Transitional bridge contract for the soft-to-hard structural cut. More...

Concept definition

template<typename Shell, typename Manifold, typename Ω bool>
concept dedekind::category::IsMereologicalCutCandidate =  requires(Shell s, Manifold m) {
  
  typename Shell::FilteredSpace;
 
  requires IsPartOfRelation<typename Shell::FilteredSpace, Manifold, Ω>;
 
  { s.filter(m) } -> std::same_as<typename Shell::FilteredSpace>;
}

Detailed Description

Transitional bridge contract for the soft-to-hard structural cut.

Models the structural pruning semantics of Leśniewski-style mereological cuts: a Shell filters a Manifold to a FilteredSpace that is a mereological part of the manifold (verified via IsPartOfRelation). This concept captures the "soft" half of the full IsMereologicalCut described in nn_notes/mereological_cut.cppm, without introducing a dependency on :pullback.

The full IsMereologicalCut additionally requires the filtered inclusion to be a pullback limit (unique factorization). That Axiom 7 / Issue #195 constraint is intentionally deferred here.

Note: TODO(Issue #195): strengthen to IsSubobject<FilteredSpace, Manifold> and add IsPullbackLimit uniqueness once the :pullback partition naming is stable.

Template Parameters

Shell	The filtering agent (e.g. a learned sieve or pruning mask).
Manifold	The ambient space being partitioned.
Ω	The truth-value codomain (default: bool).

See also: https://plato.stanford.edu/entries/mereology/; Lawvere & Schanuel (2009), Conceptual Mathematics, ch. 4 (subobjects).