IndisputableMonolith.Foundation.MaximalForcing.RSGravityUniverse

   1import IndisputableMonolith.Foundation.MaximalForcing.RealityClosure
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Maximal Forcing: the gravity layer (Phase 2 extension, Einstein coupling)
   6
   7Fifth single-constant instantiation, reaching the gravitational sector. Where the
   8alpha layer pins the electromagnetic coupling, this layer pins the gravitational
   9one: the Einstein field-equation coupling `κ = 8πG/c⁴`, evaluated in RS-native
  10units (`λ_rec = c = 1`, `ℏ = φ⁻⁵`), is forced to the pure number `8·φ⁵` with no
  11fitted parameter.
  12
  13* The realization carrier is a candidate Einstein-coupling value `k : ℝ`.
  14* The loose class `Lgrav0` is every candidate real.
  15* The gate class `LgravRS` pins `k` to the RS-native value `kappa_einstein`.
  16* The claim under closure is "k = 8·φ⁵".
  17
  18Over `LgravRS` the value claim is forced, wrapping the proved
  19`Constants.kappa_einstein_eq`. Over `Lgrav0` it is independent: the RS value
  20satisfies it, `0` does not (`8φ⁵ > 0`). The RS derivation of `G` from
  21`λ_rec, c, ℏ` does real work; the value `8φ⁵` is not assumed, it is forced.
  22
  23This is the gravitational analogue of `RSAlphaUniverse`: a derived physical
  24coupling forced to a parameter-free φ-expression.
  25-/
  26
  27namespace IndisputableMonolith
  28namespace Foundation
  29namespace MaximalForcing
  30
  31open IndisputableMonolith.Constants (phi kappa_einstein kappa_einstein_eq kappa_einstein_pos)
  32
  33/-- Loosest gravity class `Lgrav0`: every candidate coupling value. -/
  34def Lgrav0 : AdmissibilityClass ℝ where
  35  admissible := Set.univ
  36  label := "every candidate Einstein-coupling value"
  37
  38/-- Gate-tightened gravity class `LgravRS`: the candidate equals the RS-native
  39Einstein coupling `8πG/c⁴`. -/
  40def LgravRS : AdmissibilityClass ℝ where
  41  admissible := { k | k = kappa_einstein }
  42  label := "RS-native Einstein coupling: k = 8πG/c⁴"
  43
  44/-- `LgravRS` is a tightening of `Lgrav0`. -/
  45def tighten_Lgrav0_LgravRS : Tightening Lgrav0 LgravRS where
  46  subset := by intro a _; trivial
  47  strict_witness := True
  48
  49/-- The forced claim of the gravity layer: the coupling equals `8·φ⁵`. -/
  50def isKappaClaim : RealityClaim ℝ where
  51  label := "k = 8·φ^5 (Einstein coupling, parameter-free)"
  52  holds := fun k => k = 8 * phi ^ (5 : ℝ)
  53
  54/-- The gravity-layer claim universe. -/
  55def gravUniverse : ClaimUniverse where
  56  Realization := ℝ
  57  admissibility := LgravRS
  58  claims := { isKappaClaim }
  59
  60/-- **Einstein coupling as a forced invariant.** Over the RS-native gate, the
  61coupling equals `8·φ⁵`. Wraps `Constants.kappa_einstein_eq`; the only content is
  62the parameter-free RS derivation `G = λ_rec²c³/(πℏ)` with `ℏ = φ⁻⁵`. -/
  63theorem forced_kappa : Forced LgravRS.admissible isKappaClaim := by
  64  intro k hk
  65  have hk' : k = kappa_einstein := hk
  66  show k = 8 * phi ^ (5 : ℝ)
  67  rw [hk', kappa_einstein_eq]
  68
  69/-- The claim `isKappaClaim` is in the closure of the gravity universe. -/
  70theorem isKappaClaim_in_closure :
  71    InClosure Primitive.lawOfLogic gravUniverse isKappaClaim := by
  72  show isKappaClaim ∈ gravUniverse.claims
  73  exact Set.mem_singleton _
  74
  75/-- Forced-register entry for the Einstein coupling. -/
  76def gravForcedInvariant : ForcedInvariant Primitive.lawOfLogic gravUniverse where
  77  claim := isKappaClaim
  78  in_closure := isKappaClaim_in_closure
  79  forced := forced_kappa
  80
  81/-- The gravity-layer universe is fully classified. -/
  82theorem gravUniverse_classifier :
  83    ∀ C : RealityClaim gravUniverse.Realization,
  84      InClosure Primitive.lawOfLogic gravUniverse C → ClaimClassification gravUniverse C := by
  85  intro C hC
  86  have hCeq : C = isKappaClaim := Set.mem_singleton_iff.mp hC
  87  subst hCeq
  88  exact ClaimClassification.forced forced_kappa
  89
  90/-- A real `MaximalClosureCert` for the gravity-layer universe. -/
  91def gravUniverseCert : MaximalClosureCert Primitive.lawOfLogic gravUniverse where
  92  classifies := gravUniverse_classifier
  93
  94/-! ## The RS-native gate does real work -/
  95
  96/-- The forced value is strictly positive: `8φ⁵ > 0`. -/
  97theorem kappa_value_pos : 0 < 8 * phi ^ (5 : ℝ) := by
  98  rw [← kappa_einstein_eq]; exact kappa_einstein_pos
  99
 100/-- Over the loose class `Lgrav0`, the value claim is independent: the RS coupling
 101satisfies it, and `0` does not. -/
 102theorem kappa_independent_over_Lgrav0 :
 103    Independent Lgrav0.admissible isKappaClaim := by
 104  refine ⟨kappa_einstein, 0, ?_, ?_, ?_, ?_⟩
 105  · trivial
 106  · trivial
 107  · show kappa_einstein = 8 * phi ^ (5 : ℝ); exact kappa_einstein_eq
 108  · intro h
 109    have h0 : (0 : ℝ) = 8 * phi ^ (5 : ℝ) := h
 110    have hp := kappa_value_pos
 111    linarith
 112
 113/-- **The RS-native tightening is legitimate, not cheap.** The value claim is
 114independent over `Lgrav0` but forced over `LgravRS`. -/
 115theorem tightening_Lgrav0_LgravRS_effective :
 116    Independent Lgrav0.admissible isKappaClaim ∧
 117    Forced LgravRS.admissible isKappaClaim :=
 118  ⟨kappa_independent_over_Lgrav0, forced_kappa⟩
 119
 120end MaximalForcing
 121end Foundation
 122end IndisputableMonolith
 123