Resolution of the Fermi-LAT Galactic Center GeV Excess: Substrate Shear-Wave Radiative Damping, Convergent Gradient Stress Dissipation, and the Elimination of WIMP Annihilation

The Galactic Center Excess (GCE) observed by the Fermi Large Area Telescope (Fermi-LAT) is a prominent, statistically robust (>10σ) diffuse gamma-ray emission component peaking at 1–3 GeV and extending spherically out to ~2–3 kpc from the Galactic Center. Long interpreted as the prime indirect signature of Weakly Interacting Massive Particle (WIMP) dark matter annihilation (m_χ ≈ 30–50 GeV into b-bbar pairs), this hypothesis now faces fatal empirical exclusions from direct detection searches (LZ, XENONnT) and dwarf spheroidal galaxy observations. Furthermore, astrophysical explanations invoking thousands of unresolved millisecond pulsars fail radio survey and photon-clustering tests. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the GCE is an intrinsic elastodynamic emission produced by cosmic-ray solitons traversing the convergent hydrostatic stress gradient of the Galactic core. In our ontology, relativistic protons are topological vortex knots possessing localized volumetric dilation and core strain. As cosmic-ray solitons propagate inward toward Sgr A*, they traverse a steep background substrate compression gradient (∇P_sub ∝ r^-2). This mechanical strain inhomogeneity forces the moving soliton envelope to shed excess transverse acoustic shear modes via an elastodynamic transition-radiation mechanism. We derive the analytical spectral emission rate, showing that the peak energy E_peak ≈ 2.1 GeV, the spherical r^-2 geometric profile, and the total integrated luminosity L_GCE ≈ 2.0 × 10^37 erg/s follow directly from the constitutive elastic parameters of the vacuum substrate (P_0 ≈ 7.48 × 10^24 Pa, G_v = P_0, ℓ_0 ≈ 8.10 × 10^-35 m) under Occam's razor, completely eliminating the WIMP hypothesis without exotic dark sectors.