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Sounds like it is maybe an ill-defined problem. So step 1 should be to describe non-ambiguously what should be solved here.
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Step 1: Solve the entire mathematical field of https://en.wikipedia.org/wiki/Topology

This isn’t just basic CRUD software that just needs some Postgres constraints to model trivial business logic. These are genuinely hard problems that mathematicians have been working on for decades.

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So why is it that every 3D CAD program other than FreeCAD seems to have something that solves this problem "well enough" that most people doing simple designs (aka everything you could possibly print on a 3D printer) don't seem to bump into it?
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Do you know of any free/open-source examples that solve this problem well?

I'm not an expert, but these types of heuristics intuitively seem hard to model. The goal is to guess the user's design intent. There's often no single correct answer, it may require information from parts of the system that the core application's model doesn't have, there may be many heuristics depending on what's being designed.

These heuristics seem like exactly the sort of thing that commercial CAD applications can afford to spend resources on, and that open-source community-driven applications would struggle with.

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