coronalTime
plain-language theorem explainer
Coronal timescales sit on the phi-ladder by setting the time at rung k to the reference Alfvén time multiplied by phi to the power k. Solar physicists modeling chaotic magnetic evolution before reconnection would cite this to obtain exact multiplicative ratios between successive observed timescales. The declaration is a direct algebraic definition that multiplies the constant referenceTime by the power phi^k.
Claim. The coronal timescale at rung $k$ is defined by $τ(k) = τ_0 φ^k$, where $τ_0$ is the reference Alfvén-crossing timescale equal to 1 in RS-native units.
background
In the Recognition Science treatment of solar coronal dynamics, magnetic field lines evolve chaotically prior to reconnection. The Lyapunov time measuring exponential divergence of nearby trajectories must lie on the phi-ladder of characteristic timescales. The reference timescale is the Alfvén crossing time, fixed at 1 in native units and corresponding to roughly 1 s under typical surface conditions with B ≈ 100 G.
proof idea
The declaration is a direct definition that multiplies referenceTime by phi raised to the rung index k. No lemmas are applied inside the definition body itself; downstream results such as coronalTime_succ_ratio unfold the definition and invoke pow_succ together with ring to recover the multiplicative step.
why it matters
This definition supplies the explicit form consumed by CoronalLyapunovCert and by the ratio theorems coronal_adjacent_ratio, coronalTime_succ_ratio, coronalTime_pos and coronalTime_strictly_increasing. It realizes the phi-ladder step T6 of the forcing chain for astrophysical timescales. The module states the falsifier as any measured adjacent ratio falling systematically outside (1.5, 1.8) on a corpus of at least three active regions.
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