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Product-Bernoulli Hypercubes: A Unified Algebra for Meji, 64-State, and Odu-256 Routing | Synapse

June 18, 2026Open Access

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Product-Bernoulli Hypercubes: A Unified Algebra for Meji, 64-State, and Odu-256 Routing

WWWeslyn Cory WhiteheadKlamath Community College

Key Points

The aim is to unify different routing structures into a single framework using product-Bernoulli hypercubes.
Added a reference implementation and verification in open-source package harmonic-engine.
Numerically verified core algebraic claims for dimensions d=4,6,8 using specified scripts.
Typeset inline mathematics in proper mathematical notation.
Corollary C1 confirmed losslessness as rank-1.
Corollary C2 confirmed factorized alignment scalars.
Corollary C4 established a closed-form for product Fisher-Rao.

Abstract

The Hyp(d) product-Bernoulli hypercube family unifies the 16-Meji, 64-state, and Odu-256 spaces as one object at three sizes. This revision adds a Reference Implementation inline math has been re-typeset from code spans into proper math mode.

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Cite This Study

Weslyn Cory Whitehead (Tue,) studied this question.

synapsesocial.com/papers/6a338d85630953a74978e6f6 https://doi.org/https://doi.org/10.5281/zenodo.20710545