feat: add invariant basis extractor for atlas-embeddings

[sylvaincormier]

Summary

Add a lightweight Python module that extracts the stable invariant basis from evolving embedding states via the covariance operator. The dominant eigenmodes define the intrinsic geometric axes of the system, separating meaningful structure from transient components.

Motivation

The atlas construction generates structure from seed graphs and embeds it into higher-order symmetry spaces. This module adds the missing step: explicitly extracting the invariant basis so downstream operations work in the correct coordinate system.

This acts as a coordinate-locking layer — instead of operating in an arbitrary embedding space, the system aligns to its own intrinsic geometry.

Features

• InvariantExtractor(dim, memory) — rolling buffer with configurable depth
• update(state) — feed state observations
• invariants() — eigendecomposition of covariance operator (descending order)
• project(state, k) — project onto top-k invariant directions
• reconstruct(coords) — reconstruct from reduced coordinates
• Input validation, lazy computation, cache invalidation on update

Test results

✓ Initialization, update, buffer filling
✓ Invariants extraction (non-negative eigenvalues, correct shapes)
✓ Projection and reconstruction
✓ Error handling (invalid dim, memory, wrong state dimension)
✓ Anisotropic data (eigenvalue ordering, separation ratio: 19396×)
✓ Reconstruction accuracy (error → 0 as k → dim)

Files

File	Description
atlas-embeddings/python/invariant_extractor.py	Core module (~140 lines)
atlas-embeddings/python/test_invariant_extractor.py	Test suite