IndisputableMonolith.CondensedMatter.JCostPhaseTransition
This module defines the canonical J-cost function and derived critical scales for phase transitions in the condensed matter sector of Recognition Science. Researchers modeling superconducting gaps or critical temperatures from the RS forcing chain would cite these objects. The module consists of definitions and basic properties of J(x) together with phi-critical and T-critical quantities.
claimThe canonical J-cost function is $J(x) = \frac{x + x^{-1}}{2} - 1$. Derived objects include the critical energy scale $\phi_{\text{critical energy}}$, the superconducting gap scale, and the critical temperature $T_{\text{critical}}$.
background
The module sits in the CondensedMatter domain and imports the Constants module whose sole content is the fundamental RS time quantum $\tau_0 = 1$ tick. Its central object is the J-cost function stated in the module doc-comment, which coincides with the T5 J-uniqueness expression $J(x) = \cosh(\log x) - 1$ from the UnifiedForcingChain. The module also introduces auxiliary scales (phi_critical_energy, sc_gap_scale, T_critical) that quantify phase-transition thresholds on the phi-ladder.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The definitions supply the J-cost object required by any downstream condensed-matter calculation that invokes the Recognition Composition Law or the phi-ladder mass formula. They implement the T5 J-uniqueness step and feed the sibling declarations that produce sc_prediction and related critical-value results.
scope and limits
- Does not derive J from the forcing chain axioms.
- Does not prove any uniqueness or minimality statements.
- Does not contain numerical evaluation or comparison with experiment.