IndisputableMonolith.Combustion.StabilizationTimescaleFromJCost
This module defines the critical Damköhler number as φ together with related cost and certification objects for combustion stabilization timescales derived from the J-cost function. Combustion modelers working in Recognition Science units would cite it when fixing the dimensionless threshold that separates stable and unstable reaction regimes. The module is built as a collection of definitions and short lemmas that link J-cost directly to the Damköhler ratio without a central theorem proof.
claimThe critical Damköhler number is $Da_{crit} = φ$, where $φ$ is the self-similar fixed point of the Recognition Science forcing chain. The associated stabilization timescale is obtained from the J-cost evaluated at this threshold, yielding a dimensionless ratio that must exceed unity for flame stabilization.
background
The module sits inside the combustion domain and imports the RS-native time quantum τ₀ = 1 tick from Constants together with the J-cost machinery from the Cost module. The J-cost obeys the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y) and supplies the yardstick for all subsequent dimensionless ratios. Definitions introduced here include criticalDamkohler (set to φ), damkohlerCost, StabilizationCert, and the inhabited certificate cert_inhabited that witnesses the existence of a stable regime.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the critical Damköhler threshold φ that is required by the sibling declarations criticalDamkohler_gt_one, damkohlerCost_at_critical and StabilizationCert. It thereby closes the link between the J-cost function and the eight-tick octave (T7) used to set reaction timescales, placing the combustion model inside the D = 3 spatial setting of the UnifiedForcingChain.
scope and limits
- Does not derive the value of φ from first principles inside this file.
- Does not compute explicit numerical stabilization times.
- Does not address multi-species or turbulent combustion regimes.
- Does not incorporate external empirical data beyond the RS alpha band.