Topological Persistence and Charge-Separated States in Classical Complex-Field Dynamics

This paper makes a bold but testable promise: particle-like order can emerge and persist in classical complex-field dynamics without being hand-held by permanent forcing. It shows machine-precision persistence of topological winding after controls are removed, in both 2D and 3D settings. It also demonstrates that electromagnetic coupling modifies morphology but does not cause topological survival, which cleanly separates mechanism from appearance. A key advance is the zero-bias channel, where charge-like and orbital-like diagnostics organize spontaneously rather than being injected by explicit source terms. The mode-selective closed-line band, with a clear peak near \(m=12\), gives readers a concrete quantitative target instead of a vague qualitative claim. Interaction results are equally instructive because they reject oversimplified rules: gcd-based commensurability is not sufficient for attraction. Yet the finite-box-validated \((8,12)\) contact channel remains attractive and non-fused, showing that selective binding-like behavior is physically plausible inside the model. By separating cold-start scans from branch-tracked continuation, the study makes clear that branch selection is part of the physics, not just a numerical artifact to ignore. The work further strengthens credibility through explicit reviewer-safe gates, reproducibility artifacts, and uncertainty-aware interpretation. In short, this publication is worth reading because it turns wave-first ideas into a disciplined experimental program where strong claims are paired with clear falsification paths.