Module composition 

uor_addr::composition — the five categorical operations on the Atlas image inside E₈ (wiki ADR-061).

UOR-ADDR addresses content; this module addresses compositions of content. Each operation takes one or two operand κ-labels and mints a new κ-label for the composed object, by:

1. canonicalize (canonicalize) — apply the operation’s byte-level discipline to the operand digest bytes (ADR-061 §(3); the realization commitment per CA-5);
2. ground — fold the canonical form through the same σ-axis the operands carry (CA-3 σ-axis homogeneity), via a per-operation PrismModel whose output shape’s IRI records the operation’s provenance (ADR-001 / ADR-017 typed-iso).

The framework (ADR-061 §(3), ADR-059) names each operation’s algebraic structure; the realization commits the specific byte-level relation that implements it:

op	algebraic structure (framework)	byte-level discipline (realization)
g2 CS-G2	commutative binary product (ADR-059)	lex-min-first concatenation
f4 CS-F4	2-element equivalence relation (± mirror)	bitwise-complement lex-min
e6 CS-E6	2-class partition, 8:1 population (ADR-059)	first_byte mod 9 degree tag
e7 CS-E7	24-element equivalence relation (S₄ orbit)	quarter-permutation lex-min
e8 CS-E8	identity relation	identity on canonical-form bytes

Every operation is offered on each of the five σ-axes (crate::hash); the operand and composed κ-labels share the axis.

Re-exports

pub use e6::compose_e6_filtration;

pub use e6::compose_e6_filtration_blake3;

pub use e6::compose_e6_filtration_keccak256;

pub use e6::compose_e6_filtration_sha3_256;

pub use e6::compose_e6_filtration_sha512;

pub use e7::compose_e7_augmentation;

pub use e7::compose_e7_augmentation_blake3;

pub use e7::compose_e7_augmentation_keccak256;

pub use e7::compose_e7_augmentation_sha3_256;

pub use e7::compose_e7_augmentation_sha512;

pub use e8::compose_e8_embedding;

pub use e8::compose_e8_embedding_blake3;

pub use e8::compose_e8_embedding_keccak256;

pub use e8::compose_e8_embedding_sha3_256;

pub use e8::compose_e8_embedding_sha512;

pub use f4::compose_f4_quotient;

pub use f4::compose_f4_quotient_blake3;

pub use f4::compose_f4_quotient_keccak256;

pub use f4::compose_f4_quotient_sha3_256;

pub use f4::compose_f4_quotient_sha512;

pub use g2::compose_g2_product;

pub use g2::compose_g2_product_blake3;

pub use g2::compose_g2_product_keccak256;

pub use g2::compose_g2_product_sha3_256;

pub use g2::compose_g2_product_sha512;

Modules

canonicalize

Shared byte-level canonicalize disciplines for the five categorical operations on the Atlas image inside E₈ per wiki ADR-061 §(3).

e6

CS-E6 — degree-partition filtration (mod-9 partition) per wiki ADR-061 §(2). Five σ-axes × one shape = five unary entry points.

e7

CS-E7 — S₄-quarter-permutation orbit augmentation (lex-min of the 24-orbit) per wiki ADR-061 §(2). Five σ-axes × one shape = five unary entry points.

e8

CS-E8 — identity-on-canonical-form-bytes embedding (distinguished by realization IRI) per wiki ADR-061 §(2). Five σ-axes × one shape = five unary entry points.

f4

CS-F4 — ± involution quotient (bitwise-complement lex-min) per wiki ADR-061 §(2). Five σ-axes × one shape = five unary entry points.

g2

CS-G2 — commutative binary product (lex-min-first concatenation) per wiki ADR-061 §(2). Five σ-axes × one shape = five binary entry points.

Enums

CompositionFailure

Failure modes from the composition operations.