Determine compatibility of the positive real form with integral and character data

Determine whether the transported positive real structure on the EP tip is compatible with an integral order or with a character-induced grading.

Background

The paper distinguishes the split real structure generated by the root-vector basis from the positive real form transported from the Clifford model. It also distinguishes the character-induced root grading and integral lattice data from the positive real realization of the tip.

The authors state that compatibility between these structures has not yet been determined, leaving open whether an integral order or a character grading can be realized compatibly with the transported positive real form.

References

Thus the root-coordinate grading and the positive real structure are separate data; their compatibility, including any integral compatibility, remains to be determined.

— Okubo algebras and Exceptional Periodicity: tetracode gradings, root-lattice obstructions and Clifford cones  (2610.18643 - Marrani et al., 13 Oct 2026) in Remark “Real form and induced tip derivations,” Section 8, subsection “The normalized root-tip identification”