Module axioms 

Axioms: Mathematical Property Verifiers

This module provides generic functions to verify mathematical properties that should hold for any correct implementation of information-theoretic measures.

Functions

verify_chain_rule

Verify chain rule: H(X,Y) = H(X) + H(Y|X).

verify_conditioning_reduces_entropy

Verify conditioning reduces entropy: H(X|Y) ≤ H(X).

verify_entropy_bounds

Verify entropy is bounded by log2(alphabet_size). For bytes, max entropy is 8.0 bits/byte.

verify_identity

Verify that a distance function d(x,x) is close to 0 (allow for small overhead).

verify_mi_nonnegative

Verify mutual information non-negativity: I(X;Y) ≥ 0.

verify_ncd_bounds

Verify NCD range: 0 ≤ NCD ≤ 1+epsilon.

verify_non_negativity

Verify non-negativity: d(x,y) ≥ 0.

verify_subadditivity

Verify subadditivity: H(X,Y) ≤ H(X) + H(Y).

verify_symmetry

Verify symmetry: d(x,y) ≈ d(y,x).

verify_triangle_inequality

Verify triangle inequality: d(x,z) ≤ d(x,y) + d(y,z).