This is the first part of the next section:
Based on the previous sections the structure of the c plane is inspired by the properties of photons. This is because of the basic idea that numbers exhibit similar properties to fast-moving objects. If this premise is correct, it should be possible to reconstruct Minkowski (or Mink) by elements of projective geometry. In the previous section, without explaining what v=inf exactly means, it was said that z=0 pertains to v=inf. An axiom of SR says that v cannot exceed c. This seems to contradict the basic structure of the projective geom. However, Mink consists of space-like and time-like zones and the x-axis pertains to v=inf. Although v=inf carries no physical meaning (because SR is concerned with velocities in the time-like zone only), velocities greater than c exist in Mink. Not only do v>c exist in Mink they are critical parts of that, they refer to the spatial axes for different frames of reference.
So it’s clear that z=0 is the spatial axis. Now z=1 refers to the spatial axis at time ct. This means z=0 and z=1 are in fact the same, the former is the spatial axis at time t=0 and the latter is the same axis at time ct. So there is no fundamental difference between the lines.
Slopes in the time-like zone will then produce lengths v*t on z=1. To summarize, z=0 and z=1 both refer to v=inf. The distinction is that elements in z=1 are in 1-1 correspondence with slopes in the time-like zone. For massive objects passing through the origin at time t=0, z=1 is formed at infinity. This concludes the construction of Mink as a projective space. The main difference between the projective space which contains R and Mink is the metric. Currently, there is no metric connected to the z-axis in R. But motion of z=1, as constructed in the paper model, strongly suggests metric should be extended to the z-axis too.