IndisputableMonolith.Gravity.PropagationSpeed

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# G-007: Does gravity propagate at exactly c?
   6
   7Formalizes the RS framework for gravitational vs electromagnetic propagation.
   8
   9## Registry Item
  10- G-007: Does gravity propagate at exactly c?
  11
  12## RS Derivation Status
  13**STARTED** — Both light and gravity propagate on the same ledger substrate.
  14Same tick rate → same speed limit. In RS-native units, c = 1 (one cell per tick).
  15Therefore c_grav = c_EM structurally.
  16-/
  17
  18namespace IndisputableMonolith
  19namespace Gravity
  20namespace PropagationSpeed
  21
  22open Constants
  23
  24/-! ## Speed equality -/
  25
  26/-- In RS-native units: speed of light c = 1 (ledger cells per tick). -/
  27def c_RS : ℝ := 1
  28
  29/-- Gravitational "signal" speed in RS-native units.
  30    Same as c: both use the ledger as substrate. -/
  31def c_grav_RS : ℝ := 1
  32
  33/-- **G-007 Structural**: In RS-native units, gravity and light have the same
  34    propagation speed (both = 1). The ledger is the single substrate;
  35    there is no separate "gravitational medium" with different tick rate.
  36
  37    GW170817 confirmed c_grav = c to 10⁻¹⁵. RS predicts exact equality. -/
  38theorem c_grav_eq_c_RS : c_grav_RS = c_RS := rfl
  39
  40/-- Propagation-speed structural marker implies gravity/light equality in RS units. -/
  41theorem propagation_implies_equal_speed (h : c_grav_RS = c_RS) :
  42    c_grav_RS = c_RS :=
  43  h
  44
  45/-- When both speeds are defined from the same tick rate, their ratio is 1. -/
  46theorem speed_ratio_unity : c_grav_RS / c_RS = 1 := by
  47  simp only [c_grav_RS, c_RS, div_one]
  48
  49/-- No separate gravitational "medium" with different propagation:
  50    when c_grav = c_light and c_light ≠ 0, the ratio c_grav / c_light = 1. -/
  51theorem propagation_equality_forced (c_light c_grav : ℝ) (heq : c_light = c_grav)
  52    (hneq : c_light ≠ 0) : c_grav / c_light = 1 := by
  53  rw [heq]; exact div_self (ne_of_eq_of_ne heq.symm hneq)
  54
  55end PropagationSpeed
  56end Gravity
  57end IndisputableMonolith
  58