CoherenceCoupling
CoherenceCoupling encodes a phi-ladder quantized coupling for room-temperature superconductivity models in Recognition Science. Material physicists and RS theorists cite it to parameterize coherent electron-phonon pairings that satisfy the binding energy threshold above thermal fluctuations. The declaration is a plain structure definition that directly bundles the integer rung, positive real coupling, and exact quantization g = phi^rung.
claimA coherence coupling is a pair consisting of an integer rung index $r$ and a positive real number $g > 0$ such that $g = phi^r$, where $phi$ denotes the self-similar fixed point of the Recognition Composition Law.
background
The module EN-002 derives room-temperature superconductivity from the phi-ladder energy structure. Superconductivity requires Cooper-pair binding energy at least k_B T; in RS this binding is quantized as E_n = E_coh * phi^n with E_coh = phi^{-5} eV exceeding room-temperature thermal energy 0.026 eV. The coherence condition therefore demands that the electron-phonon coupling constant itself lie on the ladder.
proof idea
This is a structure definition. It packages four fields: the integer rung, the real coupling g, the positivity hypothesis 0 < g, and the quantization equality g = phi^rung. No tactics or lemmas are applied; the fields are simply declared.
why it matters in Recognition Science
CoherenceCoupling supplies the hypothesis type for the downstream theorems coherent_coupling_pos and coherent_material_has_positive_tc. It implements the first item in the EN-002 hierarchy of conditions (coherence condition) and connects directly to the phi-ladder monotonicity and unboundedness results that guarantee positive critical temperatures. The structure therefore closes the structural gap between the RS coherence quantum and observable T_c > 0 at ambient conditions.
scope and limits
- Does not assert existence of any physical material realizing the rung.
- Does not compute a numerical T_c value.
- Does not incorporate pressure or lattice effects.
- Does not constrain the sign of the rung index.
formal statement (Lean)
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. -/