Sharp moment bounds for reversible negative eigenfunctions and spectral graph homomorphisms

Sharp moment inequalities for reversible negative eigenfunctions, with positive-map and strict-vector-colouring consequences. The graph extension concerns exponents greater than two; the square-energy endpoint is inherited, including a stronger ordinary-vector predecessor. The ordinary-vector conjecture above two is not resolved. Complex-Hermitian and residual-error statements are elementary corollaries. AI-assisted, unrefereed candidate; finite exact and numerical checks are distinct from the analytic proofs and do not constitute formal verification or unaffiliated reproduction.