IndisputableMonolith.Energy.VacuumPump

   1import Mathlib
   2import IndisputableMonolith.Flight.SolidState.VirtualRotor
   3
   4/-!
   5# RS Hypothesis: Vacuum Pump (Entropic Energy Generation)
   6
   7This module formalizes the thermodynamics of a Metric Engine acting as a generator.
   8
   9## The Mechanism: Entropic Pumping
  10Standard thermodynamics: Work → Heat (Entropy Increase).
  11RS thermodynamics: Ordering Vacuum → Heat Absorption (Entropy Decrease).
  12
  13The device acts as a "Maxwell's Demon" for the metric.
  14It sorts vacuum fluctuations (lowering J-cost) and pays for it by absorbing
  15thermal entropy from the environment.
  16
  17## Energy Balance
  18Input: Initial Pulse (Battery) + Thermal Heat (Environment).
  19Output: Ordered Vacuum (Thrust/Metric) + EMF (Electricity).
  20Net: Over-unity relative to *stored* fuel, but unity relative to *total* environment.
  21-/
  22
  23namespace IndisputableMonolith
  24namespace Energy
  25namespace VacuumPump
  26
  27open IndisputableMonolith.Flight.SolidState
  28
  29/-- The Entropic Pump condition: dS_vacuum < 0 implies dQ_env < 0 (cooling). -/
  30def EntropicCooling (delta_S_vacuum : ℝ) (delta_Q_env : ℝ) : Prop :=
  31  delta_S_vacuum < 0 → delta_Q_env < 0
  32
  33/-- The Self-Sustaining Threshold.
  34    The induced EMF must exceed the drive power required to maintain resonance. -/
  35def SelfSustaining (P_out P_drive : ℝ) : Prop :=
  36  P_out > P_drive
  37
  38/-- RS Hypothesis: Vacuum Power Scaling.
  39    Power output scales with the "Metric Stiffness" (coherence) and Frequency.
  40    P ~ f * sigma_gradient. -/
  41def VacuumPower (f : ℝ) (sigma_grad : ℝ) : ℝ :=
  42  f * sigma_grad -- Simplified scaling law
  43
  44/-- RS Falsifier: Runaway Acceleration.
  45    Without a load, the pump will accelerate until failure.
  46    This signature distinguishes it from conventional generators. -/
  47def RunawaySignature (load : ℝ) (rpm : ℝ) : Prop :=
  48  load = 0 → rpm > 0 -- RPM increases without bound (simplified)
  49
  50end VacuumPump
  51end Energy
  52end IndisputableMonolith
  53