// recursively merge each key's register with the incoming state for that key
This step rapidly finds the optimal sequence of border points and shortcuts to get from your start cluster's periphery to your target cluster's periphery. It's incredibly fast because it's ignoring all the tiny roads within intermediate clusters.
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The Claude C Compiler illustrates the other side: it optimizes for passing tests, not for correctness. It hard-codes values to satisfy the test suite. It will not generalize. Property-based testing would likely catch this particular case, but the general problem remains: for any fixed testing strategy, a sufficiently adversarial system can overfit to it. A proof cannot be gamed. It covers all inputs by construction.
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--this-is=an-option some-argument --this-is-not-an-option