wellPosed
plain-language theorem explainer
An octave is well-posed precisely when its state space contains at least one state whose strain satisfies the zero-total-cost balance condition. Researchers constructing concrete RRF models cite this definition to certify consistency of specific octave instances before proving transfer or equivalence properties. The declaration is introduced as a direct existential proposition over the state type and the balance predicate.
Claim. An octave structure $O$ is well-posed if there exists a state $x$ in the state space of $O$ such that the strain of $x$ has total cost zero.
background
The RRF Core Octave module treats an octave as a scale of manifestation in which the same pattern recurs at different levels, with scaling by powers of phi treated as a hypothesis rather than a definition. The state type is the discrete 2D Galerkin state at a fixed truncation level, while the balance predicate requires that total cost over the associated spacetime region equals zero. Upstream results supply the active-edge count per tick (equal to 1) and the actualization operator that selects a minimal J-cost configuration from the possibility set.
proof idea
The declaration is a direct definition that packages the existential statement over states satisfying the balance predicate.
why it matters
This definition is invoked to establish that the quadratic one-dimensional octave and the trivial octave are well-posed, and it is used in the equivalence theorem showing that octave morphisms preserve the property. It supplies the consistency check required for the abstract octave structure before physical constants or the phi-ladder are introduced, aligning with the eight-tick octave period and the ledger-balance requirement of the Recognition Science framework.
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