Hi Lorraine,
Sorry for late reply!
Great way to think about this! In this respect I'd suggest physical reality apprehends numbers as dimensions. So a singularity is zero with regard to spatial dimensionality. 1-dimension could exist as equivalent if we look at simplexes as fundamental geometry.
The two vertices of a line segment are equidistant to their average position - a point - 0-dimensional simplex. So creating 1-dimension from 0-D conserves 0-D point.
We can indeed then do this equivalency for any n-dimension simplex. However, starting at 0 and moving to the next dimension 1 allows us to then follow Fibonacci.
As you rightly say - why this rather than all numbers?
To answer this I'd point to the negative part of the sequence. The -1, 1, 0. Without this we would be saying that 0D can fluctuate to higher dimensions, but always must fluctuate back down to nothingness again.
If 0D however fluctuates of "decays" to -1 +1 we have two 1-dimensionalities. One positive and one negative (whatever that means).
I'd suggest this is the real approach to solving Baryon Asymmetry.
With -1 AND +1 existing, we could of cause have a type of annihilation. BUT a further "decay" of each dimensionality would do this:
-1 -> -3 +2 AND (+1 -> 0 +1 then +1 -> +2 -1)
Giving us -3, 2, AND 2, -1.
We'd have an asymmetry with two distinct spaces. One made of -3+2 dimensionality and another of +2-1 dimensionality.
I.e. one overall -1 the other overall +1. But geometrically unable to annihilate.
Not getting sidetracked from your question, but this highlights why the sequence might be foundational and special.
The other point re- numbers obtained from measurement. I'd say they are cumulative just as we know them.
For example, the geometries arising from my theory are quantised yet real numbers, as angles such as the dihedral angle of the tetrahedron and Pi apply.
Best wishes,
Antony