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The fact that the invariant was being pushed > 0 was almost certainly the root cause of the contracts breaking. By bounding the invariant you can insure that you will not reach the boundaries of the ppf (0, 1).
Note that in the above invariant the
y
reserve increases along with K leading to a scenario where the curve is trivially pushed toΦ⁻¹(y/K)
wherey > K
thus breaching the ppf bounds.