IndisputableMonolith.Combustion.IgnitionThresholdFromJCost
This module defines the J-cost specialized to combustion chains via the branching-to-termination ratio. It supplies IgnitionThreshold, Ignites, and IgnitionCert for use in Recognition Science models of physical ignition. Researchers applying the phi-ladder to combustion processes would cite these definitions. The module consists entirely of definitions that import and extend the general Cost machinery.
claimLet $r$ denote the branching-to-termination ratio. The module defines chainCost$(r)$ as the J-cost on this ratio, together with the ignition threshold function IgnitionThreshold, the predicate Ignites, and the certificate IgnitionCert.
background
Recognition Science uses the J-cost $J(x) = (x + x^{-1})/2 - 1$ to quantify deviation from the fixed point at unity. The imported Constants module fixes the RS time quantum at $τ_0 = 1$ tick. The Cost module supplies the general chainCost and its algebraic properties (non-negativity, symmetry under reciprocal, positivity off unit). This module specializes those objects to the combustion domain by taking the argument to be the branching/termination ratio.
proof idea
This is a definition module, no proofs. It introduces chainCost, IgnitionThreshold, Ignites, ignition_threshold_band, IgnitionCert, and ignitionCert by direct specialization of the imported J-cost definitions.
why it matters in Recognition Science
These definitions supply the J-cost foundation for the ignition threshold band and certification objects used in higher-level combustion modeling. They instantiate the general J-uniqueness property (T5) for the specific ratio that governs chain branching versus termination. The module therefore bridges the abstract Cost layer to concrete physical thresholds without introducing new hypotheses.
scope and limits
- Does not derive numerical values for any ignition threshold.
- Does not prove existence or occurrence of ignition events.
- Does not extend to multi-step or spatially extended combustion chains.
- Does not incorporate additional constants beyond those imported from Cost and Constants.