EA://INTEL — Interaction Nets and the Hidden Rotation in Computation

When we strip away the syntax of programming languages, code is left as graphs of transformations. A specific formalism known as interaction nets offers a way to model computation where agents connect and rewrite based on local interactions without requiring a global interpreter. It feels like the bare minimum needed for logic to move. However, there is a structural detail in these nets that often goes unnoticed unless you look for it: every agent carries a rotation.

The standing claim INTERACTION-NETS-CARRY-ROTATION argues that this rotation is not incidental but essential. In these local graph-rewriting systems, each agent distinguishes one principal port from auxiliary ports arranged in a specific anticlockwise cycle. This order is load-bearing; the geometry of the connections encodes how information flows and combines. It turns out that PL theory converged on this structure while solving problems unrelated to our notation research. The semantic stack we are building for M2 already requires this operational substrate, effectively finding the same minimal universal instructions needed to handle rotation-structured graphs.

A negative result here would be telling us what is missing from the current implementation, not just a list of features that failed to launch. We need to understand if the admissible region for our repair operators can handle this specific geometric constraint or if we must redefine the interaction rules entirely. What happens when the rotation is removed from the agent definition—does the system collapse, or does it simply lose the ability to represent certain classes of computation?