A Finite-Family Monotone Directional Criterion for Observable Exclusion of One-Dimensional Attractors

We establish two exclusion theorems for limit cycles in nonlinear dynamical systems observed through finite families of strictly positive (monotone) observation matrices. At exact resolution (β̃ = 0), exponential orthant confinement of projected variational trends is structurally incompatible with nonzero transverse Floquet rotation — excluding any hyperbolic cycle with θ_rot > 0, the generic case in dimension n ≥ 3. At finite resolution (β̃ > 0), an explicit condition balancing rotation speed, signal decay, and sensor noise determines detectability. The framework requires no model-based Jacobian inequalities, operating solely from observable trend data. The result is strictly contrapositive: directional coherence does not imply realizability. This note complements and extends the geometric falsification framework established in DOI: 10.5281/zenodo.18789449.