propagation_implies_equal_speed
The theorem records that assuming gravitational propagation speed matches the RS light speed in native units immediately yields their equality. Researchers formalizing unified ledger propagation for gravity and electromagnetism would cite this structural marker. The proof is a direct term application of the supplied hypothesis with no additional steps.
claimIf the gravitational propagation speed in RS units equals the electromagnetic speed, then $c_{grav,RS}=c_{RS}$.
background
The module addresses G-007 on whether gravity propagates at exactly c. Both light and gravity are defined on the same ledger substrate with identical tick rate, so their speed limits coincide in RS-native units where c=1. The fundamental time quantum is the tick τ₀=1, and c_RS is given by the two-sided 8-tick washout prefactor (1−φ^{-8})^2.
proof idea
The proof is a one-line term wrapper that returns the hypothesis h.
why it matters in Recognition Science
The marker fills the structural equality step for registry item G-007. It rests on the shared tick substrate and eight-tick octave (T7) from the forcing chain, confirming c_grav equals c_EM once the common rate is fixed. No downstream theorems are recorded.
scope and limits
- Does not derive an independent value for c_grav_RS.
- Does not treat propagation outside RS-native units.
- Does not incorporate corrections from non-ledger models.
formal statement (Lean)
41theorem propagation_implies_equal_speed (h : c_grav_RS = c_RS) :
42 c_grav_RS = c_RS :=
proof body
Term-mode proof.
43 h
44
45/-- When both speeds are defined from the same tick rate, their ratio is 1. -/