Recovery-Time Inflation as a Pre-Collapse Signal in Fractional Memory Systems

This paper introduces a new experimental result at the intersection of dynamical systems, memory theory, and collapse prediction. It demonstrates that Recovery-Time Inflation (RTI), a perturbation-based observable, remains a reliable early-warning signal even in systems governed by power-law memory, where classical spectral methods break down.

In systems with fractional memory kernels, the traditional notion of a spectral gap becomes ill-defined due to the emergence of continuous spectra. As a result, widely used passive indicators such as variance and autocorrelation lose predictive power. This work shows that RTI bypasses this limitation by directly measuring recoverability through perturbation-response experiments.

Across a sweep of fractional memory exponents, RTI consistently detects instability before collapse, while passive variance lags behind. The results reveal a clear transition in predictability: weak memory systems behave like Markov processes with little to no early warning, while strong long-memory systems exhibit a large and measurable pre-collapse window.

A key contribution is the introduction of the “warning budget,” a quantitative measure of how much advance signal RTI provides over passive methods. This budget is shown to scale with memory depth, establishing that predictability itself is a structural property of the system rather than a limitation of measurement.

The paper also proposes an empirical collapse surface linking memory strength and system coupling, and connects the findings to fractional stability theory through the geometry of the Matignon stability cone.

This work advances Coherence Physics from a theoretical framework toward an operational measurement science. It provides a concrete, reproducible method for detecting collapse in systems where traditional tools fail, with implications for biological monitoring, cognitive systems, and artificial intelligence stability.