IndisputableMonolith.Foundation.OptionAEmpiricalActionPlan

   1import Mathlib
   2import IndisputableMonolith.Foundation.OptionAEmpiricalSchedule
   3
   4/-!
   5# Option A Empirical Action Plan
   6
   7Concrete analysis action classes for the scheduled Option A empirical tests.
   8The schedule says what to run first; this file says what kind of computation
   9each scheduled test requires.
  10
  11Lean status: 0 sorry, 0 axiom.
  12-/
  13
  14namespace IndisputableMonolith
  15namespace Foundation
  16namespace OptionAEmpiricalActionPlan
  17
  18open OptionAFalsifierRegistry
  19open OptionAEmpiricalProtocol
  20open OptionAEmpiricalQueue
  21open OptionAEmpiricalSchedule
  22
  23/-- Coarse computational action needed to test a protocol. -/
  24inductive AnalysisAction where
  25  | fitFactorModel
  26  | fitDiscreteCollapse
  27  | plateauDetection
  28  | countRegulatoryStates
  29  | estimatePhiPowerRatio
  30  | trainMultiaxisDecoder
  31  | fitSharedResponseCoefficient
  32  | benchmarkCircuitAddressing
  33  | orderProgressionTest
  34  deriving DecidableEq, Repr, Fintype
  35
  36theorem analysisAction_count : Fintype.card AnalysisAction = 9 := by
  37  decide
  38
  39/-- Action required by each implemented Option A combination. -/
  40def analysisAction : CombinationID → AnalysisAction
  41  | .c3OncologyTensor => .fitFactorModel
  42  | .c8MillerSpan => .fitDiscreteCollapse
  43  | .c5AttentionTensor => .plateauDetection
  44  | .c9RegulatoryCeiling => .countRegulatoryStates
  45  | .c2PlanetStrata => .estimatePhiPowerRatio
  46  | .c1CognitiveTensor => .trainMultiaxisDecoder
  47  | .c7UniversalResponse => .fitSharedResponseCoefficient
  48  | .c4QuantumMolecularDepth => .benchmarkCircuitAddressing
  49  | .c6EriksonReverse => .orderProgressionTest
  50
  51theorem analysisAction_injective : Function.Injective analysisAction := by
  52  intro a b h
  53  cases a <;> cases b <;> simp [analysisAction] at h ⊢
  54
  55theorem c3_action :
  56    analysisAction .c3OncologyTensor = .fitFactorModel := rfl
  57
  58theorem c8_action :
  59    analysisAction .c8MillerSpan = .fitDiscreteCollapse := rfl
  60
  61theorem c5_action :
  62    analysisAction .c5AttentionTensor = .plateauDetection := rfl
  63
  64theorem c9_action :
  65    analysisAction .c9RegulatoryCeiling = .countRegulatoryStates := rfl
  66
  67theorem c2_action :
  68    analysisAction .c2PlanetStrata = .estimatePhiPowerRatio := rfl
  69
  70/-- Every scheduled first-pass item has an analysis action. -/
  71def HasAnalysisAction (c : CombinationID) : Prop :=
  72  ∃ a : AnalysisAction, analysisAction c = a
  73
  74theorem hasAnalysisAction_all (c : CombinationID) :
  75    HasAnalysisAction c := by
  76  exact ⟨analysisAction c, rfl⟩
  77
  78theorem scheduled_has_analysis_action
  79    {c : CombinationID} (_h : c ∈ firstPassSchedule) :
  80    HasAnalysisAction c :=
  81  hasAnalysisAction_all c
  82
  83/-- First-pass actions in schedule order. -/
  84def firstPassActions : List AnalysisAction :=
  85  firstPassSchedule.map analysisAction
  86
  87theorem firstPassActions_eq :
  88    firstPassActions =
  89      [ .fitFactorModel
  90      , .fitDiscreteCollapse
  91      , .plateauDetection
  92      , .countRegulatoryStates
  93      , .estimatePhiPowerRatio
  94      ] := by
  95  decide
  96
  97theorem firstPassActions_length :
  98    firstPassActions.length = 5 := by
  99  rw [firstPassActions_eq]
 100  decide
 101
 102theorem firstPassActions_nodup :
 103    firstPassActions.Nodup := by
 104  rw [firstPassActions_eq]
 105  decide
 106
 107structure EmpiricalActionPlanCert where
 108  nine_actions : Fintype.card AnalysisAction = 9
 109  action_injective : Function.Injective analysisAction
 110  c3_first_action : analysisAction .c3OncologyTensor = .fitFactorModel
 111  c8_second_action : analysisAction .c8MillerSpan = .fitDiscreteCollapse
 112  c5_third_action : analysisAction .c5AttentionTensor = .plateauDetection
 113  scheduled_actions : ∀ {c : CombinationID}, c ∈ firstPassSchedule → HasAnalysisAction c
 114  first_pass_actions :
 115    firstPassActions =
 116      [ .fitFactorModel
 117      , .fitDiscreteCollapse
 118      , .plateauDetection
 119      , .countRegulatoryStates
 120      , .estimatePhiPowerRatio
 121      ]
 122  first_pass_actions_length : firstPassActions.length = 5
 123  first_pass_actions_nodup : firstPassActions.Nodup
 124
 125def empiricalActionPlanCert : EmpiricalActionPlanCert where
 126  nine_actions := analysisAction_count
 127  action_injective := analysisAction_injective
 128  c3_first_action := c3_action
 129  c8_second_action := c8_action
 130  c5_third_action := c5_action
 131  scheduled_actions := scheduled_has_analysis_action
 132  first_pass_actions := firstPassActions_eq
 133  first_pass_actions_length := firstPassActions_length
 134  first_pass_actions_nodup := firstPassActions_nodup
 135
 136end OptionAEmpiricalActionPlan
 137end Foundation
 138end IndisputableMonolith
 139