semanticFreeEnergy
plain-language theorem explainer
Semantic free energy is defined as reference cost reduced by attention-weighted entropy and Berry-weighted phase. Control theorists analyzing stability in the recognition bandwidth model cite it when deriving monotonicity bounds for the load ratio inside the sub-saturation band. The definition is a direct linear combination of the five real parameters with no further reduction or lemmas.
Claim. The semantic free energy is given by $F = C_{ref} - A S - W B$, where $C_{ref}$ is reference cost, $S$ is entropy, $A$ is the attention coefficient, $W$ is Berry weight, and $B$ is the Berry phase term.
background
The Critical Recognition Loading module sketches control lemmas for operation inside the narrow band rho_min < rho < 1, where rho = R_dem / R_max is the load ratio and stability is judged on the 360-tick supervisory horizon forced by lcm(8,45). Entropy is imported from upstream: proportional to total defect in InitialCondition, and thermodynamically as beta times average energy plus log of the partition function in BoltzmannDistribution and PartitionFunction.
proof idea
The definition is a one-line algebraic expression that subtracts the attention-scaled entropy term and the Berry-weighted term from the reference cost. No lemmas are invoked and no tactics are required.
why it matters
This definition supplies the functional whose monotonicity is proved in higher_berry_lowers_freeEnergy and higher_entropy_lowers_freeEnergy. It fills the query-level free-energy slot inside the critical recognition loading control theorem, linking attention and Berry phase to the eight-tick octave and recognition bandwidth. It leaves open explicit connection to the phi-ladder and full runtime deployment.
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