Four-collinearity-free walks in dimension three

Determine whether there exists an infinite walk in three-dimensional integer space using only standard unit basis vector steps and containing no four collinear points.

Background

The paper constructs an infinite three-dimensional standard-basis walk with no seven collinear points, substantially improving the previously known bound. It also reports a finite walk of length 32768 with no four collinear points, but does not establish whether this property can persist indefinitely.

The unresolved question is whether the finite construction can be extended to an infinite walk, equivalently whether the collinearity bound in dimension three can be reduced from seven to four for standard unit basis steps.