NRR.Multivalued — nice multivalued functions and top–bottom separators

Public aggregator for the nice-multivalued-function and top–bottom-separator machinery used in the Akopyan–Avvakumov–Karasev prime-refinement argument.

SignedInterval is [-1,1]. A NiceMV X is a continuous scalar function on X × SignedInterval with strict opposite signs at the endpoints. Connectedness of the interval gives a zero in every vertical fiber. The API includes pullback, rescaling, reflection, observable models, perimeter observables, and simultaneous evaluation on variable-body partition children.

A TopBottomSeparator X consists of a closed carrier together with disjoint open lower and upper regions covering its complement and containing the bottom and top boundaries. Every vertical fiber meets the carrier. Over a nonempty metric base, signed distance converts such a separator into a NiceMV with exactly the same zero set. Separators and nice multivalued functions both support continuous pullback.