Detective Dent went to Paul's house and started to search his car without presenting any paperwork to Paul. What amendment does this violate?

The 4th Amendment

The Fourth Amendment to the U.S. Constitution places limits on the power of the police to make arrests, search people and their property, and seize objects and contraband (such as illegal drugs or weapons). These limits are the bedrock of search-and-seizure law. This article covers basic issues you should know, beginning with an overview of the Fourth Amendment itself.

It is meant that like tapestry scientific theories often need to pull out since they are not relevant and often times the whole chain of theories may be pulled out.