How to prove integrity or authenticity

http://www.clir.org/pubs/reports/pub92/lynch.html

we want to ask questions about the authenticity of the object: If its integrity is intact, are the assertions that cluster around the object (including those embedded within it, if any) true or false?

How do we begin to answer questions about authenticity and integrity? There are only a few fundamental approaches.

We examine the provenance of the object (for example, the documentation of the chain of custody) and the extent to which we trust and believe this documentation as well as the extent to which we trust the custodians themselves.
We perform a forensic and diplomatic examination of the object (both its content and its artifactual form) to ensure that its characteristics and content are consistent with the claims made about it and the record of its provenance.
We rely on signatures and seals that are attached to the object or the claims that come with it, or both, and evaluate their forensics and diplomatics and their consistency with claims and provenance.
For mass-produced and distributed (i.e., published) objects, we compare the object in hand with other versions (copies) of the object that may be available (which, in turn, means also assessing the integrity and provenance of these other versions or copies).