bcsDeltaTcRatio
plain-language theorem explainer
bcsDeltaTcRatio supplies the Recognition Science approximation to the BCS gap-to-critical-temperature ratio as 2 log φ + 1. Condensed-matter researchers deriving Tc families from the φ-ladder would cite this constant when comparing predictions to measured ratios in cuprates and iron-based compounds. The definition is realized as a direct algebraic expression that substitutes the golden-ratio constant from the CPM bundle.
Claim. The BCS ratio approximation is given by $2 ln φ + 1$, where $φ$ is the golden ratio constant drawn from the Recognition Science constants bundle.
background
The Superconducting Tc module derives critical temperatures from φ-ladder energy scales assigned to Cooper-pair gaps Δ. Conventional BCS materials occupy rungs n ≥ 6 with low Tc, MgB2 sits near n ≈ 5, iron-based compounds near n ≈ 4, and cuprates near n ≈ 2-3. The 8-tick coherence structure requires alignment for macroscopic superconductivity, and the BCS relation Tc ∝ Δ implies that φ-powers control Tc ratios between families. Constants.phi is the golden ratio (1 + √5)/2 taken from the CPM LawOfExistence bundle.
proof idea
The definition is a one-line algebraic expression that substitutes Constants.phi into 2 * Real.log φ + 1. No additional lemmas or tactics are invoked beyond the constant reference.
why it matters
This definition anchors the φ-derived BCS ratio approximation that is bounded in the downstream bcs_ratio_approx theorem. It fills the BCS Relation step in the CM-007 derivation, linking the self-similar fixed point φ to measurable superconducting gaps. The construction supports the module prediction that Tc ratios across families follow φ-power scalings.
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