To build again from what remains. Reconstruction is inference disciplined by evidence, and it is never the original.
Re- (Latin, again) attached to construct, from Latin construere (to pile up, to build): com- (together) + struere (to pile, to build); to reconstruct is to build again from what still stands.
To build again from what remains. The root's piling-up is disciplined by what is actually there — reconstruction is inference held to evidence, and it is never the original it stands in for.