T_critical
plain-language theorem explainer
T_critical defines the phase transition temperature scale as one thousand times the critical energy obtained by evaluating the J-cost at the golden ratio. Condensed matter researchers modeling phi-structured superconductors cite this scaling when deriving critical temperatures in the 80-120 K band. The definition is a direct one-line scaling of the upstream phi_critical_energy value.
Claim. The critical temperature scale satisfies $T_c = 1000 E_φ$, where $E_φ$ is the energy obtained by evaluating the J-cost function at the golden ratio $φ$.
background
In this module the J-cost function measures the recognition cost of a scaling parameter. The upstream phi_critical_energy is defined as the J-cost evaluated at phi and is described as the superconducting energy gap scale. This temperature definition supplies the scale for phase transitions inside recognition-based thermodynamic systems, connecting the energy scale to temperature via a fixed numerical factor.
proof idea
This is a one-line definition that multiplies the phi_critical_energy value by 1000.
why it matters
The definition supplies the critical temperature appearing in the sc_prediction theorem, which asserts that phi-structured lattices exhibit critical temperatures between 80 K and 120 K when the coherence energy matches phi^{-5}. It is also referenced inside the CoherenceThreshold structure, which marks the boundary between coherent (frozen) phases below T_critical and disordered phases above it. The scaling is consistent with the phi-ladder and self-similar fixed-point constructions of the Recognition Science framework.
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