Tridom: A Minimal Causal Unit for Substrate-Invariant Network Dynamics

## Abstract We introduce **Tridom**, a conceptual and formal unit defined as a strongly connected directed graph on three nodes,endowed with a signed coupling structure (excitatory/inhibitory) and a qualitative dynamical class.Drawing on the network motif literature and on the theory of feedback circuits,we argue that the triadic level constitutes a **minimal grain** at which non-trivial causal organization — multi-stability, oscillation, minimal chaos — becomes generically possible.We further show that this grain is **substrate-invariant**: the binary sign pattern of couplings (topology + E/I labels) is preserved across biological, digital, and logical implementations.This repository provides the formal specification, an enumerated atlas of 78 canonical signed triad topologies classified by dynamical regime,a PyTorch reference implementation with local Hebbian plasticity, and a self-organizing multi-agent system (TridomGroupSystem / Nona²) with endogenous birth and death.