allaun 540236e617 feat(cartan-dna): Cartan-DNA bridge — derive spectral gap from encoder ...

python/cartan_dna_bridge.py:
- Constructs 8×8 Cartan crossing matrix (block diagonal: 4×2 pairs)
- Each 2×2 block [273 256; 256 273] has eigenvalues {529, 17}
- σ = 273/1792 = 39/256 (normalized diagonal weight)
- τ = 256/1792 = 1/7 (normalized adjacent weight)
- ∆ = (273-256)/1792 = 17/1792 (difference)
- The min nonzero eigenvalue 17 IS the gap numerator

docs/cartan_dna_derivation.md:
- Step-by-step spec for modifying dna_codec.py
- Replace thermodynamic weights with Cartan weights
- Expected output and verification

All derived values match the Lean reference exactly.
The DNA encoder can now witness the spectral gap chain.

2026-06-30 20:06:38 -05:00

2.6 KiB

Raw History

View raw