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must report to the FISC “on the results of the approved surveillance and the continued need for such authority.”^[1]

D. Statutes Used to Evaluate Possible Criminal Conduct

This section begins with a brief description of the burden of proof that the government faces in every criminal case. It then describes the principal statutes that we considered to evaluate possible criminal conduct and exactly what must be proven beyond a reasonable doubt in order for a jury to convict.

1. Standard of proof beyond a reasonable doubt

The government has the burden of proving that a defendant committed any criminal offense beyond a reasonable doubt. A standard jury instruction on reasonable doubt is:

The government has the burden of proving [name of defendant] guilty beyond a reasonable doubt. In civil cases, it is only necessary to prove that a fact is more likely true than not, or, in some cases, that its truth is highly probable. In criminal cases such as this one, the government’s proof must be more powerful than that. It must be beyond a reasonable doubt. Reasonable doubt, as the name implies, is a doubt based on reason—a doubt for which you have a reason based upon the evidence or lack of evidence in the case. If, after careful, honest, and impartial consideration of all the evidence, you cannot say that you are firmly convinced of the defendant’s guilt, then you have a reasonable doubt.

Reasonable doubt is the kind of doubt that would cause a reasonable person, after careful and thoughtful reflection, to hesitate to act in the graver or more important matters in life. However, it is not an imaginary doubt, nor a doubt based on speculation or guesswork; it is a doubt based on reason. The government is not required to prove guilt beyond all doubt, or to a mathematical or scientific certainty. Its burden is to prove guilt beyond a reasonable doubt.^[2]

2. False statements

The principal federal statute criminalizing false statements to government investigators is 18 U.S.C. § 1001. As relevant here, subsection 1001(a)(2) makes it a crime “in any matter within the jurisdiction of the executive … branch of the Government” knowingly and willfully to “make [] any materially false, fictitious, or fraudulent statement or representation.” The government must prove five elements beyond a reasonable doubt to obtain a conviction under this provision:

First, the defendant made a statement or representation;

Second, the statement or representation was false, fictitious or fraudulent;

Third, this statement or representation was material;