Does the gap change sign between hole and electron pockets
In plain words
The leading theory says the pairing amplitude has opposite sign on different pockets of the Fermi surface ($s\pm$ pairing); several experiments support it but a direct sign measurement is lacking.
Precise statement
In bulk iron pnictides with both hole pockets at $\Gamma$ and electron pockets at $M$ (for example Ba1-xKxFe2As2, LiFeAs), establish by a phase-sensitive probe whether the gap changes sign between them ($s\pm$) or not ($s++$). An answer is a measurement in which the sign enters directly, such as a Josephson interferometer or phase-referenced quasiparticle interference with known impurity potentials.
What would settle it
A phase-sensitive interference or Josephson experiment with an unambiguous sign signature reproduced in two materials.
Status in the literature
Neutron spin resonance and phase-referenced quasiparticle interference support $s\pm$; some impurity-scattering results were argued to favor $s++$.