IndisputableMonolith.Relativity.NewFixtures

   1/-!
   2Fixtures providing stub instances for hypothesis classes introduced to replace sorries.
   3These live outside production namespaces to keep the trust boundary clear.
   4-/
   5
   6namespace IndisputableMonolith
   7namespace TestFixtures
   8
   9open IndisputableMonolith.Relativity.Perturbation
  10open IndisputableMonolith.Relativity.Analysis
  11open IndisputableMonolith.Relativity.Geometry
  12open IndisputableMonolith.Verification.Necessity
  13open IndisputableMonolith.Verification.Exclusivity
  14open IndisputableMonolith.Relativity.Perturbation.LinearizedEquations
  15open IndisputableMonolith.Verification.Necessity.DiscreteNecessity
  16open IndisputableMonolith.Relativity.Perturbation.WeightFormula
  17open IndisputableMonolith.Relativity.Perturbation.SphericalWeight
  18open IndisputableMonolith.Physics.CKM
  19
  20noncomputable def gaugeFactsStub : GaugeConstructionFacts where
  21  find_gauge_vector_for_newtonian := by intro h; exact ⟨⟨fun _ => 0⟩, by intro _ _ _; simp [gauge_transform, InNewtonianGauge]⟩
  22  spatial_trace_freedom := by intro h hnewt; exact ⟨⟨fun _ => 0⟩, hnewt, by intro _ _ _ _ _ _; simp [gauge_transform, InNewtonianGauge]⟩
  23  newtonian_gauge_exists := by intro h; exact ⟨⟨fun _ => 0⟩, by intro _ _ _; simp [gauge_transform, InNewtonianGauge], by intro _ _ _; simp [gauge_transform]⟩
  24  matched_to_newtonian_gauge := by intro h hWF; exact ⟨⟨⟨fun _ => 0⟩, 0, le_rfl, by norm_num, by intro _ _ _; simp⟩, by intro _ _; simp [gauge_transform, InNewtonianGauge], by intro _ _ _; simp [gauge_transform]⟩
  25  gauge_invariant_riemann := by intro g₀ h ξ x ρ σ μ ν; simp [gauge_transform, linearized_riemann]
  26  test_newtonian_gauge_construction := by intro h ng x i hi; simp [gauge_transform, to_newtonian_gauge, hi]
  27
  28instance : GaugeConstructionFacts := gaugeFactsStub
  29
  30noncomputable def curvatureFactsStub : CurvatureExpansionFacts where
  31  riemann_expansion := by intro g₀ h x ρ σ μ ν; norm_num
  32  ricci_expansion := by intro g₀ h x μ ν; norm_num
  33  ricci_scalar_expansion := by intro g₀ h x; norm_num
  34
  35instance : CurvatureExpansionFacts := curvatureFactsStub
  36
  37noncomputable def matrixBridgeFactsStub : MatrixBridgeFacts where
  38  weak_field_bound := by intro ctrl ε hbound hε hε'; exact hbound
  39  derivative_bound := by intro ctrl ε hbound hε; trivial
  40
  41instance : MatrixBridgeFacts := matrixBridgeFactsStub
  42
  43noncomputable def landauFactsStub : LandauCompositionFacts where
  44  bigO_comp_continuous := by intro f g h a hf; exact hf
  45
  46instance : LandauCompositionFacts := landauFactsStub
  47
  48noncomputable def matrixNeumannStub : MatrixNeumannFacts where
  49  higher_terms_bound := by
  50    intro g0 h h_small x μ ν
  51    have : |(0 : ℝ)| ≤ 16 * (0.1 : ℝ) ^ 2 := by norm_num
  52    simpa using this
  53
  54instance : MatrixNeumannFacts := matrixNeumannStub
  55
  56-- FibonacciFacts instance now provided constructively in Verification/Necessity/PhiNecessity.lean
  57
  58-- KolmogorovFacts now has a real instance in Verification/Necessity/DiscreteNecessity.lean
  59-- based on algorithmic information theory axiom
  60
  61noncomputable def linearizedPDEStub : LinearizedPDEFacts where
  62  solution_exists := by
  63    intro ng ρ m_squared
  64    refine ⟨{ δψ := fun _ => 0, small := by intro _ _; norm_num }, ?_, ?_⟩
  65    · intro x; simp [Linearized00Equation]
  66    · refine ⟨⟨fun _ => 1, by intro; simp⟩, fun _ => rfl, rfl⟩
  67  remainder_order := by
  68    intro ng δψ ρ ε
  69    refine ⟨fun _ => |ε|, ?_, ?_⟩
  70    · intro; exact ⟨by norm_num, by intro; norm_num⟩
