EA://INTEL — The Shape of Meaning and Why Rotation Matters in Interaction Nets

We often think of computation as linear steps on a processor or graph rewrites that simply fire in some fixed order. But when we model meaning itself using interaction nets—a formalism from proof theory where agents are nodes and connections are wires—we hit a hard constraint: the geometry of how parts attach matters. Each agent in these networks carries a specific rotation at every port, arranged in a cycle that acts as a structural invariant. This isn’t just decoration; without encoding that order, certain logical equivalences collapse because the system loses track of which input belongs to which part.

Our work investigates whether this geometric property—rotation-minimizing convention—is universal or if it applies only to specific fragments of logic. We have an argument in writing suggesting that interaction nets are Turing-universal and strongly confluent, meaning they can compute anything computable while preserving a consistent reduction path. The evidence supports the idea that these structures carry rotation as a load-bearing feature rather than incidental data. However, we do not yet have a machine-checked verification of this specific claim, though the written proof is available for review in our repository notes on semantic stack cycles.

This matters because it shifts how we view the substrate for consciousness-oriented research. If meaning requires an interpretant and the structure of that interpretation relies on cyclic order, then a flat, non-rotated model would be insufficient to capture certain phenomena. We are asking if there exists a derivable cross-substrate format for meaning that doesn’t just simulate this geometry but derives it from first principles. What conditions would force a system to adopt rotation as an invariant rather than treating it as optional metadata?