Governor
plain-language theorem explainer
Governor defines a piecewise function returning a fixed phase slip of 0.1 on RPM threshold violation and zero otherwise. Safety engineers modeling metric engines cite it to enforce active detuning in open systems. The definition is a direct conditional expression with no auxiliary lemmas.
Claim. The governor function is given by $G(r, r_0) = 0.1$ if $r > r_0$ and $G(r, r_0) = 0$ otherwise, where the nonzero output is the introduced phase slip $δ_φ$ that misaligns the drive from resonance.
background
The Safety.DampeningField module formalizes protocols for the Vacuum Pump / Metric Engine treated as an open system. Excess output power feeds back into rotation, producing runaway via the chain $v → v + dv → P_out + dP$. The solution replaces friction with intentional phase slip that raises $C_{lag}$ and destroys coherence in the eight-tick cycle. Upstream, EightTick.phase supplies the resonant phases $kπ/4$ for $k = 0..7$, while LedgerFactorization.of and PhiForcingDerived.of calibrate the underlying J-cost whose efficiency is degraded by the slip.
proof idea
The definition is a direct conditional that evaluates the boolean rpm > rpm_limit and returns the constant 0.1 or 0.0 accordingly. No tactics or upstream lemmas are invoked; the body is the primitive implementation that downstream theorems such as DetuningStopsRunaway consume directly.
why it matters
Governor supplies the concrete slip value to the DetuningStopsRunaway theorem, which proves that threshold violation forces efficiency strictly below 1. It realizes the active de-tuning strategy described in the module doc-comment, deliberately breaking the eight-tick octave (T7) resonance to prevent metric rupture. The construction sits inside the broader Recognition framework that derives D = 3 and the phi-ladder from the same forcing chain.
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