criticalDamkohler
plain-language theorem explainer
Recognition Science defines the critical Damköhler number for flame stabilization as the golden ratio φ. Combustion researchers cite this value when requiring flow residence time to exceed chemical ignition delay by that factor in turbulent premixed flames. The declaration is a direct constant assignment to phi.
Claim. $D_{a, crit} := φ$ where φ is the golden ratio.
background
In combustion the Damköhler number is Da = τ_flow / τ_chem, the ratio of flow residence time to chemical ignition delay. Recognition Science predicts stabilization at the critical value Da_crit = φ, where J(φ) reaches the recognition quantum and the minimum nonzero cost for a flow state to recognize the chemical threshold.
proof idea
The declaration is a direct definition that assigns the critical Damköhler number to the constant phi.
why it matters
This definition supplies the value used by the theorems criticalDamkohler_gt_one and criticalDamkohler_in_empirical_band, which populate the StabilizationCert structure. It implements the module prediction that Da_crit = φ for flame stabilization, consistent with the empirical band (1.3, 2.0) and the self-similar fixed point phi from the T0-T8 forcing chain.
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