Nondegeneracy of the spectral pseudo-norm

Determine whether the spectral pseudo-norm $\\widetilde\\gamma$ on the universal cover of the Hamiltonian diffeomorphism group vanishes only at the identity element.

Background

The spectral pseudo-norm is defined on the universal cover of the Hamiltonian diffeomorphism group, while its descended function on the group itself is a genuine norm. The unresolved issue is whether the pseudo-norm itself is nondegenerate before passing to the quotient.

References

It is an open problem whether $\widetilde\gamma([H])=0$ if and only if $[H]$ is the identity.

— Biran decomposition and relative symplectic cohomology  (2610.01334 - Jo et al., 1 Oct 2026) in Section 2, subsection “Spectral norm”