recoveryTime
plain-language theorem explainer
Recovery time after a cascade of depth k is defined to equal phi^k in phi-ladder units of the base recovery scale tau_0. Modelers of extinction dynamics on finite recognition graphs cite this scaling when converting cascade depth into observable recovery intervals. The declaration is a direct one-line assignment with no further computation or hypotheses.
Claim. The recovery time after a cascade of depth $k$ is given by $phi^k$, where $phi$ is the golden-ratio fixed point of the Recognition Composition Law and the result is expressed in units of the natural recovery scale $tau_0$.
background
The module models an ecosystem as a finite recognition graph in which each species carries a rung value Z and each edge supplies rung support. Ledger bankruptcy occurs when removal of an extinct species drops a neighbor's total rung below the life-ignition threshold Z_life = phi^19. The cascade is the monotone closure of this process on the finite vertex set. Recovery time is introduced to quantify the duration of the subsequent recovery phase once the cascade terminates.
proof idea
One-line definition that directly assigns recoveryTime k to phi ^ k.
why it matters
The definition supplies the phi^k scaling invoked by extinction_cascade_one_statement and by deep_cascade_recovery_lower, which shows phi^16 < recoveryTime 17 and links the result to 10^4-10^5 year K-Pg mammal recovery under canonical tau_0 calibration. It instantiates the phi-ladder scaling for recovery processes within the Recognition Science framework.
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