Struct AtlasE8Embedding 

pub struct AtlasE8Embedding { /* private fields */ }

Atlas→E₈ embedding

Maps the 96 vertices of the Atlas to 96 of the 240 E₈ roots, preserving the graph structure.

Implementations

impl AtlasE8Embedding

pub const fn new() -> Self

Create the canonical Atlas→E₈ embedding

This embedding was computed via backtracking search and certified in the Python implementation. It is the unique embedding (up to E₈ symmetry) that preserves edges and produces exactly 48 sign classes.

pub const fn map_vertex(&self, atlas_vertex: usize) -> usize

Map an Atlas vertex to its corresponding E₈ root

Arguments

• atlas_vertex - Atlas vertex index (0..96)

Returns

E₈ root index (0..240)

Panics

Panics if atlas_vertex >= 96

pub const fn mapping(&self) -> &[usize; 96]

Get the full mapping as a slice

pub fn verify_root_norms(&self) -> bool

Verify all mapped roots have correct norm

All 96 embedded E₈ roots must have norm² = 2.

Returns

true if all roots have norm² = 2

pub fn verify_injective(&self) -> bool

Verify that the embedding is injective

No two Atlas vertices should map to the same E₈ root.

pub fn count_sign_classes(&self) -> usize

Count sign classes in the embedding

A sign class is a pair of Atlas vertices that map to negatives of each other in E₈. The canonical embedding has exactly 48 sign classes.

Returns

Number of sign class pairs (should be 48)

pub fn verify_all(&self) -> bool

Verify all embedding properties

Checks:

• Injectivity (96 distinct roots)
• Root norms (all have norm² = 2)
• Sign classes (exactly 48 pairs)

Returns

true if all properties verified

Trait Implementations

impl Clone for AtlasE8Embedding

fn clone(&self) -> AtlasE8Embedding

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for AtlasE8Embedding

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for AtlasE8Embedding

fn default() -> Self

Returns the “default value” for a type.