Quantum-Informed Topological Transition Networks in Mid-Mass Nuclei

We present a quantum–topological framework that reconstructs nuclear excitation spectra as directed, weighted networks, mapping γ transitions between discrete states. Using Technetium-89 (⁸⁹Tc) and Technetium-99 (⁹⁹Tc) as representative systems, each nuclear level is treated as a node and each transition as a directed edge weighted by γ intensity. Network analysis reveals hierarchical, treelike structures with low clustering, acyclicity, and small-world efficiency ( Theorems A1–A3), while mid-energy gateway states maximize betweenness and mediate energy flow between collective domains (Theorem A2). We introduce the topon (τ) as a unit of decay topological length, quantifying the average path from excited states to sinks. Metrics including degree, betweenness, modularity, bridge fraction, and entropy capture collectivity, inter-band coupling, and scenario-dependent structural responses, while band clustering and rotational constants (ħ ² /2ℑ) distinguish vibrational and rotational regimes. Force-directed and linear layouts highlight dominant hubs and bridge nodes, linking spectral structure to emergent topological organization. This approach provides a reproducible, graph-based method to decode γ-decay schemes and refine mid-mass nuclear models.