damkohlerCost
plain-language theorem explainer
This definition computes the J-cost of the ratio between a measured Damköhler number and its critical value for flame stabilization. Combustion modelers cite it when quantifying the recognition cost at the ignition threshold. It is implemented as a direct one-line wrapper around the J-cost function applied to the input ratio.
Claim. The Damköhler cost is defined by $J(da_{measured}/da_{critical})$, where $J$ is the J-cost function $J(x)=(x+x^{-1})/2-1$ and $da$ denotes the Damköhler number (flow residence time divided by chemical ignition delay).
background
In Recognition Science the J-cost function quantifies the recognition cost of a normalized state variable. The Damköhler number is the ratio of flow residence time to chemical ignition delay time. The module states that flame stabilization occurs when this ratio reaches the critical value equal to the golden ratio φ, at which point J(φ) supplies the minimum nonzero recognition quantum.
proof idea
This definition is a one-line wrapper that applies the Jcost function to the ratio of the measured Damköhler number to the critical value.
why it matters
The definition supplies the cost metric required by StabilizationCert, which certifies that the critical Damköhler number lies in the empirical band (1.2,2.5) consistent with φ. It thereby links the combustion stabilization problem to the J-uniqueness property in the forcing chain (T5) and to the self-similar fixed point φ (T6).
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