Closed-Form Storage Stability, Induction Delay, and Thermal-Feedback Criticality of Melt-Gated Autocatalytic Cure

A theoretical paper. No experimental data are used and all parameters are illustrative. Prepared for submission to The Journal of Chemical Physics. For a cure triggered by the melting of an encapsulated catalyst (distribution of capsule melting temperatures, Kamal-Sourour autocatalytic kinetics, exothermic feedback), the lumped model is largely solvable in closed form: the gated cure is the isothermal cure on the clock of integrated catalyst availability; the isothermal cure time is exact by quadrature and its sharpness is logarithmic in the rate-constant ratio; the storage conversion of a Gaussian capsule population gives a closed-form design rule for the admissible melting-temperature spread; thermal feedback has a critical number e^-1 (1+n)^(1+n)/n^n with Lambert-W overshoot and an Arrhenius correction exp(1/Ar); and a continuous-flow reactor shows ignition-extinction hysteresis whose static loop area is the zero-sweep-rate limit of the dynamic loops. Every result is tested against the full equations. The parameter set and capsule-population picture come from an earlier numerical preprint of the author (doi 10.5281/zenodo.22073390). Code and results: https://github.com/sandlerleon/gated-autocatalysis-criticality, archived at 10.5281/zenodo.23201763.