Linear simplicial Tutte flow conjecture

Let $d$ be the dimension of a simplicial complex, and let $\kappa(d)$ denote the least finite flow bound asserted by the preceding simplicial Tutte flow conjecture.

Linear simplicial Tutte flow conjecture.

$$\kappa(d)=d+4.$$

The paper presents this as the stronger, natural analogue of Tutte's conjecture and as a proposed linear value for the higher-dimensional flow bound. Its resolution is not supplied in the stated context.