The Coherence Reconstruction Problems: Twelve Incomplete Dynamical Systems in Complex Infrastructure and Human Networks

This document defines a series of twelve reconstruction challenges in complex systems. Each problem presents observational signals and partially specified governing equations describing real-world infrastructure, geophysical, economic, and human systems. The governing equations are intentionally incomplete. Participants are invited to reconstruct the missing operator responsible for observed regime transitions and cascading instability. The challenge framework is based on a shared dynamical template in which unexplained system behavior is traditionally modeled as stochastic noise. This archive explores the alternative hypothesis that such behavior may arise from structural coupling across interacting subsystems. The problems span multiple domains including power grids, telecommunications networks, water infrastructure, healthcare systems, transportation networks, financial systems, and human behavioral systems. Researchers are invited to propose mathematical closures, simulate system dynamics, and identify indicators of regime transition using the provided framework. Submissions may include analytical models, simulations, or alternative theoretical formulations. Partial reconstructions are welcome. Datasets associated with these problems will be released separately and linked to this archive.