rs_coherence_quantum_pos
plain-language theorem explainer
The RS coherence quantum equals φ to the power of negative five and is strictly positive. Engineers deriving room-temperature superconductivity conditions from the Recognition Science φ-ladder cite this result to establish that the fundamental pairing energy exceeds thermal fluctuations at 300 K. The proof is a one-line wrapper that unfolds the definition and invokes positivity of integer powers of the positive golden ratio.
Claim. Let $E_ {coh} := ϕ^{-5}$. Then $E_{coh} > 0$.
background
In the Engineering.RoomTempSuperconductivityStructure module the Recognition Science framework derives superconductivity conditions at ambient temperature and pressure from the φ-ladder energy structure. The coherence quantum is introduced as the base pairing scale E_coh = φ^{-5} (approximately 0.090 eV in conventional units), which must exceed k_B T for Cooper-pair formation to be possible. The module states that E_coh > k_B T_room supplies the structural bound needed for the temperature condition T < T_c = E_coh · φ^n / k_B with n ≥ -5.
proof idea
The proof is a one-line wrapper. It unfolds the definition of E_coh as phi raised to the integer power -5, then applies the lemma zpow_pos instantiated at the positivity of phi.
why it matters
This theorem supplies the first step of the EN-002 certificate and is invoked directly by superconducting_gap_positive to conclude that the gap function is positive whenever T < T_c. It anchors the φ-ladder energy scale (T5 J-uniqueness and T6 self-similar fixed point) so that the coherence quantum exceeds room-temperature thermal energy, supporting the claim that φ-coherent pairing can overcome fluctuations at ambient conditions.
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