C_lag_eq_cLagLock_inv
plain-language theorem explainer
The equality fixes the lag coupling at phi to the negative fifth power using the canonical definition. Modelers of resonance weights in the gravity module cite it to set the coupling near 0.09 when bounding interpolation effects. The proof is a direct reflexivity step that confirms definitional identity with no further reduction.
Claim. $C_{lag} = phi^{-5}$
background
In the EightTickResonance module the lag coupling is introduced as the constant C_lag equal to phi inverse raised to the fifth power. This value enters bounds on resonance weights through the interpolation cost, which is at most one half. Upstream results supply the cost function as the J-cost of a recognition event from ObserverForcing and the derived cost from a multiplicative recognizer comparator.
proof idea
The proof is a one-line reflexivity that matches the definition of C_lag directly to the expression (phi inverse) raised to the fifth power.
why it matters
This equality anchors the lag coupling used in resonance weight bounds and frequency statements inside the eight-tick octave. It supplies the concrete value required by downstream siblings such as w_resonant and weight_reduction_at_resonance. The result sits inside the T7 period and phi-ladder constants of the Recognition Science framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.