The outdated things most in need to be included on wikis, but do not have citable papers are:

For bases between 0 and 1, tetration is a periodic function, damped for basis and very rapidly converging to a square wave function for basis . (no proof, just numerical results).

There is a direct connection to partition numbers (number theory), in the Taylor series.

There is a direct connection to graph theory this way and this way.

Also, many equations in use of different areas of mathematics already use iterated logarithms. But to consider those tetration to negative exponents, is necessary to consider tetration a multivalued function, with multiple branches.

I threw the ball on those threads, but nobody got interested.

For bases between 0 and 1, tetration is a periodic function, damped for basis and very rapidly converging to a square wave function for basis . (no proof, just numerical results).

There is a direct connection to partition numbers (number theory), in the Taylor series.

There is a direct connection to graph theory this way and this way.

Also, many equations in use of different areas of mathematics already use iterated logarithms. But to consider those tetration to negative exponents, is necessary to consider tetration a multivalued function, with multiple branches.

I threw the ball on those threads, but nobody got interested.

I have the result, but I do not yet know how to get it.