shared_coupling
In the eight-tick resonance model the lag coupling constant equals phi to the negative fifth power. Gravity derivations in Recognition Science cite this shared value across kernels. The proof reduces directly via reflexivity to the definition of the lag coupling.
claimThe lag coupling constant satisfies $C_{lag} = phi^{-5}$.
background
C_lag is defined as phi inverse to the fifth power, approximately 0.09, and serves as the RS-derived lag coupling in the gravity module. The EightTickResonance module develops resonance properties on top of constants imported from IndisputableMonolith.Constants. This result rests directly on the upstream definition of C_lag, which supplies the exact expression without additional hypotheses.
proof idea
The proof is a one-line wrapper that applies reflexivity to equate C_lag with its defining expression phi to the minus five.
why it matters in Recognition Science
This result anchors the shared coupling value for kernels in the eight-tick resonance, consistent with the T7 eight-tick octave in the forcing chain. It enables consistent gravity calculations by fixing the constant without further derivation. No immediate downstream theorems depend on it in the current graph.
scope and limits
- Does not establish the numerical value of phi from other constants.
- Does not extend the equality beyond the resonant frequency case.
- Does not provide error bounds or approximations for C_lag.
formal statement (Lean)
214theorem shared_coupling : C_lag = phi⁻¹ ^ 5 := rfl
proof body
One-line wrapper that applies end.
215
216end IndisputableMonolith.Gravity.EightTickResonance