E_coh
plain-language theorem explainer
The RS coherence quantum is defined as phi to the power of negative five in real numbers. Researchers deriving room-temperature superconductivity conditions cite this as the base pairing energy scale in the phi-ladder quantization. The definition is a direct assignment realizing the self-similar fixed point without further computation.
Claim. $E_{coh} = phi^{-5}$ in RS-native units, where $phi$ is the self-similar fixed point satisfying the Recognition Composition Law.
background
The module EN-002 derives superconductivity conditions at ambient temperature and pressure from the phi-ladder energy structure. Pairing requires binding energy at least k_B T, with energies quantized as E_n = E_coh * phi^n. The coherence quantum supplies the fundamental scale exceeding thermal energy at 300 K (0.026 eV), enabling coherent ledger states to support room-temperature superconductivity under structural conditions on electron-phonon coupling.
proof idea
The declaration is a direct definition assigning the real number phi raised to the integer power negative five. No lemmas or tactics are applied beyond the built-in real exponentiation.
why it matters
This definition anchors the EN-002 hierarchy by supplying the base energy for T_c = E_coh * phi^n / k_B and the coherence condition. It realizes the phi fixed point from T6 in the forcing chain and supports the claim that E_coh exceeds room-temperature thermal energy. It feeds sibling results such as rs_coherence_quantum_pos and superconducting_gap_positive.
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