Geometric Dynamics: Spectral Emergence Under SDiff(M) Constraints

We propose a geometric-dynamical framework in which physical reality is not fundamentally composed of pre-assigned particles and fields, but instead emerges from the spectral evolution of intrinsic geometric operators on a manifold M constrained by the volume-preserving symmetry group SDiff(M). In this construction, standard physical observables are interpreted as infrared projections of deeper geometric response structures rather than fundamental primitives. The manifold is treated as an elastic geometric medium characterized by intrinsic response parameters including a shear modulus K0 and bending modulus gamma. These quantities naturally define emergent infrared scales associated with the effective propagation velocity c and a geometric cutoff scale l_P. Maxwell-type gauge dynamics arise as rotational and stretching responses of the manifold displacement field within the tangent bundle, without imposing external gauge symmetry as a primary axiom. Within the spectral flow generated by the operator D_hat, the infrared sector dynamically suppresses unstable higher-order topological excitations while selecting two robust attractor sectors denoted W1 and W3. These sectors are associated with stable matter-like excitations whose effective mass and charge correspond to geometric overlap integrals of the underlying operator modes. Gravitational dynamics are reinterpreted as a long-range geometric stress-balancing response of the manifold. The conventional gravitational constant is replaced by a geometric flux-response coefficient Gamma_geom, while Einstein-type field equations appear as infrared self-consistency conditions required to redistribute topological stress generated by localized excitations. The framework further predicts possible nonlinear shifts in the effective mass ratio mp/me under sufficiently strong curvature gradients, providing a potential observational criterion for falsifying or constraining the proposed geometric-spectral construction. Manuscript submitted to Foundations of Physics on 30 May 2026.