E8 theta-class identification

Determine whether the modular-form edge of the TMF-valued closed class associated with the positive-definite even unimodular lattice E8 equals the E8 theta class.

Background

The paper establishes that multiplication by the Hopf element ν annihilates the class associated with every positive-definite unimodular lattice of positive rank, but it does not compute the class associated with E8 itself. Consequently, the proposed identification of its modular-form edge with the E8 theta class remains separate from the value theorem proved in the paper.

References

Neither computes $_{E_8}$. The conjectural identification of its modular-form edge with the $E_8$ theta class in therefore remains independent of the value theorem proved here.

— The hyperbolic class and vanishing laws in a TMF-valued four-manifold invariant  (2609.09819 - Li et al., 9 Sep 2026) in Section 6, “Interpretation and further questions”