Module canonicalize 

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

Each function operates on the raw digest bytes of operand κ-labels — the lowercase-hex digest body, decoded back to its 32- or 64-byte raw form — and emits canonical-form bytes that the composition shape’s ψ-pipeline folds into the composed κ-label via the bound σ-axis.

Per CA-5, these are uor-addr’s realization commitments under ADR-061 §(3). The framework names each operation’s algebraic structure (commutative binary product, 2-element equivalence relation, 2-class partition, 24-element equivalence relation, identity); the realization commits the specific byte-level relation that implements that algebraic structure.

Functions

canonicalize_e6

CS-E6 canonicalize discipline: the 2-class partition with 8:1 population ratio per ADR-059. Per wiki ADR-061 §(3) the framework names the algebraic structure (a 2-class partition with population ratio 8:1 per ADR-059); the realization commits the partition derived from first_raw_digest_byte mod 9.

canonicalize_e7

CS-E7 canonicalize discipline: the 24-element equivalence relation on operands under the S₄ quarter-permutation orbit. Per wiki ADR-061 §(3) the framework names the algebraic structure (a 24-element equivalence relation per ADR-059); the realization commits the S₄ action by quarter-permutation of the raw digest.

canonicalize_e8

CS-E8 canonicalize discipline: the identity. Per wiki ADR-061 §(3) the framework names the algebraic structure (the identity relation per ADR-059 — every operand is its own equivalence class); the realization commits identity on canonical-form bytes.

canonicalize_f4

CS-F4 canonicalize discipline: the 2-element equivalence relation on operands under the ± mirror involution. Per wiki ADR-061 §(3) the framework names the algebraic structure (a 2-element equivalence relation per ADR-059); the realization commits bitwise-complement of the raw digest as the partition-inducing mirror.

canonicalize_g2

CS-G2 canonicalize discipline: the commutative binary product of two operand κ-labels. Per wiki ADR-061 §(3) the framework names the algebraic structure (commutativity at the C-level per ADR-059); the realization commits lex-min-first ordering as the byte-level rule realizing that algebra.

check_axis

Validate that an operand’s σ-axis matches the expected axis (per CA-3 σ-axis homogeneity).

decode_operand

Decode a κ-label’s raw digest bytes (the lowercase-hex body after the σ-axis prefix). Returns the σ-axis name (the prefix without trailing :) and the raw digest bytes (32 or 64 bytes).