timescaleAtRung
plain-language theorem explainer
Coronal timescales are indexed by natural number rungs k with value phi to the power k on the Recognition Science phi-ladder. Solar MHD researchers would cite this when modeling the progression from Alfvén times to active region lifetimes across five decades. The declaration is introduced as a direct exponential definition without supporting lemmas.
Claim. The timescale at rung $k$ equals $phi^k$, where $phi$ is the golden ratio fixed point of the Recognition Science forcing chain.
background
The phi-ladder in Recognition Science orders quantities by successive factors of the golden ratio phi, which satisfies the self-similar fixed point condition from the forcing chain T6. This module applies the ladder to solar coronal phenomena, enumerating five timescales: Alfvén crossing time approximately 10 seconds, granulation convection around 600 seconds, chromospheric evaporation 6000 seconds, coronal loop lifetime 60000 seconds, and active region lifetime 600000 seconds. The definition provides the rung values whose ratios are later shown to equal phi, realizing the RS prediction of consistent phi^k scaling for adjacent timescales.
proof idea
This declaration is a one-line definition that directly assigns phi^k to timescaleAtRung k.
why it matters
It forms the foundation for the structure CoronalTimescaleCert, which requires five timescales and the phi ratio between consecutive rungs, and for the theorem timescaleRatioPhiRung proving that ratio. In the broader framework it instantiates the phi-ladder for astrophysical timescales, consistent with the eight-tick octave and the prediction that adjacent steps scale by phi, here spanning D=5 decades from Alfvén to active region.
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