Recovery-Time Inflation as a Spectral Measure of Stability

This paper introduces Recovery-Time Inflation (RTI), a new way to measure how close a system is to failure.

Most early-warning methods rely on passive signals like variance or autocorrelation. These approaches assume that instability shows up in observable fluctuations. In many real systems, that assumption breaks. Collapse can emerge from hidden dynamics, memory effects, or nonlinear observation layers where standard signals remain quiet.

RTI takes a different approach. Instead of watching the system, it probes it.

By applying small perturbations and measuring how long the system takes to recover, RTI directly captures its stability margin. The key result of the paper is that recovery time scales with the inverse spectral gap of the system, meaning RTI acts as an empirical measurement of underlying dynamical stability.

The method is validated across:

• Linear systems with known spectra
• Nonlinear systems near critical transitions
• Network systems undergoing structural degradation

It is further tested in adversarial conditions where classical early-warning signals fail, including hidden-mode systems, memory-driven dynamics, and clipped observables. In these cases, RTI detects instability where traditional metrics do not.

The paper also establishes clear limits: RTI is not a universal replacement for existing methods. In fully observable, low-noise systems, classical indicators can still detect instability earlier. RTI is best understood as a complementary, active measurement tool, particularly useful when observability is incomplete or misleading.

This work reframes collapse not as a spike in noise, but as a loss of recoverability—and provides a concrete, testable way to measure it.