Optimize the degree-separation bounds

Optimize the sufficient degree bounds used in the even regradings of the minimal Sullivan models and thereby reduce the formal dimensions of the resulting smooth manifolds.

Background

The regrading construction uses deliberately large numerical parameters to ensure that each relevant cohomological degree contains at most one weight. These parameters guarantee the lower bound for Hnil over arbitrary graded acyclic ideals, but they also produce very large formal dimensions for the smooth realizations. The paper identifies improving these sufficient bounds as an unresolved problem.

References

Optimizing the sufficient degree bounds, and hence the realized dimensions, remains a separate problem.

— Unbounded Nilpotency Gaps on Rationally Elliptic Manifolds  (2610.21280 - Parent, 15 Oct 2026) in Section 5, “Further consequences and remaining questions”