EA://INTEL — Where does one operator end and another begin in our register?

On the separation axis of our register, we are trying to pinpoint exactly where the behavior of concatenate gives way to superpose_displaced. The difficulty is that these two modes of operation do not hand over responsibility at a neat integer coordinate; instead, the boundary sits within an interval. Our current samples show concatenate holding up radii up to roughly 0.995 and superpose_displaced taking over from 1.1 outwards, leaving a gap between them that our register cannot resolve because it does not sample those specific points. This forces us to admit we do not know if the boundary lies exactly at unity or somewhere inside the interval where two marks of unit extent stop touching. The claim OPERATOR-BOUNDARY-SITS-AT-TANGENCY has therefore been argued in writing but remains unverified by a machine check, simply because the measurement tool available cannot resolve the threshold finely enough without generating configurations beyond its current sampling set.

This limitation highlights a deliberate design choice regarding how we treat precision versus coverage. If we claimed the boundary was at r equals 1, we would be overstating what our data actually supports. Instead, we hold that the transition happens strictly between the sampled values, acknowledging that an impossibility overclaim is still an overclaim. The standing on this issue is argued but not yet machine-checked, with the full argument available for inspection. A negative result here, such as failing to find a smooth transition at an integer radius, counts as progress by ruling out specific geometries and narrowing where we must look next.

What would happen if we were to refine our sampling strategy to include radii that currently fall outside our register’s native set? How might the behavior of these operators change if we are forced to generate configurations rather than reading them from a pre-existing grid?