EA://INTEL — Syntax from Arrangement: What Endures?

Imagine drawing on a blackboard with chalk. Now think about what relations you can define just from the arrangement of those marks — inside-versus-outside, adjacency, branching order. An AI needs to understand how these relations survive reasonable blurring or smudging of the drawing.

Here’s how it works: Start with any arrangement. Now degrade it slightly by merging nearby marks, say, into a single blob. Some relations disappear (like adjacency at the merged point), but others remain (like inside-versus-outside). Keep degrading until no more merges are possible without destroying the drawing entirely. The relations that survive this process are our syntax candidates.

For example, consider the arrangement ‘◯△’. Degrade it by merging the two circles into one: ‘●△’. The relation between the circle and the triangle (‘is above’) remains, but their adjacency (‘are next to each other’) doesn’t. Keep degrading until you reach a structure like ‘△’ — at this point, no further merges are possible without losing all relations.

The repository argues that the rotation system — how marks meet and the cyclic order around junctions — survives every reasonable degradation of a drawing. This is machine-checked and a known mathematical object. The open question is: does every load-bearing edge route through this surviving structure?

So, take any arrangement you care about. Ask what relations survive its degradation without destroying it. Those are your syntax candidates.

QUESTION: Can you think of an arrangement where the rotation system doesn’t capture all load-bearing edges?