The fundamental problems of these extrapolations seem lost in the confusion of reality.
As a mist voiceless, like a gray cloud and bitter.
AdS spaces with their hyperbolic extentions, Lorentz would agree with the restriction of the referential.
We can invent, extrapolate, differentiate, overlay .. but our main field is what it is.
Take arguments and Cartesian coordinates.
If for example we stipulate that x, y and z are coordinates of the point.
how could you represent the geometry with x, y, z ,......, t?
We are in the heart of general relativity with the cosmological constant.
And therefore it is imperative to respect the gravity and proportionality.
We are in need also to include the evolution and its dynamics,specifics. Integers and thus reveal their first dance in a closed system evolving.
The 3-dimensional sphere is the best explanation of course.
The time will never be a certain irreversibility with loops and speudos dimensions.
You can invent all the matrix you want, our intrinsic laws will not change.
There are no other redundant dimension, the sphere in 3D and its time constant are fundamental.
All math games remain in this universal logic.
Take a hyperboloid of one sheet, we have real and imaginary axes, but this remains purely in 3 dimensions.
If you extrapolate with the infinity inside a closed system, you shall see the generatrices and the real geometrical form.An infinity inside a system is different than an infinite system itself ???? This point is very important,even foundamental.
Think about the transition of hyperboloids and ellispoids .....x²+y²+c²=a²....your quotient are just falses imaginaries..
In fact in all paraboloid, hyperboloids, ......it's the sphere the referential.
The symmetries are in 3 dimensions.And the time is not a dimension.Even with some parameters inserted inside the system.
How can we understand the cosmological constant without the evolution and the spherization.That seems not possible.
I am surprised sometimes with some analyzes or interpretations of datas.