VOLUME-PRESERVING RIGHT-HANDED VECTOR FIELDS ARE CONFORMALLY REEB

The paper proves that a volume-preserving right-handed vector field X on a closed oriented rational homology 3-sphere is conformally Reeb by showing the closed two-form ω = ι_XΩ is contact-type, using positivity of a Gauss-linking-based functional Lk_ω(μ) for every invariant measure and McDuff’s contact-type criterion, then setting the Reeb field R = fX with f > 0. The candidate solution proves the same theorem via a different route: it identifies λ with dλ = ω and uses a duality/separation argument to find f with λ(X) + X(f) > 0, hence λ' = λ + df is contact and R = X/λ'(X). Both arguments hinge on positivity implied by right-handedness; the paper uses Vogel’s Gauss linking form plus McDuff’s criterion, while the model uses Ruelle–Sullivan averaging and Hahn–Banach separation. Aside from a minor functional-analytic subtlety in the model’s cone-separation step (membership vs closure, easily fixed by an ε-margin argument), both are correct. See Theorem 1.1–1.2 and their proofs in the paper, including the definition and positivity of Lk_ω(μ) (Proposition 3.2) and the application of McDuff’s theorem (Theorem 4.1) leading to R = fX .