thermal_ratio_pos
plain-language theorem explainer
The theorem establishes that the room-temperature thermal ratio, defined as k_B T_room divided by the RS coherence quantum E_coh, is strictly positive. Engineers checking ambient superconductivity conditions in the Recognition Science φ-ladder would cite it to confirm the basic inequality before comparing binding energies to thermal fluctuations. The proof is a one-line wrapper that unfolds the explicit constant definition and applies norm_num.
Claim. $0 < k_B T_{room} / E_{coh}$ where $E_{coh} = φ^{-5}$ eV is the Recognition Science coherence quantum and the ratio evaluates numerically to 0.289 at $T_{room} = 300$ K.
background
The Engineering.RoomTempSuperconductivityStructure module derives superconductivity conditions from the φ-ladder energy structure. Superconductivity requires Cooper-pair binding energy E_binding ≥ k_B T, with quantized levels E_n = E_coh · φ^n and E_coh = φ^{-5} eV ≈ 0.090 eV. The thermal ratio is introduced as k_B T_room / E_coh ≈ 0.026 / 0.090 ≈ 0.289, which is less than 1, so the coherence quantum exceeds room-temperature thermal energy.
proof idea
The proof is a one-line wrapper that unfolds the definition of thermal_ratio_room_temp to its explicit numerical value 0.289 and applies norm_num to obtain the strict inequality.
why it matters
This fills the EN-002.3 slot in the room-temperature superconductivity hierarchy, confirming positivity of the normalized thermal energy so that the coherence condition can be checked against the φ-ladder. It supports the module's claim that coherent pairing can overcome thermal fluctuations at ambient temperature and pressure, anchoring the temperature condition within the T0-T8 forcing chain and the phi-ladder rung structure. No immediate downstream theorem consumes it yet.
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