FHN-ThresholdCert: interval-arithmetic software for certifying periodic orbits and firing thresholds of the FitzHugh–Nagumo neuron

FHN-ThresholdCert is a small C++ and Python package that produces computer-assisted proofs about periodic orbits of the FitzHugh–Nagumo (FHN) neuron model. For every parameter interval it either returns a certificate or reports failure; a certificate proves, up to the correctness of the implementation and of IEEE interval arithmetic, that a periodic orbit exists, is locally unique on a Poincaré section, is hyperbolic, and has a period and a section crossing inside explicit intervals. The core is an interval-arithmetic kernel with directed rounding, validated Taylor integration of order 20–24, an order-one Taylor model in the initial condition and the parameter that controls the wrapping effect, and the Krawczyk operator applied to the first-return map. The package certifies the repelling "threshold" cycle of the FHN model by integrating in backward time on a transversal ray through the resting state, and records rigorous bounds that turn the certificate into a statement about voltage kicks. It also contains an exact-arithmetic computation of the first Lyapunov coefficient and floating-point cross-checks. The archived snapshot (11,688 certificates, raw output of two independent passes, scripts and figure) is available on Zenodo. Software descriptor prepared for submission to the Journal of Data- and Knowledge-integrated Simulation Science (JoDaKISS).