Paper B-Topology: Spectral Gap Is Not Resilience — Objective-Dependent Containment in Networked Systems

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, pc) = +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.