhancement of the primordial power spectrum by ∼8∼8 orders of magnitude on scales k∼1021 Mpc−1k∼1021Mpc−1. This enhancement is naturally generated by the H4H4 term in the framework's modified Friedmann equation during the final stage of inflation. The scenario yields specific, falsifiable predictions for gravitational wave and cosmic microwave background observations.