A prior statement is exempt from the federal hearsay rule and is admissible to prove the truth of the matter asserted by the declarant with the prior statement if the prior statement was made under oath in another proceeding and if the prior statement is inconsistent with the declararant's testimony or with the admitted hearsay statement of the declarant.

United States v. Brothers Construction Company of Ohio, Inc., 219 F.3d 300, 310-311 (4th Cir. 2000) (upholding trial court's admission of the grand jury testimony of co-defendant Tri-State's officer as an admission by party's agent because (1) "[a]t the time....A statement by an agent or an employee who is not authorized to speak on behalf of the agent's principal or the employee's employer may nonetheless be treated as the statement of the principal or the employer and thus as a vicarious admission that is exempt from the prohibition against hearsay; but such a statement can be imputed to the principal or the employer only if the statement, if by an agent, is about a matter within the scope of the agent's agency or, if by an employee, the statement is about a matter within the scope of the employee's employment.

Fed. R. Evid. 608.Under some circumstances untruthfulness is admissible to impeach a witness.

Fed. R. Evid. 902 ("Extrinsic evidence of authenticity as a condition precedent to admissibility is not required" in the circumstances described by subdivisions 1-12 of the Rule).Some things or documents -- some things and documents with certain characteristics or appearances -- do not have to be authenticated: some things or documents are "self-authenticating."