Paper B-Topology: Spectral Gap Is Not Resilience — Objective-Dependent Containment in Networked Systems
Year: 2026
Type: article
Abstract: This record contains Document 05 of the DFG Empirical Programme submission package: Paper B-Topology — Spectral Gap Is Not Resilience: Objective-Dependent Containment in Networked Systems. This synthesis paper re-examines the topology-containment component of the DFG H5 family. Earlier H5-α and H5-β operationalisations treated graph-Laplacian spectral gap λ₂ as a recovery-time predictor, but prior neural recovery tests produced wrong-sign results. This paper argues that those results do not globally falsify the topology-level claim; instead, they reveal an operationalisation mismatch. The paper separates structural containment, spread containment, and dynamical recovery. It tests graph λ₂ across 14 networks, including 5 SNAP real-network corpora and 9 synthetic baselines. The central finding is that λ₂ is a robust predictor of structural connectivity and mixing strength, but its containment consequences are objective-dependent. Key results include:- Random-attack robustness: Spearman(λ₂, robustness) = +0.876; high λ₂ helps structural robustness.- Percolation threshold: Spearman(λ₂, p_c) = +0.876; high λ₂ helps maintain connectivity under random removal.- SIR final size: Spearman(λ₂, final size) = +0.83; high λ₂ increases epidemic spread and therefore hurts epidemic containment.- Cascade halt time: Spearman(λ₂, halt time) = −0.80; high λ₂ accelerates spread.- Dynamical recovery time: not predicted by graph λ₂; recovery is addressed separately by H5-γ Jacobian spectral radius in Paper B-H5. The bounded conclusion is that spectral gap is not resilience in the abstract. Graph-Laplian λ₂ measures connectivity strength. Whether high λ₂ is beneficial or harmful depends on the containment objective: it helps robustness to random structural attack, but can worsen epidemic containment by increasing spread capacity. This record is part of the DFG Empirical Programme submission package. It assumes the regime-atlas methodology established in Document 01, the Compatibility Atlas v1.3. Cell-level incompatibility should be interpreted as a regime-boundary marker rather than theory-level falsification. AI use disclosure. Generative AI (OpenAI GPT) was used substantively in preparing this work, including source comparison, drafting and editing, and, where applicable, mathematical and counterexample checks and the writing and running of supplementary code. The research questions, framework and final claims were directed and reviewed by the author, who takes full responsibility for the content, including the accuracy of all references and reported numbers.
Author: Seol, Bin
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7159647531
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