The Fragmentation Gap: A Topology-Dependent Diagnostic for Coherence–Optionality Decoupling Under Targeted Perturbation

Many complex systems appear operationally healthy immediately before catastrophic failure. Traditional resilience metrics frequently monitor global coherence, connectivity, or performance, yet these quantities often remain stable until collapse becomes unavoidable. This paper introduces the Fragmentation Gap, a topology-dependent metric designed to measure the divergence between local optionality and global coherence during network degradation: [F(t)=O_{norm}(t)-C_{norm}(t)] where (O_{norm}(t)) represents normalized local optionality and (C_{norm}(t)) represents normalized global coherence. The work began from an unsuccessful hypothesis that optionality collapse would consistently precede coherence collapse. After normalization and reanalysis, that hypothesis was not supported. Instead, a different pattern emerged: local optionality frequently persisted while global coherence degraded, producing measurable fragmentation gaps prior to visible collapse. Using controlled graph-degradation experiments across: Random Erdős–Rényi networks, Grid lattice networks, Modular bridge networks, the study demonstrates that targeted perturbations can generate substantial decoupling between local branching capacity and global integration. The strongest effects occur in modular bridge structures, where bridge-targeted attacks rapidly fragment global connectivity while preserving significant local functionality. The resulting interpretation is straightforward: Systems do not necessarily lose options before they fail.They lose the bridges connecting those options before they lose the options themselves. The Fragmentation Gap is proposed as a dynamic process metric rather than a static structural descriptor. Potential applications include: network resilience analysis, organizational silo detection, infrastructure vulnerability assessment, cascading failure diagnostics, adaptive systems research, and studies of fragmentation in complex social or biological networks. This release is presented as an exploratory technical note. Results are based on simplified graph models and single-run simulations. The paper focuses on introducing the metric, documenting the experimental correction process, and identifying promising directions for future investigation. Keywords fragmentation gap network science complex systems graph theory network resilience cascading failure modular networks bridge failure coherence optionality adaptive systems system collapse topology community structure interdependent networks organizational resilience infrastructure resilience complex adaptive systems fragmentation dynamics coherence-optionality decoupling