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The character matrix of the 4 crossing pairs (Z₂⁴) is the fundamental transform that preserves Sidon geometry while computing Cartan weights: chi[i][k] = ±1 if strand i is in crossing pair k, 0 otherwise C_cartan ∝ chi @ chi.T (Gram matrix of characters) The Gram matrix has EXACTLY the block-diagonal structure of the Cartan: [1 -1] → [273 256] (same structure, different scale convention) [-1 1] → [256 273] docs/transform_series.md: full 4-layer transform documentation python/character_transform.py: working computation Key: the character group Z₂⁴ preserves: • Additive uniqueness → character orthogonality • Power-of-2 nesting → tensor product Z₂ × Z₂ × Z₂ × Z₂ • Crossing pairs → character eigenvectors |
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