IndisputableMonolith.Safety.DampeningField

   1import Mathlib
   2import IndisputableMonolith.Energy.VacuumPump
   3
   4/-!
   5# RS Safety: Dampening Field (Governor)
   6
   7This module formalizes the safety protocols for a Vacuum Pump / Metric Engine.
   8Because the device is an Open System, it is prone to "Runaway" (positive feedback).
   9
  10## The Danger
  11If P_out > P_drive, the excess energy feeds back into the rotation/field.
  12v → v + dv → P_out + dP → v + 2dv ...
  13Result: Mechanical failure or metric rupture.
  14
  15## The Solution: Active De-Tuning
  16To brake the engine, we do NOT use friction. We use **Phase Slip**.
  17We intentionally misalign the drive pulse from the 8-tick resonance.
  18This destroys the coherence, increasing C_lag, and killing the efficiency.
  19-/
  20
  21namespace IndisputableMonolith
  22namespace Safety
  23namespace DampeningField
  24
  25open IndisputableMonolith.Energy
  26
  27/-- The Governor Function.
  28    If RPM exceeds limit, introduce phase slip (delta_phi). -/
  29def Governor (rpm rpm_limit : ℝ) : ℝ :=
  30  if rpm > rpm_limit then
  31    0.1 -- Introduce 10% phase slip
  32  else
  33    0.0 -- Perfect resonance
  34
  35/-- Effect of Phase Slip on Efficiency.
  36    Efficiency drops exponentially with phase error. -/
  37def Efficiency (phase_error : ℝ) : ℝ :=
  38  Real.exp (-phase_error ^ 2)
  39
  40/-- Safety Theorem: De-tuning prevents runaway. -/
  41theorem DetuningStopsRunaway (rpm rpm_limit : ℝ) :
  42  let slip := Governor rpm rpm_limit
  43  let eff := Efficiency slip
  44  rpm > rpm_limit → eff < 1 := by
  45  intro slip eff h_over
  46  simp [slip, Governor, h_over]
  47  -- exp(-0.1^2) = exp(-0.01) < 1
  48  exact Real.exp_lt_one_iff.mpr (by norm_num)
  49
  50end DampeningField
  51end Safety
  52end IndisputableMonolith
  53