T-SQL CTE for finding Parent, Prior Peer, Next Peer, Child

I actually need to generate the data in columns E-H, not just select it.  Please, how would I generate the data in these columns.

Data in E-H is already generated. How is it generated? How have you generated them.

What is data source? What is the algorithm to create them?

I think the example I sent you was not very good.  Attached is a better example.  column I shows what I am trying to get with an explanation on some of them.  I hope this helps.  I need some sort of subquery maybe with a CTE?
ExampleParentChild-2.xlsx

Unless someone else post a solution, I will be back on this question this evening (now it is about 7:30 AM).

thank you sorry for the initial confusion

example of what I need:

1. col E - Parent  <--Parent  depends on two columns: itemno, assemblyseq as described under note A below..
2. col F - PriorPeer            <-- PriorPeer depends on columns: ...  
3. col G - NextPeer           <-- NextPeer depends on columns: ...  
4. col H - Child                  <-- Child depends on columns: ...  

note A
itemno      assemblyseq
1.1.1.1             4                               you say Parent is 3  why?
1.1.1.2             5                               you say Parent is 3  why?
complete the rest

Your information so far is incomplete and super confusing.

This post has been revised...

yes it is super confusing.  I have to clean up data and put it into this format so we can import it into another system that wants data in this format.  In reference to:
note A
itemno      assemblyseq
1.1.1.1             4                               you say Parent is 3  why?
1.1.1.2             5                               you say Parent is 3  why?

parent is 3 for 1.1.1.1 and 1.1.1.2 because the prefix for these is 1.1.1 and itemno 1.1.1 says assemblyseq  = 0

The rules are:
if itemno = 0.0 then parent = 0
if itemno ends with .0 then parent = 0
otherwise, look at the prefix of the itemno and use the prefix to find the matching itemno. For example:
itemno = 1.1.1, prefix is 1.1, we need sql to find the itemno 1.1, and look up its assemblyseq.  the assemblyseq will be what we set "parent" = assemblyseq

example 1:
itemno = 1.1.1, prefix is 1.1, we find that for itemmo 1.1, the assemblyseq = 2, so for itemno 1.1.1, set parent = 2

example 2:
itemno = 1.1.1.1, prefix is 1.1.1, we find that for itemmo 1.1.1, the assemblyseq = 3, so for itemno 1.1.1, set parent = 3

example 3:
itemno = 1.1.2, prefix is 1.1.1, we find that for itemmo 1.1.1, the assemblyseq = 3, so for itemno 1.1.2, set parent = 3

example 4:
itemno = 1.1.2, prefix is 1.1, we find that for itemmo 1.1, the assemblyseq = 2, so for itemno 1.1.2, set parent = 2

example 5:
itemno = 2.7.1, prefix is 2.7, we find that for itemmo 2.7, the assemblyseq = 40, so for itemno 2.7.1, set parent = 40

The article was helpful and I was able to put some queries together that worked.