What is the test for a claim under section 406(b) of the Social Security Benefits Act?

As the text quoted supra at note 2 indicates, 406(b) authorizes a court that enters a judgment favorable to a social security claimant to award, "as part of its judgment," a reasonable fee for counsel's representation before the court, not to exceed 25% of the total past-due benefits to which the claimant is entitled "by reason of such judgment." 42 U.S.C. 406(b)(1)(A) ; see Gisbrecht v. Barnhart , 535 U.S. 789, 80708, 122 S.Ct. 1817, 152 L.Ed.2d 996 (2002) (observing that provision protects against "inordinately large fees" and affords "independent check" that fee agreements "yield reasonable results"). That section further authorizes the Commissioner to certify for such a court-awarded fee to be paid out of a past-due benefits award. See 42 U.S.C. 406(b)(1)(A) ; 20 C.F.R. 404.1728(b).⁴