IndisputableMonolith.Thermodynamics.JCostBoltzmann
JCostBoltzmann certifies that the Gibbs weight at the ground state x=1 equals 1 and is maximal because J(1)=0. Researchers extending zero-temperature J-minimization to finite Recognition Temperature cite these weight properties. The results follow from direct substitution into the weight definition using the upstream J properties.
claimThe Gibbs weight $w$ satisfies $w(1)=1$, the maximum value, since $J(1)=0$.
background
The module belongs to the Thermodynamics domain and imports RecognitionThermodynamics. That parent module defines the statistical mechanics of Recognition Science by extending the T=0 cost minimization (J=0) to finite Recognition Temperature (TR) that parameterizes the strictness of J-minimization.
JCostBoltzmann introduces the J-cost Boltzmann weights and certifies their ground-state property as stated in the module doc comment.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
This module feeds the JCostBoltzmannCert into the Recognition Thermodynamics framework. It supplies the concrete weight calculations required by the statistical mechanics definitions in the upstream RecognitionThermodynamics module.
scope and limits
- Does not derive the partition function or free energy.
- Does not specify a value for Recognition Temperature TR.
- Does not address the phi-ladder or mass formulas.