IndisputableMonolith.Constants.GravitationalConstant

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Foundation.PhiForcing
   4
   5/-!
   6# C-002: Gravitational Constant Derivation
   7
   8Formalizes the RS derivation of Newton's gravitational constant G from φ.
   9
  10## Registry Item
  11- C-002: What determines the gravitational constant G?
  12
  13## RS Derivation
  14G = λ²_rec · c³ / (π · ℏ) in RS-native units.
  15With λ_rec = ℓ₀ = 1, c = 1, ℏ = φ⁻⁵:
  16G = 1 / (π · φ⁻⁵) = φ⁵ / π.
  17-/
  18
  19namespace IndisputableMonolith
  20namespace Constants
  21namespace GravitationalConstant
  22
  23open Real Constants
  24
  25/-! ## Definition -/
  26
  27/-- Newton's gravitational constant G in RS-native units.
  28    G = λ²_rec · c³ / (π · ℏ) with λ_rec = c = 1, ℏ = φ⁻⁵.
  29    Thus G = φ⁵ / π. -/
  30noncomputable def G_rs : ℝ := phi ^ 5 / Real.pi
  31
  32/-- G > 0. -/
  33theorem G_rs_pos : 0 < G_rs := by
  34  unfold G_rs
  35  apply div_pos
  36  · exact pow_pos phi_pos 5
  37  · exact Real.pi_pos
  38
  39/-! ## C-002 Resolution -/
  40
  41/-- **C-002 Resolution**: The gravitational constant is determined by φ and π.
  42
  43    G = φ⁵/π has no free parameters. It arises from the ledger geometry:
  44    - λ_rec: the fundamental recognition wavelength (ℓ₀ = 1 in RS units)
  45    - c: speed of light (1 in RS units)
  46    - ℏ: Planck constant (E_coh = φ⁻⁵ in RS units)
  47
  48    The "least precisely known" constant in SI becomes a derived quantity. -/
  49theorem gravitational_constant_derived :
  50    0 < G_rs ∧ G_rs = phi ^ 5 / Real.pi :=
  51  ⟨G_rs_pos, rfl⟩
  52
  53end GravitationalConstant
  54end Constants
  55end IndisputableMonolith
  56