Abstract
Abstract
Language-model affective behaviour is commonly influenced through weight adaptation, prompting, or direct manipulation of internal activations. We formulate MAT-3 as an external pre-inference operator that instead constructs a complementary vector while preserving the original input and embedding. Local covariance geometry defines an affine set, and MAT-3 is an averaged projection toward that set with an intervention radius ε. Under frozen geometry, the operator is non-expansive in the full space and strictly contractive in transverse directions, with the exact rate dist(M₃ⁿ(z), A_z) = (1 − η)ⁿ dist(z, A_z). A sufficient perturbation bound extends transverse contraction to adaptive geometry when ε_adapt < η. The intervention is selectively withheld when neighbourhood size, conditioning, eigengap, out-of-distribution distance, or other declared validity conditions fail, yielding safe abstention z_aux = z. A coercive Lyapunov condition connects the MDEI state dynamics to bounded states and absorbing sets. Synthetic tests validate the algebra, implementation, covariance convention, abstention logic, and numerical identities. They do not establish downstream language-model benefit. Evaluation on frozen LLMs remains the principal empirical limitation and the next falsifiable step.