should deal intelligently with 3-wall intersections about loom HOT 6 OPEN

Andy, indeed Figure 16 of 1204.4824 illustrates a nice example of such cancellation, but on the other hand I can't come up with an algorithmic way of implementing such signed counting of soliton number off the top of my head. I think you once mentioned that you implemented that in your Mathematica code, could you briefly describe how we can do that?

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Actually, the relative signs between solitons shouldn't be hard to compute, at least in principle. We just need to properly integrate the change in tangent direction along the soliton path (including possible discrete corrections from joints and branch points).

What I find a little harder is how to understand when a 3-wall intersection is stable against perturbations in \vartheta (without actually changing \vartheta).

But strictly speaking, do we even need to know if the intersection is 'stable'?
If we have two overlapping S-walls S_{\alpha+\beta} (one incoming, and one generated at the joint) it's fine to cluster them together into a single wall, with soliton content given by the sum. I think the formal parallel transport would be the same.

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Thank you for the insights, knowing that integration of the phase is generally superfluous will save us quite a few headaches with numerics, plus CPU time.

There is one more detail which I forgot previously, but is important: to sum solitons we should classify them by relative homology, or some surrogate of that notion. Did your code handle this too?
In the simplest cases, where C is just the complex plane it shouldn't be too difficult.
But if C is e.g. a cylinder it could be tricky to correctly match solitons within the same relative homology class (I'm thinking of herds in SU(3), where solitons can wind around C).

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I see, thanks for the clarification. Handling the generic case would already be a wonderful step for us at this point.
More generic cases may not be too hard to deal with, on a case-by-case basis if necessary. But that's for later.

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