N_galactic
N_galactic gives the phi-ladder rung count separating the fundamental RS tick from the galactic memory timescale. Galaxy dynamics modelers using Recognition Science to predict the acceleration scale a0 would cite this when calibrating the forcing chain. The definition is a direct application of the logarithm base phi to the ratio of the two timescales.
claim$N = log_φ(τ★ / τ₀)$ where τ★ is the galactic memory timescale in seconds and τ₀ is the fundamental RS tick in seconds.
background
The module GalacticTimescale sets tau_star_s to 133 million years converted to seconds and tau0_SI to the SI value 7.3e-15 seconds. Phi is the self-similar fixed point imported from PhiForcing. The definition extracts the continuous rung count on the phi-ladder between these two calibrated timescales.
proof idea
One-line definition that applies the change-of-base formula for logarithms to the ratio tau_star_s / tau0_SI.
why it matters in Recognition Science
N_galactic supplies the exact rung count used by the downstream theorem N_galactic_approx to establish the integer bounds 140 < N < 145. It also feeds galactic_status and the amplitude bounds in GravityParameters. This realizes the timescale constraint linking a0 and r0, consistent with the phi-forcing chain.
scope and limits
- Does not derive the galactic timescale from the forcing chain.
- Does not prove that N is an integer.
- Does not invoke the Recognition Composition Law or J-uniqueness.
formal statement (Lean)
27def N_galactic : ℝ := Real.log (tau_star_s / tau0_SI) / Real.log phi
proof body
Definition body.
28
29/-- **THEOREM: N_galactic Approximation** -/