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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]>
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atlas-embeddings/src/lib.rs

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@@ -773,6 +773,7 @@ pub mod e8;
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pub mod embedding;
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pub mod foundations;
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pub mod groups;
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pub mod spectral;
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pub mod weyl;
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#[cfg(feature = "visualization")]

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