Resolution of the Missing Baryon Problem and FRB Dispersion Anomaly: Substrate Soliton Delocalization, Intergalactic Vacuum Shear Impedance, and the Non-Thermal Origin of the Macquart Relation

Cosmological observations of the CMB (Planck) and Big Bang Nucleosynthesis tightly constrain the cosmic baryon density to Ω_b ≈ 4.9%. However, an exhaustive census of all stars, cold gas, and virialized clusters at z < 1 accounts for at most 50% of this budget. Standard astrophysics attributes the missing half to a shock-heated Warm-Hot Intergalactic Medium (WHIM) at T ~ 10^5–10^7 K. While localized Fast Radio Bursts (FRBs) confirmed the Macquart relation (⟨DM_cosmic⟩ ∝ z), establishing that the column density of free electrons exists, deep X-ray surveys (Chandra, XMM-Newton) and UV spectroscopy persistently fail to detect the diffuse bremsstrahlung or O VII/O VIII emission lines mandated by a 10^7 K plasma. Furthermore, the empirical Macquart relation exhibits an anomalous, non-Gaussian dispersion scatter (σ_DM ~ 150–250 pc cm^-3) at z ≤ 0.5 exceeding cosmological simulation predictions. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the missing baryons are cold, non-thermal topological solitons delocalized within the uncompressed intergalactic vacuum substrate. In our ontology, baryons are topological vortex knots whose boundary profile depends on ambient hydrostatic pre-stress (P_0 ≈ 7.48 × 10^24 Pa). In deep voids, the absence of gravitational compression allows the soliton envelope to relax, swelling into a macroscopic acoustic coherence halo (R_halo ~ 0.1–0.4 mm) that renders the matter completely transparent to optical and X-ray emission. Transverse radio wavepackets from FRBs excite the collective shear compliance of these delocalized solitons, producing an intrinsic elastodynamic plasma frequency without requiring thermal ionization. We analytically derive the Macquart slope (⟨DM⟩ ≈ 915 z pc cm^-3) and intrinsic scatter σ_DM ≈ 185 pc cm^-3, proving that the missing baryons exist in mechanical equilibrium with the cosmic ground state, eliminating the high-temperature WHIM paradox under Occam's razor.