fragilityIndex
plain-language theorem explainer
The fragility index in the Recognition Science glass-transition model assigns to each natural-number rung k the value phi raised to the power k. Materials physicists constructing Angell plots for the five canonical regimes would cite this when placing fragility on the phi-ladder. The declaration is introduced as a direct power expression using the native phi constant.
Claim. The Angell fragility index at rung $k$ is defined by $f(k) = phi^k$, where $phi$ is the self-similar fixed point of the J-cost function.
background
The module derives glass-transition properties from the J-cost function and identifies five regimes (fragile liquid, strong liquid, supercooled, vitreous, aging) that correspond to configDim equal to 5. The fragility index is placed on the phi-ladder so that the ratio between adjacent rungs equals phi. This construction rests on the definition of phi in the Constants module as the positive real fixed point forced by the Recognition Composition Law and the J-uniqueness condition.
proof idea
The declaration is a one-line definition that directly sets the fragility index at rung k to phi raised to the power k.
why it matters
This definition supplies the explicit rung values used by fragility_pos to establish positivity, by fragility_ratio to prove the constant adjacent ratio equals phi, and by the GlassTransitionCert structure to certify the five-regime model. It instantiates the T6 phi fixed point inside the materials application of the framework and closes the basic scaling step for the glass-transition ladder.
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