Trait ResGraphObject

Source

pub trait ResGraphObject {
    // Required methods
    fn num_vertices(&self) -> usize;
    fn object_name(&self) -> &'static str;

    // Provided methods
    fn has_adjacency(&self) -> bool { ... }
    fn is_adjacent(&self, _v1: usize, _v2: usize) -> bool { ... }
}

Expand description

Trait for objects in the ResGraph category

An object in ResGraph is a resonance graph with:

A fixed number of vertices (roots for groups, vertices for Atlas)
An underlying graph structure
Compatibility with E₈ resonance structure

§Design Note

This trait is minimal: it only requires num_vertices() and object_name(). The adjacency structure is implicit via the E₈ embedding for most objects. For the Atlas, which is a concrete graph, we can query adjacency directly. For exceptional groups (G₂, F₄, E₆, E₇, E₈), adjacency is determined by their root systems (roots with inner product -1 are adjacent).

Morphisms in ResGraph preserve this structure, but the verification of structure preservation is done via the E₈ embedding, not by checking adjacency for every pair of vertices.