ignitionCert
The ignitionCert definition packages the zero-at-unit, reciprocal symmetry, non-negativity and threshold-band properties of the recognition cost on branching ratio into the IgnitionCert structure. Combustion modelers working with radical-chain kinetics would cite it to fix the autoignition point inside the universal recognition band. It is a direct record instantiation that applies the four upstream J-cost lemmas without further reduction.
claimThe combustion ignition certificate asserts that the recognition cost function $C(r)$ on the branching ratio $r$ satisfies $C(1)=0$, $C(r)=C(r^{-1})$ for all $r>0$, $C(r)≥0$ for all $r>0$, and that the ignition threshold lies in the open interval $(0.11,0.13)$.
background
The module treats autoignition as governed by the recognition cost on the radical-chain branching ratio $r$ = branching_rate / termination_rate. Below $r=1$ radicals terminate faster than they branch and combustion fails to propagate; at $r=1$ the cost reaches its global minimum but the system is marginally stable; above $r=1$ the cost rises and propagation follows the phi-ladder. The chainCost function is the J-cost restricted to this ratio, inheriting non-negativity, unit-zero and reciprocal symmetry directly from the Cost module. IgnitionThreshold is defined as the J-cost evaluated at the golden ratio phi and is shown to lie in the canonical band $(0.11,0.13)$ that also bounds plaque vulnerability and Stage-2 hypertension. The upstream cost_nonneg result from ObserverForcing supplies the general non-negativity of any recognition event cost.
proof idea
The definition is a one-line record constructor that supplies chainCost_zero_at_unit to the unit_zero field, chainCost_reciprocal_symm to the reciprocal_symm field, chainCost_nonneg to the cost_nonneg field, and ignition_threshold_band to the threshold_band field.
why it matters in Recognition Science
This definition supplies the minimal certificate required by any Recognition Science combustion model. It instantiates the IgnitionCert structure with the J-cost properties that place the ignition threshold inside the universal phi-band $(0.11,0.13)$, the same interval that appears across pathology and the T5 J-uniqueness step of the forcing chain. Because the band is derived from the self-similar fixed point phi forced at T6, the certificate closes the link between microscopic recognition cost and macroscopic ignition without introducing new axioms.
scope and limits
- Does not derive the explicit time evolution of radical concentrations.
- Does not incorporate mixture-specific activation energies or transport coefficients.
- Does not address turbulent or multi-stage combustion regimes.
- Does not prove that the band $(0.11,0.13)$ is the unique ignition threshold across all fuels.
formal statement (Lean)
77def ignitionCert : IgnitionCert where
78 unit_zero := chainCost_zero_at_unit
proof body
Definition body.
79 reciprocal_symm := chainCost_reciprocal_symm
80 cost_nonneg := chainCost_nonneg
81 threshold_band := ignition_threshold_band
82
83end
84end IgnitionThresholdFromJCost
85end Combustion
86end IndisputableMonolith