Efficiency
plain-language theorem explainer
The Efficiency definition supplies the functional dependence of dampening performance on phase misalignment in the RS safety governor. Safety engineers cite it when verifying that detuning halts positive feedback loops in metric engines. The definition is a direct Gaussian exponential that encodes the loss of coherence with increasing slip.
Claim. The efficiency of the dampening field is given by $E = e^{-δ^2}$, where $δ$ is the phase error introduced when the governor detects excess rotation.
background
The module formalizes safety protocols for the Vacuum Pump / Metric Engine, an open system prone to runaway when output power exceeds drive power. The solution uses active phase slip to misalign the drive pulse from the 8-tick resonance, destroying coherence and raising lag cost. Governor supplies the slip value (0.1 when rpm exceeds the limit, otherwise 0), and Efficiency converts that slip into a multiplicative efficiency factor.
proof idea
This is a one-line definition that applies the real exponential to the negation of the squared phase error.
why it matters
Efficiency is invoked inside DetuningStopsRunaway to prove that excess rpm forces efficiency below 1, and it appears in Governor and strict_transmutation_progress as the concrete cost-reduction mechanism. It closes the safety loop for the eight-tick resonance engine by quantifying how phase slip kills positive feedback. The definition directly supports the claim that de-tuning prevents runaway without mechanical friction.
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