//! Topological Flow Matching scaffolding.
//!
//! This module will host primitives for defining **flows on simplicial complexes**
//! and using persistent homology features as conditioning signals for flow matching.
//!
//! The core idea: a **cohomological flow** assigns to each cochain a vector field
//! on the underlying space, with the constraint that the flow respects the
//! coboundary operator \(\delta\).  This connects the combinatorial structure of
//! the simplicial complex to continuous dynamics.
//!
//! # Status
//!
//! Work-in-progress.  The trait below is a placeholder; signatures will be refined
//! as the theory solidifies.
//!
//! # Connection to topology.rs
//!
//! The coboundary operator \(\delta\) is the algebraic dual of the boundary
//! operator \(\partial\) defined in [`topology`](crate::topology).  Where
//! \(\partial\) maps chains "downward" (triangles to edges to vertices),
//! \(\delta\) maps cochains "upward."  A cohomological flow respects this
//! duality: the flow field on \(k\)-cochains is compatible with the flow
//! on \((k+1)\)-cochains via \(\delta\).
//!
//! # References
//!
//! - Girish et al. (2025), "Persistent Topological Structures and
//!   Cohomological Flows" -- theoretical foundation for the
//!   CohomologicalFlow trait; connects persistent homology features to
//!   continuous dynamics on cochain spaces.
//! - Maggs et al. (2023), "Simplicial Representation Learning with Neural
//!   k-Forms" -- concrete architectures that learn on cochains using
//!   coboundary operators; demonstrates how k-form representations on
//!   simplicial complexes outperform node-only baselines.

/// A placeholder for a cohomological flow field on a simplicial complex.
///
/// Future methods will define how cochains induce vector fields and how those
/// fields compose with the coboundary operator \(\delta\).  The coboundary
/// operator is the dual of the boundary operator in
/// [`topology`](crate::topology): it maps \(k\)-cochains to
/// \((k+1)\)-cochains, and satisfies \(\delta\delta = 0\).
pub trait CohomologicalFlow {
    // TODO: Define the signature for flows on chains/cochains.
}
