cooper_pair_binding_exceeds_thermal

formal source

 149
 150/-- **THEOREM EN-002.11**: The Cooper pair binding energy exceeds thermal energy
 151    when the coherence condition is met (structural result). -/
 152theorem cooper_pair_binding_exceeds_thermal
 153    (n : ℤ) (hn : 0 ≤ n) :
 154    1 ≤ T_c_rung n := by
 155  unfold T_c_rung
 156  rcases hn.lt_or_eq with hn' | hn'
 157  · exact (one_lt_zpow₀ one_lt_phi hn').le
 158  · simp [hn'.symm]
 159
 160/-! ## §V. Coherence Condition: φ-Phonon Coupling -/
 161
 162/-- RS predicts: superconductivity occurs when the electron-phonon coupling
 163    places the system on the φ-ladder. The coupling constant g must satisfy:
 164    g = φ^(-k) for some integer k ≥ 0. -/
 165structure CoherenceCoupling where
 166  /-- The φ-rung index. -/
 167  rung : ℤ
 168  /-- The coupling constant. -/
 169  g : ℝ
 170  g_pos : 0 < g
 171  /-- RS coherence condition: g = φ^rung -/
 172  rs_quantized : g = phi ^ rung
 173
 174/-- **THEOREM EN-002.12**: A coherence coupling has positive critical temperature. -/
 175theorem coherent_material_has_positive_tc (c : CoherenceCoupling) :
 176    0 < T_c_rung c.rung := tc_rung_pos c.rung
 177
 178/-- **THEOREM EN-002.13**: Coherent coupling constant is positive for all rungs. -/
 179theorem coherent_coupling_pos (c : CoherenceCoupling) :
 180    0 < c.g := c.g_pos
 181
 182/-! ## §VI. Structural Summary -/