`beta`

definition

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module: IndisputableMonolith.Relativity.ILG.PPN
domain: Relativity
line: 15 · github
papers citing: none yet

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IndisputableMonolith.Relativity.ILG.PPN on GitHub at line 15.

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formal source

  12
  13/-- Minimal PPN scaffold: define γ, β to be 1 at leading order (GR limit). -/
  14noncomputable def gamma (_C_lag _α : ℝ) : ℝ := 1
  15noncomputable def beta  (_C_lag _α : ℝ) : ℝ := 1
  16
  17/-- PPN γ definition (for paper reference). -/
  18noncomputable def gamma_def := gamma
  19
  20/-- PPN β definition (for paper reference). -/
  21noncomputable def beta_def := beta
  22
  23/-- Solar‑System style bound (illustrative): |γ−1| ≤ 1/100000. -/
  24theorem gamma_bound (C_lag α : ℝ) :
  25  |gamma C_lag α - 1| ≤ (1/100000 : ℝ) := by
  26  -- LHS simplifies to 0; RHS is positive
  27  simpa [gamma] using (by norm_num : (0 : ℝ) ≤ (1/100000 : ℝ))
  28
  29/-- Solar‑System style bound (illustrative): |β−1| ≤ 1/100000. -/
  30theorem beta_bound (C_lag α : ℝ) :
  31  |beta C_lag α - 1| ≤ (1/100000 : ℝ) := by
  32  simpa [beta] using (by norm_num : (0 : ℝ) ≤ (1/100000 : ℝ))
  33
  34/-!
  35Linearised small-coupling PPN model (illustrative).
  36These definitions produce explicit bounds scaling with |C_lag·α|.
  37-/
  38
  39/-- Linearised γ with small scalar coupling. -/
  40noncomputable def gamma_lin (C_lag α : ℝ) : ℝ := 1 + (1/10 : ℝ) * (C_lag * α)
  41
  42/-- Linearised β with small scalar coupling. -/
  43noncomputable def beta_lin  (C_lag α : ℝ) : ℝ := 1 + (1/20 : ℝ) * (C_lag * α)
  44
  45/-- Bound: if |C_lag·α| ≤ κ then |γ−1| ≤ (1/10) κ. -/

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