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

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Last Modified: 2015-07-20
Attached is a spreadsheet.  I have this data in a table "asm"  I need to produce the columns:
col E - Parent
col F - Prior Peer
col G - NextPeer
col H - Child
The numbers in the columns E, F, G, H are the "AssemblySeq" numbers.  How would I write a sql server 2012 CTE procedure to derive these values in col E-H?  

Please provide complete SQL statement.
example-parent-child.xlsx
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