Relational Sovereignty Calculus

We introduce the Relational Sovereignty Calculus (RSC), a formal framework for reasoning about multi-agent interaction under irreversible partiality, gated updates, and resource-sensitive composition. The system is presented as a category RelSys* with partial objects, a non-Cartesian monoidal structure, and endofunctors representing perturbation (V), audit/compression (A), contraction (Σ), and a polarity functor. We prove that no non-trivial involutive duality can exist without violating the structural axioms (no diagonal, no weakening, non-neutral unit, lossy tensor). This is recast as a categorical obstruction to *-autonomous closure (duality collapse theorem). Given the absence of a symmetric dual, we construct a minimal order-sensitive protocol that exhibits persistent path dependence due to the non-commutativity (AV − VA)(xi) = δi(1−λ)⊥i. A deterministic closed form D = δ(1−λn) is derived. Controlled simulations with paired randomness, commutative null, η-interpolation, recovery, and synchronisation pressure confirm that the first-order commutator accounts for the majority of the observed divergence, while a small residual is bounded via a discrete Magnus decomposition (Appendix A). The protocol provides a diagnostic lens for alignment architectures that implicitly assume commutativity of preprocessing steps.