Are the deep mantle slow regions denser or lighter than their surroundings?
In plain words
If the two big regions are denser than normal mantle they are chemically different and long-lived; if lighter they are probably just hot. Different methods give opposite answers.
Precise statement
Determine the sign and magnitude of the density anomaly $\delta \rho/\rho$ in the lowermost 300 to 500 km of the LLSVPs. Normal-mode and Stoneley-mode inversions have favored lighter material while body-tide tomography (Lau and coauthors, Nature 2017) favored denser material. An answer is $\delta \rho/\rho$ with uncertainty below about 0.3 percent from mutually consistent methods.
What would settle it
Combined normal-mode, body-tide and satellite-gravity inversions with shared parametrization and resolution tests.
Status in the literature
Unverified note
A 2026 satellite-gravity analysis (arXiv:2606.09296) adds new constraints; methods still disagree.