Resolution of the Lower Mass Gap Anomaly and Compact Object Stability in GW190814: Substrate Bulk Modulus Hardening, Non-Singular Cauchy Equilibrium, and the Natural Extension of the Tolman-Oppenheimer-Volkoff Limit

The maximum gravitational mass of a cold, non-rotating neutron star in General Relativity is bounded by the Tolman-Oppenheimer-Volkoff (TOV) limit (M_TOV^max ≈ 2.1–2.2 M_sun), establishing an empirical "lower mass gap" between the heaviest neutron stars and the lightest astrophysical black holes (M_BH ≳ 5.0 M_sun). However, the gravitational-wave detection of GW190814 by the LIGO-Virgo collaboration revealed a secondary compact object of mass M_2 = 2.59 (+0.08/-0.09) M_sun, residing directly in the forbidden mass gap. Reconciling this object as a neutron star within standard general-relativistic astrophysics requires extreme near-breakup rotation frequencies (f > 1100 Hz) that are strongly excluded by the measured spin prior (χ_2 ≤ 0.07). Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the mass gap anomaly is an artifact of treating space as an empty geometric manifold. In continuum elastodynamics, a neutron star is an ultra-dense cluster of topological nucleon strain solitons embedded directly within an elastic substrate possessing bulk modulus K_v ≈ (5/3) P_0 and pre-stress P_0 ≈ 7.48 × 10^24 Pa. Under extreme compression (ρ_c ≳ 2–3 ρ_nuc), the intervening substrate undergoes non-linear volumetric stiffening, generating an opposing Cauchy elastic counter-stress ∇P_elasto = K_v ∇(∇·u). We derive the modified elastodynamic TOV equation, proving that the vacuum's bulk elasticity provides an additional ~0.48 M_sun of non-divergent hydrostatic support, raising the maximum stable mass to M_max^elasto ≈ 2.63 ± 0.07 M_sun. The 2.59 M_sun object in GW190814 is thus proven to be a stable, non-singular, ultra-heavy neutron star under Occam's razor, eliminating the mass gap paradox without exotic quark cores or singular event horizons.