Product-Bernoulli Hypercubes: A Unified Algebra for Meji, 64-State, and Odu-256 Routing
Year: 2026
Type: article
Abstract: The AAMT corpus uses three discrete archetypal routing spaces developed independently: the 16-Meji routing basis (WP-01), the 64-state consciousness system, and the Odu-256 curriculum grid (WP-05). We show they are one object at three sizes: each is the vertex set of a Boolean hypercube {0,1}^d carrying a product-Bernoulli measure parameterized by a coordinate v ∈ [0,1]^d, with d = 4, 6, 8 giving 2^d = 16, 64, 256 — the family Hyp(d). From this single definition, results scattered across the corpus become corollaries: lossless recovery is rank-1 factorization; alignment scalars factorize per axis; the rank-1 gate's expressiveness ceiling is the rank-1 tensor limitation, and Multiverse Superposition (WP-08) is its rank-lift; the Fisher–Rao metric has a closed product form (adopted in WP-15 Rev. 2 and WP-08 Rev. 2). We further resolve the 64↔TERA axis bridge: the 6-axis 64-state system contains the 4-axis TERA system as a coordinate subspace with a 4-element Hopf-style fiber (64 = 16 × 4), and Odu-256 is the tensor square Hyp(4)×Hyp(4). The entire AAMT discrete taxonomy is a tower of fibrations of Hyp(4).
Author: Whitehead, Weslyn Cory
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164856385
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