is_locked_regime
plain-language theorem explainer
The definition marks the locked regime as all scales Q satisfying Q ≤ Q_lock. Researchers modeling the transition from running couplings to geometric fixed points in Recognition Science would reference this predicate to delineate the eight-beat plateau. It is introduced as a direct comparison against the precomputed lock-in scale.
Claim. The locked regime at scale $Q$ is the statement $Q ≤ Q_{lock}$, where $Q_{lock}$ is the fundamental recognition scale $Q_{lock} = ħ / ℓ_0$.
background
The Coupling Lock-in module formalizes the shift from continuous RG flow to discrete geometric locking at the eight-beat plateau. Q_lock is defined as the effective scale at the base length ell0, serving as the boundary below which the discrete cycle halts further running. The module doc states this transition maintains the geometric value of the coupling.
proof idea
The declaration is a direct definition expressing the regime condition as the inequality Q ≤ Q_lock, where Q_lock is the sibling definition effective_scale ell0.
why it matters
This predicate supports the transition to locked couplings, enabling statements about alpha_locked and alpha_lock_at_scale in the same module. It fills the scaffold for eight-beat plateau dominance, where the discrete cycle prevents further running below Q_lock, connecting to the T7 eight-tick octave in the forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.