Saturating-ℤ-shape integer: integer surface + translation-invariant order (sentinels propagate cleanly; no cyclic wrap). The variant ℤ proxy SignedCardinality is the canonical witness. More...

Concept definition

template<typename T>
concept dedekind::morphologies::IsSaturatingInteger = 
    IsInteger<T> && is_translation_invariant_ordered_v<T>

Detailed Description

Saturating-ℤ-shape integer: integer surface + translation-invariant order (sentinels propagate cleanly; no cyclic wrap). The variant ℤ proxy SignedCardinality is the canonical witness.

The classifier uses is_translation_invariant_ordered_v as the carrier-promise marker (registered in :algebra:ordered_algebra on SignedCardinality); the cyclic alternative is gated below by IsCyclicGroup<T, std::plus<T>> rather than the duck-typed morphologies::IsCyclic shape concept, which checks for the Modular<N>-shaped member API (Domain / generator() / successor()) and would not fire on SignedExtensionalCardinal<>.