room_temp_superconductivity_structure
plain-language theorem explainer
Recognition Science shows existence of an integer rung n on the phi-ladder where the critical temperature meets or exceeds room temperature, permitting ambient superconductivity under the coherence condition. Materials scientists mapping high-Tc candidates to the phi-ladder energy structure would cite this existence result. The proof is a one-line wrapper that directly invokes the prior theorem ambient_superconductivity_possible, which supplies rung zero as witness.
Claim. There exists an integer rung $n$ such that the critical temperature satisfies $T_c(n) = E_{coh} · φ^n / k_B ≥ T_{room}$, where $E_{coh} = φ^{-5}$ eV is the coherence quantum.
background
The module EN-002 derives room-temperature superconductivity from the phi-ladder energy structure. Pairing energy is quantized as $E_n = E_{coh} · φ^n$ with $E_{coh} ≈ 0.090$ eV. Ambient superconductivity requires $E_n ≥ k_B T_{room} ≈ 0.026$ eV, which holds once the rung satisfies the ambient_sc_condition definition: $1 ≤ T_c_rung n$ (in units where $T_{room} = 1$). The upstream theorem ambient_superconductivity_possible establishes the existence claim by exhibiting rung zero.
proof idea
The proof is a one-line wrapper that applies ambient_superconductivity_possible. That theorem uses the witness 0, unfolds ambient_sc_condition and T_c_rung, then closes by simp.
why it matters
This registers the existence result inside the engineering implications section of EN-002. It anchors the claim that coherent pairing on the phi-ladder can overcome thermal fluctuations at room temperature, consistent with the Recognition Science phi-ladder quantization and the coherence quantum exceeding room-temperature energy. No downstream uses are recorded yet; the result remains available for material-specific extensions.
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