Hardness radius of Triangle Partition under edge-edit distance

Determine the hardness radius of Triangle Partition under the edge-edit distance, where the distance between two graphs on the same vertex set is the number of edited edges.

Background

The paper notes that Sidestep(Triangle Partition, dist, 2n/3) is polynomial-time solvable under the edge-edit distance and asks how far the tractability radius can be improved. The corresponding exact hardness radius is not established.

References

What is the hardness radius of Triangle Partition under $dist$?

— Answering Related Questions  (2501.10633 - Bonnet, 18 Jan 2025) in Question 6, Section 1, subsection “Open questions and potential future work”