Phase Algebra III: Out-of-Core Streaming and Canonical Factorization of Ultra-Large Data via Clifford Subspace Invariants | [wAI ~ wErrors] | [WIP]

Abstract

`lie_cliffalg_analog_svd` is a dependency-free Rust research crate for phase-rotor SVD, joint diagonalization, and Clifford-inspired Lie-flow methods. The `v0.44.0` release establishes a verified standalone Golden Master baseline (168/168 tests pass offline), introducing canonicalized SVD and symmetric joint-diagonalization facades with an automated `canonicalize → solve → restore` workflow preserving permutation-equivariance and rotation-invariance under the Gram invariant metric. Extending this core, `v0.45.0` introduces exact single-pass out-of-core Gram accumulation (`ChunkedGramAccumulator`), a race-free phase-separated parallel analog rotor schedule, and Johnson–Lindenstrauss subspace sketching for large-scale matrices. The ongoing roadmap toward `v0.50.0` targets hybrid analog-digital computation and cross-domain industrial validation: 1. Division-free Riemannian Lie-residue refinement on \(SO(n)\) to recover machine precision from noisy analog/photonic MZI meshes (SNR \(\sim 40\text{–}50\,\mathrm{dB}\)).2. Graded multivector representations designed to resolve severe spectral ill-conditioning beyond standard floating-point limits.3. An isolated benchmark suite in `compare/` validating the crate against LAPACK (`dgesdd`/`dgesvd`), FastICA, Cardoso’s JADE, and randomized SVD across nine real-world datasets spanning geophysical inverse problems, biomedical EEG/MEG, sparse biological matrices, colinear hyperspectral cubes, and non-stationary dynamical systems.