cert
plain-language theorem explainer
The definition cert assembles a StabilizationCert record by supplying three properties of the critical Damköhler number. Combustion researchers would cite it when confirming that the recognition cost vanishes exactly at the stabilization threshold predicted by the golden ratio. The construction is a direct record literal that invokes the three upstream theorems establishing the lower bound, the empirical interval, and the zero-cost condition.
Claim. Let $Da_{crit}$ denote the critical Damköhler number. The stabilization certificate is the record asserting $1 < Da_{crit}$, $1.2 < Da_{crit} < 2.5$, and that the Damköhler cost function satisfies $damkohlerCost(d,d)=0$ for every nonzero real $d$.
background
The module develops the Recognition Science treatment of flame stabilization. The Damköhler number is the ratio of flow residence time to chemical ignition delay. Recognition Science predicts that the critical value equals the golden ratio φ, at which point the J-cost reaches its minimum nonzero value for a flow state to recognize the chemical threshold. Empirical ignition and extinction boundaries lie in (1.3,2.0), consistent with φ≈1.618. The structure StabilizationCert packages the three required assertions: the strict inequality above 1, membership in the empirical band (1.2,2.5), and vanishing cost at criticality for nonzero arguments. These rest on the upstream results one_lt_phi together with the bounds phi_gt_onePointSixOne and phi_squared_bounds.
proof idea
The definition is a direct record literal that supplies the three fields of StabilizationCert by referencing the theorems criticalDamkohler_gt_one, criticalDamkohler_in_empirical_band, and damkohlerCost_at_critical. No further tactics or reductions are performed.
why it matters
This definition supplies the concrete certificate that closes the structural theorem for flame stabilization in the Combustion module. It confirms that the J-cost vanishes at the predicted critical Damköhler number φ, aligning with the phi-ladder and the eight-tick octave landmarks. The module falsifier remains any laminar or turbulent flame experiment placing the critical Damköhler number outside (1.2,2.5).
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