because Gardner does not define the scope of the waiver that is effected by a state’s filing of a proof of claim. Unanswered by Gardner is whether such a filing waives immunity with respect to all claims against the state, whether it waives immunity with respect to only some claims and not others, or whether it just prevents the state from asserting its immunity in response to objections lodged against its claim (as in Gardner itself). The Supreme Court has never had the occasion to address these questions left open by Gardner. Most circuits agree, however, that when a state files a proof of claim, it waives its immunity as to at least some counterclaims, specifically compulsory counterclaims. See, e.g., Arecibo Cmty. Health Care, Inc. v. Puerto Rico, 270 F.3d 17, 28 (1st Cir.2001) (<HOLDING>); Schulman v. California (In re Lazar), 237
holding that eleventh amendment bars federal suits against state courts recognizing that claims against a state under  1981 are barred by the eleventh amendment recognizing that section 1983 claims against a state agency are barred by the eleventh amendment holding an exception to eleventh amendment immunity inapplicable in a suit against state officials on the basis of state law holding that the eleventh amendment permits assertion of compulsory counterclaims by debtor against state where state has filed a proof of claim