equilibria
plain-language theorem explainer
The equilibria of an octave are the states at which its strain functional is balanced. Researchers modeling recurring patterns across scales in recognition-based physics would cite this when locating stable configurations within a given octave. The definition is realized as a direct alias to the balanced states of the octave's strain functional.
Claim. Let $O$ be an octave with state space and strain functional $S$. The equilibrium states of $O$ are the set of states $x$ such that $S$ is balanced at $x$.
background
In the RRF core an octave is an abstract scale of manifestation in which the same recognition pattern recurs at different levels. Its state space is drawn from a discrete 2D Galerkin truncation, and the strain functional assigns a cost whose balanced points are the equilibria. The module treats the octave as a structure with its own display channels and defers any concrete scaling to a separate hypothesis on the phi-ladder.
proof idea
This definition is a one-line alias that directly references the equilibria set of the underlying strain functional.
why it matters
The definition supplies the equilibrium set consumed by octave morphism composition and by the minimizer predicate in the strain module. It is used downstream to identify primes as recognition equilibria with unit cost and to transfer order properties across octaves. Within the framework it anchors the eight-tick octave period by marking the fixed points of strain dynamics at each scale.
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