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Bibliographic Details
Main Author:	Lahtee, Yaoharee
Format:	Recurso digital
Language:
Published:	Zenodo 2026
Online Access:	https://doi.org/10.5281/zenodo.18345135
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Table of Contents:

When System Memory Meets a Bottleneck: Why the Most Dangerous Stress Can Be Invisible . We often describe the spread of information, signals, or even epidemics using a familiar picture: diffusion, like a drop of ink slowly dissolving into water. In this view, obstacles or narrow passages merely slow the flow, but the process remains smooth, gradual, and predictable. This intuition is deeply embedded in many physical and social models. . Recent simulations under the Telegraph-on-Graph Bottleneck Stress Test (ToG-BST) reveal a very different reality once the system has memory, or inertia in its response. When a system does not instantly forget its past, its dynamics change qualitatively. The past actively resists rapid change, and this resistance reshapes how energy or information moves through the network. . In a network with a bottleneck, such as two large communities connected by a narrow bridge, a diffusion-based model predicts only a mild slowdown at the constriction. But when causal memory is present, the bottleneck no longer behaves like a passive channel. It turns into a stress amplifier. Energy does not simply pass through; it collides, overshoots, and accumulates in front of the bottleneck, reaching intensities far beyond what diffusion models would ever predict. . This leads to a pile-up effect, where stress concentrates on a small set of nodes instead of being smoothly distributed. In memory-bearing systems, risk is not averaged out across the network. Instead, it is forced to localize, guided by the spectral structure of the graph rather than by simple connectivity or physical distance. . The most striking result is a form of geometric blindness. If one measures the system exactly at its geometric midpoint, the signal can appear close to zero, as if nothing is happening. Meanwhile, severe stress is building up nearby. This is not a contradiction, but a warning: in systems with memory, stress and energy do not propagate along straight, geometric paths. They travel along structural and spectral pathways, making visually “safe” locations potential blind spots. . The central lesson of ToG-BST is clear. Once a system has both memory and structural constraints, intuition based on smooth diffusion breaks down. It is no longer enough to ask who is connected to whom. The critical question becomes: where does the system’s inertia force stress and energy to accumulate. The most dangerous points in a network may be precisely those that look calmest on the surface.

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