GeoVac (The Geometric Vacuum): Structurally Sparse Qubit Hamiltonians and the Discrete Spectral Triple

GeoVac is a spectral-graph-theory framework for computational quantum chemistry and mathematical physics. The discrete graph Laplacian on the three-sphere S^3 is mathematically equivalent to the Schrodinger equation via Fock's 1935 conformal projection (Paper 7, 18/18 symbolic proofs), and this equivalence is exploited to build structurally sparse qubit Hamiltonians whose angular-momentum (Gaunt) selection rules enforce block-diagonal electron-repulsion integrals. The result is O(Q^2.5) Pauli-term scaling, a 51x-1712x reduction versus Gaussian baselines across LiH, BeH2, and H2O (Paper 14), with a 38-molecule library exported to OpenFermion, Qiskit, and PennyLane (Paper 20). Classical validation benchmarks include He at 0.019% and H2 at 96.0% of the dissociation energy. Beyond quantum-computing applications, the framework's structure has been developed as a discrete almost-commutative spectral triple in the Marcolli-van Suijlekom gauge-network lineage: state-space Gromov-Hausdorff convergence of the Camporesi-Higuchi truncations is established unconditionally at explicit rate (4/pi) log(n)/n via a translation-seminorm metrization (Paper 38), a degeneracy theorem closes the natural route to a Lorentzian quantum metric on truncated Krein spectral triples (Paper 45; an earlier convergence claim is retracted, see docs/claims_register.md), and the framework's transcendental periods are classified as cyclotomic mixed-Tate at level 4 via a master Mellin engine (Papers 55-56). Developed with an AI-augmented agentic research workflow; all results validated against analytical solutions, NIST reference data, and a symbolic proof suite.