Dark matter pearls: compact objects from topological Fermi pressure, with falsifiable signatures

We show that any dark-matter candidate with a non-vanishing topological hard core — a minimum exclusion distance arising from a non-trivial topology of its underlying field excitation — generically forms gravitationally bound, electromagnetically invisible compact objects whose properties are quantitatively predicted by a Chandrasekhar-like calculation. For dark-matter constituents of mass mχ ~ 1–103 GeV, the resulting dark-matter pearls have masses in the range 1020–1027 kg (asteroid – planet – brown-dwarf scale) and radii in the range 10−3 m to 104 m. For the canonical WIMP scale mχ = 20 GeV, a pearl of M = 3 lunar masses has equilibrium radius ~ 1 mm and mean density ~ 1032 kg/m3. Three formation channels operating at distinct cosmological epochs: Channel A: boundary nucleation around baryonic potential wells (e.g. brown dwarfs accumulate a DM hair over ~109 years); Channel B: primordial relics of an early-universe phase transition (Gaussian-tail overdensities at Tc ≈ 100 MeV, surviving expansion); Channel C: stabilization of any pre-existing overdensity above the Fermi threshold ρF. Five observational signatures testable in the 2025–2030 horizon: Astrometric perturbations of nearby stars (Gaia DR4, Roman, LSST): ~μas on stars within 10 pc; Dark microlensing events without luminous counterpart (OGLE, KMTNet, Subaru/HSC); Anomalous mass-to-luminosity ratios in old brown dwarfs (JWST cycle 5+); Gravitational-wave bursts from neutron-star + pearl mergers (LIGO-A+, Virgo+); Partial resolution of the JWST early-galaxy excess at z > 10 (DM hair contribution). Each signature has a published null hypothesis; non-detection by 2030 excludes the scenario at the specified mass range. The combined non-detection across all five channels would refute the entire class at the percent-of-DM level. The construction is independent of any specific ultraviolet completion: it relies only on the existence of a topological hard core (e.g. Pauli exclusion, soliton incompressibility, Chern–Simons knot reconnection barriers). The analysis was developed within the Quantum Theory of Topological Knots (TQNT-V5) framework, where the hard core arises from CS barriers and the constituent masses are predicted in the 1–300 GeV range, but the results stand on their own. Companion code at github.com/CA9-sas/TQNT. Companion papers: A CP-violating phase from the Jones polynomial (doi:10.5281/zenodo.20552673) and From the AJ conjecture to emergent Schrödinger dynamics (doi:10.5281/zenodo.20552914). The wider framework is documented in the V5 monograph (doi:10.5281/zenodo.19131538).