Deep Lagrangian connectivity in the global ocean inferred from Argo floats

The paper defines the dynamic Cheeger functional h(A) and the dynamic Laplacian ∆D, and explains a computational pipeline to identify eight coherent sets from the leading eight Dirichlet eigenfunctions, but it does not supply rigorous proofs about existence of minimizers, higher-order Cheeger-type comparisons, or dominance; it focuses on numerical methodology and applications. In particular, the paper states ∆D is symmetric, elliptic, with real nonpositive spectrum and then computes the leading eight eigenfunctions and extracts eight sets via SEBA and thresholding, but does not claim theorems of the type asserted by the model (existence/near-optimality/dominance) . The model provides a plausible proof outline for (i) existence of area-constrained minimizers, (ii) extracting eight disjoint near-minimizers from eigenfunctions with h ≲ √μ8, and (iii) dominance via min–max and an eigengap. However, it leaves key gaps and contains inaccuracies: reliance on H2- and L∞-bounds not justified under the stated domain/coefficients; the claim that raising thresholds to enforce disjointness can only improve h is generally false; and the eight-way Cheeger comparison and smoothing-to-Rayleigh steps are stated but not rigorously derived for the dynamic Dirichlet setting. Hence, the paper is incomplete with respect to the posed theory, and the model’s solution is also incomplete.