Minimal canard networks in planar mass-action systems: data and code

Supplementary data and code for the paper “Canard points in planar mass-action networks: a flux criterion, a duality, and a complete classification”. For mass-action networks on two species, X fast and Y slow, with complexes of molecularity at most three, the record lists all 138 754 minimal canard networks. A minimal canard network is a set of reactions with a nondegenerate canard point for some rate constants, no proper subset of which has one. Each network is labelled exactly by the criticalities of the canard explosion it admits. The record also contains the 15 804 elementary flux modes from which the list is built, the logs of all computations and independent checks, and the Julia code (exact arithmetic with Oscar), with which the classification can be reproduced in about 30 minutes. Version 1.1.0 adds the certificates of all labels, with rational witness fluxes; an independent verifier in Python (standard library only, exact arithmetic), which re-derives the minimality and the label of every network in about a minute; the labels in the limit of strong dimerisation, which realises every network by bimolecular steps; the computations of the bimolecular realisation, of the criticality at finite time-scale ratio, of a table of robust networks and of the Oregonator; and a README section with examples of queries on the list. The list and its labels are unchanged. Data: CC BY 4.0. Code: MIT. See README.md.