Signed-Involution Sector Exclusion for Exact Zero Transfer in Finite Magnetic Graph Hamiltonians

This manuscript studies exact zero-transfer pairs in finite-dimensional Hermitian graph dynamics. Given a finite graph Hamiltonian (H), source vertex (s), and target vertex (\ell), an exact zero-transfer pair satisfies (\langle \ell|e^{-itH}|s\rangle=0) for all real times (t). The work develops a finite algebraic framework for this condition through moment cancellation, source-generated Krylov subspaces, and spectral-projector channel closure. It then gives a constructive certificate mechanism based on signed involutions: if (R^2=I), ([H,R]=0), (R|s\rangle=|s\rangle), and (R|\ell\rangle=-|\ell\rangle), then the source and target lie in orthogonal invariant sectors and exact zero transfer follows. The manuscript also reports machine-readable M3A certificate data for finite signed magnetic graph Hamiltonians, including non-cycle examples; Layer-2 spectral-projector diagnostics; perturbative sector-breaking tests; target-resolved leakage diagnostics; and Lindblad block-preservation criteria for open-system evolution. The repository and supplementary data support reproducibility of the finite graph computations reported in the paper. The results concern finite graph Hamiltonians and finite-dimensional linear algebra; they do not claim intrinsic topological protection, generic robustness, physical implementation, continuum geometry, spacetime, gravity, or a new physical theory.