Paper B-H5: From Spectral Gap to Dynamical Recovery — A Cell-Based Stress Test of DFG H5
Year: 2026
Type: article
Abstract: 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 K_trans 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. 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: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences
Open Access status: green
OpenAlex ID: W7159689019
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