IndisputableMonolith.Physics.CasimirTechnologyCertificates

   1import Mathlib
   2import IndisputableMonolith.QFT.CasimirPhiCorrections
   3
   4/-!
   5# Casimir Technology Certificates
   6
   7This module records the invention surface opened by the RS Casimir
   8formalization.  These are patent-facing MODEL/HYPOTHESIS objects, not
   9theorem-level claims about deployed devices.
  10-/
  11
  12namespace IndisputableMonolith
  13namespace Physics
  14namespace CasimirTechnologyCertificates
  15
  16open QFT.CasimirPhiCorrections
  17open QFT.CasimirPlateModes
  18open CasimirEffectCertV2
  19
  20noncomputable section
  21
  22/-- Technology families suggested by boundary-mode engineering. -/
  23inductive CasimirTechnology where
  24  | phiTunedMemsAntiStiction
  25  | repulsiveCasimirBearing
  26  | dynamicCasimirPhotonSource
  27  | casimirQubitShield
  28  | boundaryConditionCatalysis
  29  | vacuumModeThermalDiode
  30  | nanoscaleMetrology
  31  | sealedMicroActuator
  32  deriving DecidableEq, Repr, Fintype
  33
  34/-- The plan calls for eight technology families. -/
  35theorem technologyFamilyCount :
  36    Fintype.card CasimirTechnology = 8 := by
  37  decide
  38
  39/-- All technology lanes remain below theorem status until experiments close the
  40relevant material-response hypotheses. -/
  41def technologyStatus (_t : CasimirTechnology) : ClaimStatus :=
  42  ClaimStatus.hypothesis
  43
  44/-- Falsifier data common to technology hypotheses. -/
  45structure TechnologyFalsifier where
  46  observable : String
  47  predictedDirection : String
  48  falsificationCondition : Prop
  49
  50/-- Patent-facing technology claim. -/
  51structure TechnologyClaim where
  52  family : CasimirTechnology
  53  status : ClaimStatus
  54  model : PhiCorrectionModel
  55  designInput : PhiCorrectionInputs
  56  operatingPrinciple : String
  57  falsifier : TechnologyFalsifier
  58
  59/-- A well-tagged technology claim must be hypothesis- or model-level, not a
  60theorem claim. -/
  61def WellTaggedTechnologyClaim (C : TechnologyClaim) : Prop :=
  62  C.status = ClaimStatus.hypothesis ∨ C.status = ClaimStatus.model
  63
  64/-- The default status map produces well-tagged technology claims. -/
  65theorem default_status_well_tagged
  66    (family : CasimirTechnology) (model : PhiCorrectionModel)
  67    (input : PhiCorrectionInputs) (principle : String)
  68    (falsifier : TechnologyFalsifier) :
  69    WellTaggedTechnologyClaim
  70      { family := family
  71        status := technologyStatus family
  72        model := model
  73        designInput := input
  74        operatingPrinciple := principle
  75        falsifier := falsifier } := by
  76  unfold WellTaggedTechnologyClaim technologyStatus
  77  exact Or.inl rfl
  78
  79/-- Repulsive-bearing claims require a sign-reversal correction in the algebraic
  80model. -/
  81def RepulsiveBearingCondition
  82    (M : PhiCorrectionModel) (x : PhiCorrectionInputs) : Prop :=
  83  M.deltaPhi x < -1
  84
  85/-- Under the repulsive-bearing condition, the corrected pressure is positive. -/
  86theorem repulsive_bearing_pressure_positive
  87    (M : PhiCorrectionModel) (x : PhiCorrectionInputs)
  88    (h : RepulsiveBearingCondition M x) :
  89    0 < correctedPressure M x :=
  90  correctedPressure_repulsive_of_delta_lt_neg_one M x h
  91
  92/-- MEMS anti-stiction requires attraction suppression but not necessarily sign
  93reversal.  Algebraically this is the band `-1 < δφ < 0`. -/
  94def MemsAntiStictionCondition
  95    (M : PhiCorrectionModel) (x : PhiCorrectionInputs) : Prop :=
  96  -1 < M.deltaPhi x ∧ M.deltaPhi x < 0
  97
