Protective Action Availability: Acquired history and current contact

A current observation can provide no guaranteed protective action on its own, yet enlarge protective options when acquired history is accessible. This seventh paper in the Ev5 working-paper series derives that relationship in a nonlinear mathematical construction. Paper 5 supplies protected acquisition, certified readable memory, continuation and memory-margin renewal. Paper 7’s additional contribution is to derive which actions guarantee sampled-state protection across the possibilities compatible with accessible information. Equal-width, nonempty action sets can require incompatible selections, showing why action identity matters. Certified history resolves context; exact current contact refines the remaining state uncertainty. With positive reset-state uncertainty and sufficient actuator authority to prevent clipping, their interaction adds actions of total coordinate length 2ε relative to history alone. Clipping can remove the enlargement, while zero uncertainty eliminates it. Compatible information refinements preserve the joint result but allocate marginal credit differently. These are comparisons of information views, not reversed physical histories. The derived representation and quantitative interaction make a proposed Unified Coherence Model (UCM) relationship precise. Ordinary robust control explains the mechanism. Complete proofs of the additional propositions are included, with inherited results and source provenance identified separately. The results concern available protective actions, rather than demonstrated improvements in realised performance, continuous physical safety or physical resource maintenance. They do not derive the complete originating UCM rate expression. No new experiment or simulation was undertaken for this edition.