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2025
It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.
Abstract Based on variational methods, we study the spectral problem for the subelliptic ‐Laplacian arising from smooth Hörmander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction, and show Hölder regularity of eigenfunctions with respect to the control distance. Moreover, we determine the best constant for the ‐Poincaré–Friedrichs inequality for Hörmander vector fields as a byproduct.