Phononic Analogs in Dissipative Information Topology: Emergent Inertia and Negative Mass in the Vacuum Lattice

This paper presents a paradigm shift in addressing the missing mass problem in astrophysics by mapping the established quasiparticle kinematics of condensed matter physics onto the cosmological vacuum. Traditional cosmological models rely on the ad hoc inclusion of Cold Dark Matter (CDM) to explain flat galactic rotation curves, fundamentally treating mass as an intrinsic, isolated property. Utilizing the Dissipative Information Topology (DIT) and the DIT-Framework, this paper models spacetime not as a passive Euclidean manifold, but as an active, dimensionally frustrated topological lattice. Baryonic matter is consequently recontextualized as resonant topological defects within this matrix, mathematically represented by the localized defect tensor. As these defects propagate, their continuous geometric dissipation induces a global topological tension across the network. It demonstrates that at the outer perimeters of galactic structures, this cumulative macroscopic lattice-strain functionally mirrors the negative effective mass regime of acoustic phonons approaching a Brillouin zone boundary. By establishing that inertia and gravitational cohesion are emergent mechanical responses of the underlying vacuum lattice rather than intrinsic particle traits, this framework provides a rigorous mechanical derivation for the Baryonic Tully-Fisher Relation (BTFR) without necessitating novel, unobserved particles, thereby unifying macroscopic cosmological phenomena with the verified principles of solid-state mechanics.