Paper B-H5: From Spectral Gap to Dynamical Recovery — A Cell-Based Stress Test of DFG H5

This record contains Document 04 of the DFG Empirical Programme submission package: Paper B-H5 — From Spectral Gap to Dynamical Recovery: A Cell-Based Stress Test of DFG H5. This synthesis paper re-examines the DFG H5 prediction family, originally framed around spectral connectivity and recovery time. Earlier operationalisations using graph-Laplacian spectral gap λ₂ — H5-α topological λ₂ and H5-β functional λ₂ — produced wrong-sign results in tested neural recovery settings. This paper argues that those failures do not falsify H5 globally; instead, they identify an operationalisation mismatch. The paper separates graph-topological and dynamical-system-recovery readings of H5. Graph Laplacian λ₂ measures structural connectivity, while the spectral radius λ₁ of the dynamical Jacobian governs perturbation recovery in linearised dynamical systems. Under the H5-γ operationalisation, Jacobian spectral radius predicts recovery time across synthetic symmetric systems, synthetic non-normal systems, and real meso-neural cortical culture data. Key results include: - Synthetic symmetric systems: Spearman (true ρ, recovery time) = 0. 957 across 6, 000 trials. - Synthetic non-normal systems: K = D/λ₁ remains predictive across non-normality ν ∈ 0, 4, with Kₜrans improving under strong non-normality. - Real meso-neural culture, DANDI: 001611: Spearman (λ̂₁, mean recovery time) = 0. 895 at session level across 12 sessions nested in 4 subjects, with subject-level caveats explicitly reported. - H5-ζ K = D/λ₁ is synthetically stress-tested and supported through complementary D estimators, while real-substrate D estimation remains an open gate. The bounded conclusion is that the recovery-time reading of H5 is a dynamical-system-recovery prediction, not a graph-topological prediction. The structural Laplacian λ₂ belongs to a separate objective-dependent connectivity reading of the H5 family, addressed in the companion Paper B-Topology document. 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.