Before revision:  The claims that we have all non-circularizable arrangements with the given properties are based on a program that generated all connected arrangements of n\leq 6 pseudocircles and all intersecting arrangements of n\leq 7 pseudocircles . Given the complete lists of arrangements, we used heuristics to find circle representations.
After revision:  The claims that we have all non-circularizable arrangements with the given properties are based on a program that generated all arrangements up to a certain size . Given the complete lists of arrangements, we used heuristics to find circle representations.