ejectionAtRung
plain-language theorem explainer
ejectionAtRung supplies the ejecta volume scale at rung k as phi to the power k on the VEI phi-ladder. Volcanism modelers and Recognition Science geologists cite it when deriving intensity ratios or certifying category counts. The declaration is a direct one-line definition with no computational steps or lemmas.
Claim. The ejecta volume at rung $k$ is given by $phi^k$, where $phi$ is the golden-ratio fixed point of the Recognition Science forcing chain.
background
The Volcanism from Phi-Ladder module states that volcanic eruption intensity (VEI 0-8) follows the phi-ladder, with each order-of-magnitude step in ejecta volume approximately $phi^k$. Five commonly used VEI categories (0-1, 2-3, 4-5, 6-7, 8+) correspond to configDim D = 5. The definition provides the base scaling used by downstream results on ratios and certification structures.
proof idea
This is a one-line definition that directly sets ejectionAtRung k to phi raised to the power k.
why it matters
The definition feeds ejectionRatio, which proves consecutive-rung ratios equal phi, and VolcanismCert, which records five categories together with the phi ratio. It realizes the module's RS prediction that VEI units lie on the phi-ladder, consistent with T6 (phi as self-similar fixed point) and the D = 3 spatial setting of the broader framework. No open scaffolding questions are attached.
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