Civilizational Scaffolding Entropy: A Mathematical Framework for Systemic Collapse

Description

We model civilization as five coupled domains spanning ecology, culture, technology, economy, and politics, and introduce scaffolding entropy as a structural measure of how stress flows across them. Instability emerges through two routes: a spectral route, where stronger couplings or slower recovery erode a unit-free stability margin, and a threshold route, where domain breaches activate an additive trigger term along live links. These mechanisms support an early-warning dashboard centered on three quantitative indicators: the spectral margin and two threshold-relative gauges for relative entropy progression and remaining headroom. For a fixed linear baseline, the spectral test is exact; in more general settings, it is an early-warning diagnostic, not a stability proof on its own. For exogenous jump-type shocks we add a trigger-aware inward drift bound and a windowed spectral margin, and summarize window-level robustness with a single robustness strength. Reweighting domains in the reporting aggregate cannot shift the spectral stability boundary; only targeted decoupling or faster recovery can. A 2008 financial crisis panel and a complementary United States COVID disaster window illustrate how the framework can flag increasing systemic-collapse susceptibility while remaining consistent with observed stress trajectories.

Authors

DOI: 10.5281/zenodo.20740562

Publication Date: 2026-06-18

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