JMinimizationLaw
plain-language theorem explainer
The JMinimizationLaw encodes the existence of a zero-strain state for any strain functional S. Modelers of equilibrium conditions in recognition frameworks cite it as the statement that strain reaches zero. The definition is a direct existential assertion over the isBalanced predicate drawn from the Strain module.
Claim. Let $S$ be a strain functional on a state space. The J-minimization law asserts that there exists a state $x$ such that the strain cost $J(x)$ equals zero.
background
The RRF glossary module supplies canonical names for core objects: J denotes the strain or cost functional of a state, while isBalanced is the zero-strain predicate. The module positions these as the single source of truth for vocabulary across RRF files, with strain defined as deviation from balance and the J to zero law stated as the fundamental drive. Upstream results supply concrete realizations of State (discrete 2D Galerkin fields, lattice vorticity fields) and isBalanced (total cost zero in spacetime regions, J(x) exactly zero in the Strain module).
proof idea
This is a definition that directly encodes the existence of an equilibrium state satisfying the zero-strain condition. It applies the isBalanced predicate from the Strain module without further reduction or tactic steps.
why it matters
The declaration installs the core minimization principle that strain can be driven to zero, matching the J to zero law described in the module documentation. It supplies the abstract existence claim that ledger balance and equilibrium concepts in cosmology and relativity modules presuppose, even though no explicit downstream uses are recorded.
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