phi_rung_time
plain-language theorem explainer
phi_rung_time defines the timescale at rung N on the Recognition Science phi-ladder as tau0_SI multiplied by phi to the power N. Galactic dynamics researchers cite it when mapping observed periods such as stellar or rotation timescales to discrete phi-tiers. The definition is a direct algebraic scaling that inherits its SI calibration from the imported base tick tau0_SI.
Claim. $τ_N = τ_0 ⋅ φ^N$, where $τ_0$ is the fundamental Recognition Science tick in seconds.
background
In the GalacticTimescale module timescales sit on a phi-ladder whose successive rungs differ by exact factors of the golden ratio φ. The base value tau0_SI supplies the SI calibration at rung zero. Upstream results from PhiForcingDerived establish the convexity of the J-cost that forces self-similar scaling, while SpectralEmergence fixes the three spatial dimensions and eight-tick octave that underwrite the discrete ladder.
proof idea
The definition is a one-line wrapper that multiplies the imported constant tau0_SI by phi raised to the rung index N.
why it matters
This definition supplies the explicit rung function used by the downstream theorem tau_star_is_phi_rung, which places the galactic characteristic time tau_star_s at rung 142. It thereby embeds galactic timescales inside the T7 eight-tick octave and the phi-forcing chain of the Recognition Science framework.
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