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Published November 10, 2025 | Version v4
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Civilizational Scaffolding Entropy: A Mathematical Framework for Systemic Collapse

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We define civilizational scaffolding as the system‑level support that sustains human life and social order across five load‑bearing domains: ecology, culture, technology, economy, and politics. We introduce civilizational scaffolding entropy, a named family of normalized disorder measures linked to a coupling map and thresholds to trace how strain propagates. Two routes to failure emerge: stronger cross‑domain ties or slower recoveries shrink the stability margin so small shocks travel farther; once thresholds are breached, contagion accelerates along active links. The framework yields an early‑warning dashboard: slowing recoveries, a unit‑free and threshold‑free spectral margin, and two threshold‑aware gauges for progress to breach and remaining headroom. Under a stated normalization, the spectral check is a sufficient early‑warning test. We also cover exogenous catastrophic (“jump‑type”) shocks by two sufficiency‑only checks summarized in Appendix G: a trigger‑aware inward‑drift bound and a windowed spectral‑margin test; we additionally report a compact window‑level robustness strength  that aggregates these headrooms. Policy: reweighting domains only re‑averages stress and cannot move the stability boundary; adjusting couplings or recovery rates can. Targeted decoupling or faster recovery restores safety with limited performance loss. In a 2008 case study, a smoothed stability indicator entered its warning zone in 2006, over two years before the Lehman collapse; on our 0-V post‑event severity scale, the 2007-2009 window grades Level III (open); the framework guides policy within the stability boundary.

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