Struct E8EmbeddingShape 

pub struct E8EmbeddingShape<const COMPONENT_LABEL_BYTES: usize>;

E₈-via-direct-embedding composition shape — the universal embedding construction on the Atlas image inside E₈ per wiki [ADR-059]’s categorical-operation vocabulary.

E₈ is the rank-8 exceptional Lie algebra reached from the Atlas by the direct embedding φ: Atlas ↪ E₈ (injective, adjacency-preserving, 240 roots). As a categorical operation, E₈ is the direct embedding of one Atlas structure into the full E₈ root system — the shape is unary, with SITE_COUNT = COMPONENT_LABEL_BYTES per wiki [ADR-061] §(2). The universal target — any single operand factors through E₈ without further algebraic constraint per ADR-059’s Atlas-as-initial-object commitment. The embedding is the identity on canonical-form bytes; the composed κ-label is distinguished from the operand’s κ-label by realization-IRI provenance, not by digest bytes.

The composed κ-label addresses the operand’s E₈ image directly. Two operands at the same Atlas-image position modulo E₈ Weyl-orbit equivalence compose to byte-identical composed κ-labels under fixed σ-axis selection per ADR-047.

See also

• crate::std_types for the family contract and IRI namespace.
• G2ProductShape / F4QuotientShape / E6FiltrationShape / E7AugmentationShape for the other four categorical operations on the Atlas.
• crate::convergence for the convergence-tower vocabulary ADR-059 commits.
• Wiki: 05 Building Block View § Whitebox prism
• Wiki: 09 Architecture Decisions § ADR-059
• Wiki: 09 Architecture Decisions § ADR-061
• AGENTS.md § 11

Constraints

• TC-01 — admission is compile-time.
• TC-04 — bilateral compile-time enforcement.
• ADR-013 — closure under uor-foundation.
• ADR-017 — content-addressed identity via the IRI.
• ADR-058 — κ-derivation produces the composed κ-label.
• ADR-059 — codomain factors through the Atlas image inside E₈.
• ADR-061 — operational composition surface for κ-labels.

Behavior

use prism::pipeline::ConstrainedTypeShape;
use prism::std_types::E8EmbeddingShape;

// Given a unary E₈ direct embedding over one sha256 κ-label (71 bytes),
type E8 = E8EmbeddingShape<71>;
// When SITE_COUNT is queried,
// Then it equals the operand width — E₈'s direct embedding is unary.
assert_eq!(<E8 as ConstrainedTypeShape>::SITE_COUNT, 71);
assert_eq!(
    <E8 as ConstrainedTypeShape>::IRI,
    "https://uor.foundation/type/ConstrainedType",
);
assert!(<E8 as ConstrainedTypeShape>::CONSTRAINTS.is_empty());

Trait Implementations

impl<const COMPONENT_LABEL_BYTES: usize> ConstrainedTypeShape for E8EmbeddingShape<COMPONENT_LABEL_BYTES>

const IRI: &'static str = "https://uor.foundation/type/ConstrainedType"

IRI of the ontology type:ConstrainedType instance this shape represents.

const SITE_COUNT: usize = COMPONENT_LABEL_BYTES

Number of sites (fields) this constrained type carries.

const CONSTRAINTS: &'static [ConstraintRef]

Per-site constraint list. Empty means unconstrained.

const CYCLE_SIZE: u64

ADR-032: cardinality of the shape’s value-set (the cycle structure of the shape under the substrate’s discrete-clock model). Used by the prism_model! macro to lower first_admit (closure-body grammar G16) to the correct descent measure. Conventions:

const SITE_BUDGET: usize = Self::SITE_COUNT

Ontology-level siteBudget: count of data sites only, excluding bookkeeping introduced by composition (coproduct tag sites, etc.). Equals SITE_COUNT for leaf shapes and for shapes whose composition introduces no bookkeeping (products, cartesian products). Strictly less than SITE_COUNT for coproduct shapes and any shape whose SITE_COUNT includes inherited bookkeeping. Introduced by the Product/Coproduct Completion Amendment §4a; defaults to SITE_COUNT so pre-amendment shape impls remain valid without edits.