phi_critical_energy
plain-language theorem explainer
phi_critical_energy defines the critical energy scale for the J-cost phase transition model as J(phi). Condensed matter researchers in the Recognition Science framework cite it when deriving superconducting transition temperatures from the self-similar fixed point. The declaration is a direct one-line definition that applies the J_cost function at phi.
Claim. The critical energy scale is defined by $J_c = J(phi)$ where $J(x) = (x + x^{-1})/2 - 1$.
background
The J_cost function is defined as J(x) = (x + x^{-1})/2 - 1 and encodes the canonical cost appearing in the Recognition Composition Law. In the JCostPhaseTransition module this definition supplies the energy scale for phase transitions at the golden-ratio fixed point phi. Upstream results include the scale function phi^k from cosmology and the gap function F(Z) = ln(1 + Z/phi)/ln(phi) from the RSBridge anchor derivations.
proof idea
This is a one-line definition that directly applies the J_cost function to the constant phi.
why it matters
This definition supplies the energy scale used to define T_critical := phi_critical_energy * 1000 and to prove the numeric bounds 0.09 < phi_critical_energy < 0.12. It connects the J-uniqueness property from the forcing chain (T5) to condensed-matter predictions and fills the phase-transition step that feeds the large-scale structure and mass-anchor results.
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