Gravity Propagation Speed C Grav Eq C Rs

Speed equality

In Recognition Science, a framework that derives physical structure from a discrete record of events, the speed of light is set to one unit per tick. The declaration c_grav_eq_c_RS states that the gravitational signal speed equals this same value. Both light and gravity propagate on the same ledger substrate, a single discrete record of events, so there is no separate gravitational medium with a different tick rate. The equality is a definitional consequence, not an empirical finding.

The theorem is proved in the machine-checked library of formal theorems. It follows directly from the definitions: both speeds are assigned the value 1 in the framework's native units. The proof is a reflexivity step, meaning the statement holds by the very definitions of the two speeds. A companion theorem shows that when both speeds are defined from the same tick rate, their ratio is exactly 1. These results are internal to the framework; they do not invoke any measurement.

The framework's documentation notes that the gravitational wave event GW170817 confirmed the equality of gravitational and electromagnetic speeds to about 10⁻¹⁵. That confirmation is a physical measurement, not a theorem in the library. The framework predicts exact equality as a structural consequence, while the measurement provides empirical support within its uncertainty.

What the declaration does not claim: it does not assert that gravity propagates at exactly c in physical units as a derived theorem. It establishes equality in the framework's native units, where c is defined as 1. The translation to SI units, where c is approximately 299,792,458 meters per second, is not part of this declaration. The framework treats the equality as a structural fact about its own substrate, not as a derivation from more fundamental principles.

/-- In RS-native units: speed of light c = 1 (ledger cells per tick). -/
def c_RS : ℝ := 1

/-- **G-007 Structural**: In RS-native units, gravity and light have the same
    propagation speed (both = 1). The ledger is the single substrate;
    there is no separate "gravitational medium" with different tick rate.

    GW170817 confirmed c_grav = c to 10⁻¹⁵. RS predicts exact equality. -/
theorem c_grav_eq_c_RS : c_grav_RS = c_RS := rfl

/-- When both speeds are defined from the same tick rate, their ratio is 1. -/
theorem speed_ratio_unity : c_grav_RS / c_RS = 1 := by
  simp only [c_grav_RS, c_RS, div_one]

/-- **G-007 Structural**: In RS-native units, gravity and light have the same
    propagation speed (both = 1). The ledger is the single substrate;
    there is no separate "gravitational medium" with different tick rate.

    GW170817 confirmed c_grav = c to 10⁻¹⁵. RS predicts exact equality. -/
theorem c_grav_eq_c_RS : c_grav_RS = c_RS := rfl

What this page does not claim

The declaration does not prove gravity propagates at exactly c in SI units. It does not derive the speed equality from more fundamental principles beyond the definitional choice. It does not claim the framework's native unit system is physically realized.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/PropagationSpeed.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: