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Commit f1145c8
feat: Add spectral analysis module with Atlas λ₁=1 proof
Add spectral.rs (1,743 lines) and tests/spectral_properties.rs (421 lines)
implementing Chapter 10: Spectral Analysis of the Atlas Laplacian.
Core result: The spectral gap of the Atlas graph Laplacian is exactly λ₁ = 1.
Proof chain:
- Hemisphere decomposition (96 → 2×48, no cross edges)
- Q₄ block decomposition (48 → 3×16 hypercube blocks)
- Inter-block identity matchings (path graph B₋₁ — B₀ — B₊₁)
- Block tridiagonal Laplacian structure
- Reduction to five independent 3×3 problems M_ν
- Characteristic polynomial: eigenvalues {ν, ν+1, ν+3}
- Complete spectrum: 11 distinct values {0,1,2,3,4,5,6,7,8,9,11}
- Spectral gap = 1 from M₀ block
60 tests (41 unit + 19 integration), exact rational arithmetic,
zero floating-point, zero unsafe code.
Co-Authored-By: Claude Opus 4.6 <[email protected]>1 parent 3990396 commit f1145c8
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