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Study verifies algebraic claims in product-bernoulli hypercubes, suggesting a unifying model for multiple routing schemes.
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 & Verification note to Data Availability: the paper's falsifiable claims are now numerically verified in the open-source harmonic-engine package (tests/test_new_math.py, passing on CPU). Corollaries C1 (losslessness=rank-1), C2 (factorized alignment scalars), and C4 (closed-form product Fisher–Rao) are verified for d=4,6,8 in harmonic_engine/hypercube.py and geometry.py; inline math has been re-typeset from code spans into proper math mode.
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Weslyn Cory Whitehead (2026) studied this question.
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