beta
plain-language theorem explainer
beta supplies the inverse temperature factor β = 1/(k_B T) that weights ledger configurations in the partition function sum. Thermodynamic derivations and crystal-lattice calculations in the Recognition framework cite it to convert positive temperature into the exponential decay scale for J-cost. The definition is realized as a direct one-line division by the imported Boltzmann constant.
Claim. The inverse temperature is defined by $β(T) := 1/(k_B T)$ for real $T > 0$, where $k_B$ is the Boltzmann constant.
background
The THERMO-002 module constructs the partition function Z as a sum over ledger configurations weighted by their J-cost, with all thermodynamic potentials recovered from derivatives of ln Z. The inverse temperature β enters the weighting factor exp(-β E_i) that selects actualized states via the Actualization operator A. k_B is taken from ComputationLimitsStructure as the constant satisfying the Landauer bound k_B T ln(2) for the minimum energy cost of bit erasure.
proof idea
Direct definition. It applies the imported k_B from Information.ComputationLimitsStructure to the supplied positive temperature T.
why it matters
beta supplies the temperature scaling required by the ledger-sum partition function of THERMO-002 and is invoked by downstream crystal-symmetry constraints and environmental-pressure rescalings in the Chemistry module. The construction aligns with the RS derivation of statistical mechanics from J-cost minimization and the phi-ladder energy quantization. It closes the link between the fundamental period T and the exponential ensemble weighting without introducing additional hypotheses.
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