Mathematical Structure and Open Problems of the Spatiotemporal Hovering Surface at the Galactic Shell Boundary 7.8976 kpc

This note formulates the predicted spatiotemporal hovering phenomenon at the Galactic shell inner boundary R_{\mathrm{in}} = 7.8976 \, \mathrm{kpc} as a set of rigorous mathematical problems. The central object is a projection operator \Pi : H_{256} \to M^4 with a spectral gap at \tau = 7/8 . The time-flow parameter \alpha , defined as \alpha = \langle \psi | \Pi^\dagger \Pi | \psi \rangle / \langle \psi | \psi \rangle , vanishes at R = R_{\mathrm{in}} , defining a zero-time-flow surface. We pose open problems in differential geometry, asymptotic analysis, algebraic topology, number theory, and algebraic geometry regarding the existence, uniqueness, topological invariants, and arithmetic structure of this surface. No complete proofs are offered; this is a problem list submitted to the mathematical community for verification or refutation.