Endogenous Vortex Realization from Finite Latent Rotational Cores: A Source-Level Threshold Model with Application to Tornado Formation

This work develops a source-level model of vortex realization in which organized rotational structure may exist before its strong expression as observable physical flow. The model separates a latent transport field \(q\), its torsion \(\tau=\nabla\times q\), and a realization field \(\alpha\), with physical velocity and vorticity given by \(v=\alpha q\), \(\omega=\nabla\alpha\times q+\alpha\tau\). This factorization distinguishes rotational organization from the degree to which that organization is physically realized. Controlled triggering experiments show that persistent realization is a finite-support nucleation process: broader perturbations require less amplitude to produce a persistent realized state. Numerical reconstruction of the evolving vorticity source verifies the source-level decomposition and shows that rapid physical-vorticity expression can be dominated by realization of pre-existing latent structure rather than by simultaneous reorganization of the rotational source. An endogenous model is then developed in which latent torsion contributes to the realization bias. Highly localized rotational sources fail to sustain realization, while finite-core sources exhibit a resolved critical coupling \(H_{\tau,\mathrm{crit}}(a)\). Across the tested range, increasing the latent core radius lowers the critical coupling required for persistent realization, separating coherent spatial support from local rotational intensity as distinct controls on vortex realizability. Post-nucleation analysis further identifies a critical realized radius separating collapsing from expanding nuclei. Supercritical realized regions propagate toward a finite traveling-front speed, and the same critical scale appears as the maximum of the realization free-energy barrier. The resulting model therefore separates source organization, finite-support nucleation, post-threshold propagation, and strong physical vortex expression. Tornado formation provides the principal motivating example, particularly the possibility that organized precursor rotation may precede rapid intensification of observable near-surface flow. The mathematical construction is not restricted to atmospheric systems and is presented as a more general vortex-realization framework rather than as a complete tornadogenesis model. The archival release includes the Version 1.0 research paper, figure-generation scripts with corresponding generated figures, the refined \(512\times512\) finite-core realization-boundary data, and selected \(1024\times1024\) calculations used for the numerical resolution check. Coherence Geometry Institute reference: CGI-RSR-000039. This work is released as an archival research preprint and has not undergone external peer review.