Odd-order linear lower bound in dimension four

Establish whether there exists a constant γ > 0 such that NE4(n) ≥ γn for every n > 5, without restricting n to be even.

Background

A theorem cited in the paper gives a positive linear lower bound for NE4(n) when n is even. Casselgren and Pham conjectured that the parity restriction can be removed. The paper restates this unresolved issue as a question for all orders n > 5.