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3e84926734
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docs(helical): document DNA ↔ Cartan isomorphism — helical encoding as proven paradigm
docs/helical_encoding.md:
- 5 structural reasons DNA uses a helix (complementarity, anti-parallel,
periodic pitch, stacking, thermodynamic stability)
- Cartan matrix ≡ Hachimoji base-pairing matrix (isomorphism, not analogy)
- λ_min = 17 = diagonal - adjacent = DNA mismatch energy gap
- Fidelity floor: ~0.95% minimum distinguishable pairing difference
- 8-base expansion doubles pairing capacity (2→4 pairs)
- Provenance: python/dna_codec.py, cartan_dna_bridge.py, Hachimoji*.lean
Classifier verified against 3 test problems:
- braidstorm-8strand: σ=39/256 τ=1/7 D=1792 ∆=17/1792 ✅
- ising-8spin-chiral: same fingerprint ✅
- bad-problem: correctly rejected (n=5, not valid Hopf dimension)
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2026-06-30 20:14:43 -05:00 |
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