A physical transverse-current sign obstruction in a full-tensor postquantum classical gravity action

This preprint identifies a physical transverse-current sign obstruction in the static full-tensor Feynman–Vernon quadratic form displayed in a linearised two-coupling postquantum classical gravity model. A difference of two separately conserved positive-energy pressureless-dust branches has negative primary form. Six exact rational physical dust differences span the complete static conserved symmetric-tensor space, and additive composite matter turns that span into a physical branch-pair domain. The source linear fixed momentum constraint supplies no secondary current square for the symmetric pair. Conditional small-amplitude and implicit-function arguments show that an ordinary regular analytic nonzero-momentum constraint completion cannot repair the sign. Restricted domains, revised kernels, zero or degenerate modes, and genuinely nonanalytic or nonperturbative completions remain open. The result is source-specific and is not a no-go theorem for postquantum classical gravity. The record includes the manuscript, editable source, a dependency-free exact-arithmetic verification program, expected output, and immutable file hashes.