docs: add TTG (Turkel2022) as post-stability braid topology refinement

- Maps twisted trilayer graphene MLR defect classes (plaquette,
  soliton, twiston) onto BraidStateN 3 / scar structure
- References Hartree-Fock crossing energy renormalization as
  validation for interaction-aware Q16_16 crossing energy
- Filed under Post-Stability Refinements — not a blocker, but a
  concrete n=3 physical test case for the generic modules

AGENTS.md

@@ -437,3 +437,37 @@ All five must pass. If any fails, the commit is quarantined and flagged for huma
 | 3: CAS/SMT grounding | Vacuous/tautological proofs | SymPy, Z3 | ❌ Missing |
 | 4: Dual-sided proof | Smuggled quantum assumptions | PennyLane, Biopython | ⚠️ Partial (QUBO exists) |
 | 5: Claim-state ladder | Unvalidated promotion | Review protocol | ⚠️ Partial (AGENTS.md framework)
+
+## Post-Stability Refinements
+
+These refinements should be incorporated after the core braid/eigensolid formalization is stable. They are cross-references and experimental testbeds — not blockers.
+
+### Turkel et al. TTG — Braid Topology in Twisted Trilayer Graphene
+
+Turkel et al., *Science* 376, 193 (2022), DOI: 10.1126/science.abk1895.
+Supplementary materials at: `supplementary/Turkel2022_TTG_SOM.pdf` (externally sourced)
+
+**What it demonstrates:** A physical system (3-layer graphene, two independent twist angles θTM, θBM) that undergoes a Moiré Lattice Reconstruction (MLR) producing exactly three discrete topological defect classes — plaquettes, solitons, and twistons — organized in a honeycomb network at the moiré-of-moiré scale Λ. This is a braid-word structure in a real material.
+
+**Mapping to our formalism:**
+
+| TTG physical quantity | Our braid formalism |
+|---|---|
+| θTM, θBM (twist angles) | `BraidStateN 3` inter-strand crossing parameters |
+| MLR → AtA domains (no AtB) | Eigensolid convergence: `crossStep(s) = s` |
+| Λ = a/δθ (moiré of moiré) | Sidon slack / braid word period |
+| Plaquette (1.45°) / soliton (1.54°) / twiston (1.68°) | Scar types: stable / soliton / topological defect |
+| GSFE energy functional (Eq. S4) | Q16_16 crossing energy (Φ_couch_to_fourier) |
+| Relaxation displacement u_ℓ (Eq. S2) | Strand jitter + residue fields |
+| Flat band resonance at ν~±2.4 | ∅_scars (scar absence → FAMM gate pass) |
+| Disorder reduction at resonance doping | Eigensolid fixed point → uniform LDOS |
+| Hartree-Fock correction (4 meV → 19 meV width) | Crossing energy renormalization (many-body → Q16_16) |
+| Heterostrain ε_x on solitons (C3 breaking) | Braid word defect: non-trivial braid group element |
+
+**Key insight for formalization:** The MLR does *not* distribute twist-angle error as random noise — it bifurcates into discrete topological classes. This is exactly what a braid representation (Artin B_n) predicts: twist mismatch is absorbed as a word in the braid group, not as a continuous random field. The triple-domain structure is a braid word with exactly 3 defect letters.
+
+**When to apply:**
+- After `BraidStateN.lean` and `SpectralN.lean` are stable and proven
+- As a test case for n=3 (current work fixes n=8; TTG provides a natural n=3 physical instance)
+- The GSFE parameterization (Eq. S4) can be ported as a specific instance of our generalized stacking-fault energy functional
+- The Hartree-Fock vs single-particle comparison validates our requirement for interaction-aware crossing energy (no single-particle model reproduces the 19 meV VHS width correctly)