We study the geometry of networks that arise when local interactions are constrained by the absence of a globally consistent representation. Using a projection-based framework, we show that when local compatibility conditions cannot be extended to a global embedding, network structure is forced to reorganize through stratification, branching, and boundary-layer behavior. We derive universal scaling relations governing the emergence of thin branches and channelized structures as a function of a finite coherence or compatibility budget. These results are independent of optimization principles, energy minimization, or global objectives. Instead, network geometry emerges from the requirement that local descriptions remain admissible under projection. The framework yields falsifiable predictions for real networks, including monotonicity constraints, scaling exponents, and structural asymmetries near compatibility limits. Applications include biological transport networks, infrastructure systems, organizational graphs, and other systems where local consistency does not guarantee global coherence.
Peter Nero (Fri,) studied this question.