  98/-- Under MEMS anti-stiction conditions the pressure remains attractive but the
  99attraction is weaker than the ideal magnitude. -/
 100theorem mems_antistiction_remains_attractive
 101    (M : PhiCorrectionModel) (x : PhiCorrectionInputs)
 102    (h : MemsAntiStictionCondition M x) :
 103    correctedPressure M x < 0 :=
 104  correctedPressure_negative_of_delta_gt_neg_one M x h.1
 105
 106/-- Dynamic Casimir photon-source claims require nonzero boundary modulation. -/
 107structure DynamicCasimirCondition where
 108  modulationAmplitude : ℝ
 109  modulation_nonzero : modulationAmplitude ≠ 0
 110  phi_locked_schedule : Prop
 111
 112/-- Qubit-shield claims require a reduction in the effective decohering mode
 113inventory. -/
 114structure QubitShieldCondition where
 115  baselineDecoheringInventory : ℝ
 116  shieldedDecoheringInventory : ℝ
 117  baseline_pos : 0 < baselineDecoheringInventory
 118  shielded_pos : 0 < shieldedDecoheringInventory
 119  reduced_inventory : shieldedDecoheringInventory < baselineDecoheringInventory
 120
 121/-- Boundary-catalysis claims require a cavity-induced reduction in an activation
 122recognition cost. -/
 123structure BoundaryCatalysisCondition where
 124  uncavitiedActivationCost : ℝ
 125  cavitiedActivationCost : ℝ
 126  uncavitied_pos : 0 < uncavitiedActivationCost
 127  cavitied_pos : 0 < cavitiedActivationCost
 128  cost_reduced : cavitiedActivationCost < uncavitiedActivationCost
 129
 130/-- Thermal-diode claims require asymmetric corrected pressure or mode-transfer
 131response under orientation reversal. -/
 132structure ThermalDiodeCondition where
 133  forwardTransfer : ℝ
 134  reverseTransfer : ℝ
 135  rectification : forwardTransfer ≠ reverseTransfer
 136
 137/-- Metrology claims require pressure deviations to resolve a material or
 138geometry parameter. -/
 139structure MetrologyCondition where
 140  parameter : String
 141  baselinePressure : ℝ
 142  perturbedPressure : ℝ
 143  detectable_difference : baselinePressure ≠ perturbedPressure
 144
 145/-- Sealed microactuator claims require a controllable pressure difference. -/
 146structure MicroActuatorCondition where
 147  offPressure : ℝ
 148  onPressure : ℝ
 149  controllable_difference : offPressure ≠ onPressure
 150
 151/-- Technology certificate bundle. -/
 152structure TechnologyCert where
 153  family_count : Fintype.card CasimirTechnology = 8
 154  default_well_tagged :
 155    ∀ (family : CasimirTechnology) (model : PhiCorrectionModel)
 156      (input : PhiCorrectionInputs) (principle : String)
 157      (falsifier : TechnologyFalsifier),
 158      WellTaggedTechnologyClaim
 159        { family := family
 160          status := technologyStatus family
 161          model := model
 162          designInput := input
 163          operatingPrinciple := principle
 164          falsifier := falsifier }
 165  repulsive_bearing_positive :
 166    ∀ (M : PhiCorrectionModel) (x : PhiCorrectionInputs),
 167      RepulsiveBearingCondition M x → 0 < correctedPressure M x
 168  mems_remains_attractive :
 169    ∀ (M : PhiCorrectionModel) (x : PhiCorrectionInputs),
 170      MemsAntiStictionCondition M x → correctedPressure M x < 0
 171
 172/-- Certificate for the patent-facing technology taxonomy. -/
 173def technologyCert : TechnologyCert where
 174  family_count := technologyFamilyCount
 175  default_well_tagged := default_status_well_tagged
 176  repulsive_bearing_positive := repulsive_bearing_pressure_positive
 177  mems_remains_attractive := mems_antistiction_remains_attractive
 178
 179end
 180
 181end CasimirTechnologyCertificates
 182end Physics
 183end IndisputableMonolith
 184