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Marzio De Biasi mentioned this paper in this answer, and that paper's claim in part 5 would appear to resolve my question. However, there seems to be a significant gap in the proof.

Even though one may be able to figure out what the gadgets on the border of the known whitespace component are, that doesn't obviously help to figure out what the rest of the whitespace components are.

How can one "reason through wires to uncover all whitespace components" when the wires go through other components (such as crossovers)?

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  • $\begingroup$ Gadgets (crossovers included) can be put on a grid and vertical/horizontal long enough wires can be used to link them. In this way one can safely traverse the wires and discover the external border of all gadgets (the nodes of the grid); but I agree with you: Michiel should prove that the inner structure of each gadget can be exploited from its external areas (only knowing its external boundary) ... and without using the assumption that the player knows their inner structure :) $\endgroup$ – Marzio De Biasi Mar 4 '14 at 12:18

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