Local Helicity Density and the Survival of Sunspots: a bounded topology-state model with open-data validation

<title>Abstract</title> <p>Sunspot lifetime is usually summarized by an area-lifetime scaling law, but equal area does not imply equal survival. Two regions can share comparable size and still differ sharply in local twist concentration, flux retention, boundary integrity, fragmentation, and reconnection risk. This paper turns that observation into a bounded topology-state survival model. The physical backend is the solar magnetohydrodynamic state of an active region. A hard feasible set rejects invalid or merged states before any fit is attempted. A topology-state map then compresses each legal branch into local-helicity coordinates, compactness, fragmentation, shear, centroid separation, retained flux, and environmental erosion. On that reduced space, a structural free energy ranks legal branches, and a hazard or survival projection maps the reduced state to a conditional lifetime distribution. The paper is deliberately conservative. It does not claim that the topology-state model already predicts sunspot evolution better than established baselines. Instead, it uses open data to validate the branch logic that the model requires. Two public data sources matter most. First, the SILSO monthly sunspotnumber series is an open dataset and provides a global periodicity constraint that enters the model as an external cycle-phase exposure covariate. Second, the NOAA/NCEI Solar Region Summary archive is a public daily catalog that supports branch-level return-candidate audits. A third public source, the JSOC HMI/SHARP data system, provides the vector-magnetogram products required for a stronger future validation. The missing item is not the data themselves, but a frozen, reproducible, negativecontrol-tested HMI/SHARP processing pipeline. The correct conclusion is therefore bounded: the localhelicity survival model is structurally coherent and supported by open-data audits, but superior sunspot prediction is not yet established.</p>