OctaveLoop
plain-language theorem explainer
An OctaveLoop is a map from the eight indices of a Fin 8 to states of type S together with the identification of the first and last state. Researchers modeling resonant geometries in coherence technology cite the structure when representing the closed eight-step recognition sequence. The declaration is a bare structure definition with no proof obligations.
Claim. An octave loop over a state space $S$ is a function $s : Fin 8 → S$ satisfying $s(0) = s(7)$.
background
Module CoherenceTechnology formalizes the impact of recognition-resonant geometries (φ-spirals, octave-loops) on biological stability. The golden ratio φ is the unique positive fixed point of the self-similar cost recursion; geometries that follow this ratio align with the fundamental scaling law of the ledger. Constants.octave states: 'One octave = 8 ticks: the fundamental evolution period.' MusicalScale.octave supplies the ratio 2. The supplied DOC_COMMENT defines the structure as a closed recognition sequence of exactly 8 steps.
proof idea
Structure definition; the two fields steps and closure are introduced directly with no lemmas or tactics applied.
why it matters
The structure supplies the type argument to the downstream theorem octave_loop_neutrality, which proves that a complete octave loop has zero net recognition flux (σ = 0). It realizes the eight-tick octave (T7) inside the applied coherence setting and supplies the closed sequence needed for neutrality calculations. No open scaffolding is closed by this definition.
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