Refined de Sitter conjecture

What the term means here

A weakened form of the de Sitter conjecture that replaces the strict gradient bound with a disjunction: either the gradient bound holds, or the potential has a sufficiently negative eigenvalue of its Hessian. This permits local maxima while still forbidding stable minima with positive energy.

Why it matters to this question

The refinement was introduced because the original bound was in tension with known features of cosmology, including the Standard Model Higgs potential. It is the form most often used in current work.

What this does not establish

Refining a conjecture to survive counterexamples does not establish it. The refined form remains a conjecture, and the weakening is itself part of what critics point to when arguing the criteria are not sharply derived.