lambda_0
plain-language theorem explainer
The declaration supplies the bare electron-phonon coupling at φ-rung zero as a material-calibrated real parameter for hydride models. Researchers optimizing high-Tc compounds such as H₃S and LaH₁₀ cite it when fixing the base value before φ^k scaling in the McMillan formula. The definition is realized as a one-line identity that returns the supplied input unchanged.
Claim. Let λ₀ : ℝ → ℝ be the bare electron-phonon coupling at φ-rung zero, defined by λ₀(lam) := lam where lam is a material-specific constant (near 1 for H₃S, near 2 for LaH₁₀).
background
In the hydride superconductor module the electron-phonon coupling at rung k is written λ_k = λ₀ · φ^k. The bare λ₀ is held fixed while the integer rung k becomes the sole free parameter in the T_c optimization. This rests on the McMillan formula T_c(k) = (ω_p(k)/1.2) exp(−1.04(1+λ_k)/(λ_k − μ*)) together with the φ-ladder imported from PhiLadderPhononResonance.
proof idea
The definition is a one-line identity that directly returns the input parameter as the bare coupling value.
why it matters
It supplies the base coupling for the lambda_at_rung construction and the T_c optimization theorems that follow in the same module. The definition thereby supports the reduction of the hydride landscape to a single integer rung search, consistent with the Recognition Science φ-ladder scaling and the RS_PAT_010 claim.
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