Deterministic Johnson--Lindenstrauss Projections from Pisot $β$-Transformations for Zero-Knowledge Private Routing

What the math gives to ML

The paper provides a deterministic alternative to random Johnson–Lindenstrauss matrices: generate projection coefficients from a reproducible Pisot beta-transformation orbit whose correlations decay geometrically because of the map's spectral gap. The transferable asset is not merely dimensionality reduction, but a public, seed-searchable projection with no runtime randomness, predictable finite-field behavior, and an explicit bias/variance tradeoff. This is particularly attractive for embedding compression, private or verifiable routing, and systems where projection generation or commitment must be performed inside a proof circuit.