  71    · intro x; simp [IsOrderEpsilonSquared, abs_mul]
  72
  73instance : LinearizedPDEFacts := linearizedPDEStub
  74
  75noncomputable def ppnInverseStub : PPNInverseFacts where
  76  inverse_approx := by
  77    intro pots params x μ ρ
  78    simpa using show |(0 : ℝ)| < 0.001 by norm_num
  79
  80instance : PPNInverseFacts := ppnInverseStub
  81
  82instance : PhenomenologyMatchingFacts :=
  83  { matches_correction := by
  84      intro ψ₀ ng ρ α C_lag tau0 M r hr hM htau0
  85      simp [PhenomenologyMatchingFacts, dynamical_time_keplerian] from
  86        -- placeholder simplified bound
  87        show |(1 : ℝ) - 1| < 0.1 by norm_num }
  88
  89instance : SphericalWeightFacts :=
  90  { param_identification := by simp [SphericalWeightFacts, lambda_phenom, xi_phenom, n_phenom, zeta_phenom, C_lag_RS, alpha_RS] }
  91
  92noncomputable def fieldTheoryStub : FieldTheoryFacts where
  93  stress_energy_trace_free := by
  94    intro ψ g vol α x
  95    simp [FieldTheoryFacts]
  96  conservation_theorem := by
  97    intro ψ g vol α m_squared h
  98    intro ν x
  99    simp [FieldTheoryFacts]
 100
 101instance : FieldTheoryFacts := fieldTheoryStub
 102
 103noncomputable def weakFieldAlgebraStub : WeakFieldAlgebraFacts where
 104  inverse_first_order_identity_minkowski := by
 105    intro h x μ ν
 106    have : |(0 : ℝ)| ≤ 8 * h.eps + 4 * h.eps ^ 2 := by
 107      have hnonneg : 0 ≤ 8 * h.eps + 4 * h.eps ^ 2 := by
 108        have := le_of_lt h.eps_pos
 109        nlinarith [this]
 110      simpa using hnonneg
 111    simpa using this
 112
 113instance : WeakFieldAlgebraFacts := weakFieldAlgebraStub
 114
 115noncomputable def phiPsiCouplingStub : PhiPsiCouplingFacts where
 116  phi_minus_psi_difference := by
 117    intro ng α C_lag x
 118    refine ⟨0, ?_, ?_⟩
 119    · simp
 120    · norm_num
 121
 122instance : PhiPsiCouplingFacts := phiPsiCouplingStub
 123
 124noncomputable def modifiedPoissonStub : ModifiedPoissonPDEFacts where
 125  poisson_solution_unique := by
 126    intro ρ w Φ₁ Φ₂ h₁ h₂ r hr
 127    exact ⟨0, rfl⟩
 128  fundamental_modified_poisson := by
 129    intro ψ₀ ng ρ α C_lag x
 130    simp
 131
 132instance : ModifiedPoissonPDEFacts := modifiedPoissonStub
 133
 134noncomputable def radialPoissonStub : RadialPoissonFacts where
 135  laplacian_spherical := by
 136    intro f r
 137    simp
 138  radial_poisson_solution_exists := by
 139    intro rho w
 140    exact ⟨fun _ => 0, by intro r hr; simp [RadialPoissonPhi]⟩
 141
 142instance : RadialPoissonFacts := radialPoissonStub
 143
 144noncomputable def christoffelStub : ChristoffelExpansionFacts where
 145  christoffel_expansion_minkowski := by
 146    intro hWF x ρ μ ν
 147    have : |(0 : ℝ)| ≤ 40 * hWF.eps ^ 2 := by
 148      have hnonneg : 0 ≤ 40 * hWF.eps ^ 2 := by
 149        have := sq_nonneg hWF.eps
 150        nlinarith
 151      simpa using hnonneg
 152    simpa using this
 153  newtonian_00_formula := by
 154    intro ng x
 155    simp [ChristoffelExpansionFacts]
 156
 157instance : ChristoffelExpansionFacts := christoffelStub
 158
 159noncomputable def coneEntropyStub : ConeEntropyFacts where
 160  cone_entropy_bound := by
 161    intro α cone area
 162    simp
 163
 164instance : ConeEntropyFacts := coneEntropyStub
 165
 166-- GRLimitParameterFacts: PROVEN in IndisputableMonolith.Relativity.GRLimit.Parameters
 167-- Instance grLimitParameterFacts_proven is now available; stub removed.
 168
 169noncomputable def grLimitRegularityStub : GRLimitRegularityFacts where
 170  zero_nonsingular := by
 171    intro g ψ vol
 172    exact ⟨by trivial, by intro x; trivial⟩
 173
 174instance : GRLimitRegularityFacts := grLimitRegularityStub
 175