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"To supplement this inherent power, Congress in 1857 adopted an
alternative statutory contempt procedure. Sec. 2, infra. Thus, the
House may either (1) certify a recalcitrant witness to the appropriate
United States Attorney for possible indictment under this statute or
(2) exercise its inherent power to commit for contempt by detaining
the witness in the custody of the Sergeant-at-Arms. Manual Sec. 296." 

"However, once judicial proceedings to enforce
the subpoena have been initiated, the defendant cannot be purged of
contempt merely by producing the documents or testimony sought. See
United States v. Brewster, 154 F. Supp. 126 (D.D.C. 1957), cert.
denied, 358 U.S. 842 (1958)"

https://www.govinfo.gov/content/pkg/GPO-HPRACTICE-112/html/GPO-HPRACTICE-112-18.htm