DFG Empirical Compatibility Atlas v1.3: Final Programme State and Regime-Search Framework

This record contains the DFG Empirical Compatibility Atlas v1.3, the final programme-state document for the Deficit-Fractal Governance (DFG) Empirical Programme as of May 2026. The Atlas consolidates the post-search-sprint results of the DFG empirical programme and defines the programme’s current operating methodology: a regime-atlas framework rather than a theory-cemetery framework. Across eight targeted regime-search experiments (Exp 12–19), four initially quarantined theory families found at least one located, compatible-in-regime operationalisation: Cascade Universality, Topology-Level Containment, Intervention Paradox, and AGC reformulation. The central methodological principle is that cell-level incompatibility should not be interpreted as immediate theory-level falsification. Instead, failed cells are treated as regime-boundary markers that motivate targeted search across operationalisation, substrate, observable, and scale. The Atlas distinguishes between:- globally quarantined universal claims,- compatible-in-regime operationalisations,- data-gated unsearched cells,- operationalisation-limited cells, and- located regimes with multi-evidence support. Key consolidated results include:- Cascade Universality located in a Manna conservative cascade + Watts-Strogatz small-world + low-dissipation regime, finite-size robust across N = 1000–5000.- Topology-Level Containment reframed as objective-dependent connectivity prediction, where graph Laplacian λ₂ predicts connectivity strength rather than generic resilience.- Intervention Paradox located in nonlinear bistable, saturation, delayed-control, and resource-depleting regimes.- H4-β financial critical slowing down supported under substrate-matched observables.- H5-γ dynamical-Jacobian spectral-radius recovery supported across synthetic and real meso-neural tests.- H1 neural operating-point criticality supported as σ ≈ 1, while the universal τ ≈ 3/2 claim remains quarantined except for located synthetic regimes. This record is part of the DFG Empirical Programme submission package. It should be read before the associated Paper A and Paper B documents, because it defines the status taxonomy and interpretation rules used throughout the package.