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We consider the restrictions of Shi arrangements to Weyl cones, theirrelations to antichains in the root poset, and their intersection posets. Forany Weyl cone, we provide bijections between regions, flats intersecting thecone, and antichains of a naturally-defined subposet of the root poset. Thisgives a refinement of the parking function numbers via the Poincar\'epolynomials of the intersection posets of all Weyl cones. Finally, we interpretthese Poincar\'e polynomials as the Hilbert series of two isomorphic gradedrings, one arising from the Varchenko-Gel'fand ring and another, which we callthe order ring since it turns out to be naturally associated to the orderpolytope.

Shi arrangements restricted to Weyl cones