Phase Algebra: Phase-Resonance SVD as Clifford Phase Algebra (An Extension of Linear Algebra) | [wAI ~ wErrors]

Description lie_cliffalg_analog_svd is a Rust research prototype centered on PhaseFlow: a Lie/Clifford-inspired phase-rotor approach to robust dense SVD and/or joint diagonalization. The package keeps ordinary f64 matrix storage while using geometric structures as algorithmic guides: row/column phase signatures, in-place rotor updates, active-set phase flow, and phase-locking diagnostics. The main research route is PhaseFlow, where phase-health is used as an active computational mechanism rather than only as a detector. Alongside it, the project includes several related experimental branches: a conservative polar/Jacobi SVD baseline, tiny rotor kernels for small matrices, analog/photonic rotor schedules, rectangular phase diagnostics, and Phase-JADE joint diagonalization for symmetric matrix families. It is intended for research on difficult matrices, geometric numerical methods, blind source separation, and future analog or photonic linear algebra hardware. Short Description Rust prototype for PhaseFlow-based Lie/Clifford-inspired SVD, with related rotor, analog, and Phase-JADE branches. Interesting Branches PhaseFlow: active row/column phase-locking route for SVD. PhaseSignature: compact phase-health passport for matrix triage. Polar/Jacobi baseline: conservative robust SVD reference path. Tiny rotor kernels: small-matrix N <= 4 local rotor experiments. Analog/photonic schedules: rotor meshes inspired by future hardware. Rectangular phase diagnostics: separate row and column phase spaces. Phase-JADE: joint diagonalization of symmetric matrix families. ... PhaseFlow Note PhaseFlow proposes a different mental model of a matrix: not only a flat table of numbers, but a coupled row/column phase object whose hidden structure can be read through phase stress, twist, entropy, and rotor alignment. In this ontology, SVD becomes a phase-locking process: orthogonal rotors progressively synchronize the row and column “views” until off-diagonal tension collapses into diagonal spectral mass. This is not a new memory representation; the implementation still uses ordinary f64 arrays. The novelty is in the computational viewpoint: geometric phase structure guides the update laws.