I would like to get a demonstration of the stable homeomorphism conjecture (SHC$_n$), stating that any orientation-preserving homeomorphism $\mathbb{R}^n \rightarrow \mathbb{R}^n$ is stable in dimension $n$, for $n \neq 4$.

According to several sources, for example the upvoted answer to the post connectivity of the group of orientation-preserving homeomorphisms of the sphere , Robion Kirby proved it for $n > 4$ in the following paper http://www.maths.ed.ac.uk/~aar/papers/kirby.pdf .

("After that came R. Kirby (and L. Siebenmann) in 1968, who proved (using the results of surgery by Wall et al), that SHC$_n$ (hence AC$_n$) is true in all dimensions $n>4$.")

People often say in other papers that Kirby proves in fact in his paper not the SHC$_n$ for $n > 4$ but rather the annulus conjecture (AC$_n$) which would be equivalent to SHC$_n$, the equivalence being proved hypothetically in the paper of Brown and Gluck about "Stable structures on manifolds" (on JSTOR : https://www.jstor.org/stable/1970482?seq=1#fndtn-page_scan_tab_contents).

My two questions are the following : How can you justify precisely that :

1) Kirby proved AC$_n$ for $n > 4$ in his paper?

2) Brown and Gluck proved that AC$_n \Leftrightarrow$ SHC$_n$ for $n > 4$?

(I would like precise theorems in the papers and why they prove the results because after reading them a few times, I can't answer these two questions.)

PS : Nonetheless, if you have/know other research paths to prove SHC$_n$ for $n \neq 4$ don't hesitate, since it's my goal for all of this!