isBalanced
plain-language theorem explainer
A state x under strain functional S satisfies equilibrium precisely when the assigned cost J(x) equals zero. Researchers formalizing RRF consistency, ledger balance, or equilibrium preservation under morphisms cite this predicate. The definition is realized as the direct equality check S.J x = 0.
Claim. Let $S$ be a strain functional on a state space. A state $x$ is balanced if the strain cost satisfies $J(x) = 0$.
background
In the RRF framework strain quantifies deviation from equilibrium, with the law that strain tends to zero. The StrainFunctional structure assigns a non-negative real cost J to each state, satisfying J(x) = 0 exactly when x is at equilibrium. This module supplies the abstract interface for such functionals, where lower strain corresponds to greater consistency and reality.
proof idea
This is a one-line definition that directly sets the strain value equal to zero.
why it matters
This supplies the zero-strain predicate used in JMinimizationLaw (existence of a balanced state) and in Glossary.isConsistent (low strain plus closed ledger). It instantiates the J → 0 law central to Recognition Science and is referenced by equilibrium-preservation results in the Octave module.
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