A dependent child of a wage earner is entitled to "child's insurance benefits" under the Social Security Act if the wage earner is insured under the Act and dies, becomes disabled, or reaches the age of 65. 42 U.S.C. § 402(d). Problems of determining entitlement sometimes arise when, as in the present case, the wage earner (Ivory Claxton) dies and was not married to the child's mother (Cynthia Jones). The Act contains an exhaustive list of methods of establishing entitlement to child insurance benefits in such a case: proof that the wage earner would have been married to the child's mother but for a technical deficiency in the marriage; a written acknowledgment of paternity by the wage earner; a judicial decree that the wage earner was the child's father, provided the decree was issued before the wage earner died; a court order that the wage earner contribute to the support of the child because the wage earner was the child's parent; a determination by the Social Security Administration, based on satisfactory evidence, that the wage earner was the parent of the child and was living with or contributing to the child's support when the wage earner died; or proof that the child was entitled to inherit from the wage earner under the law of intestate succession of the wage earner's state of domicile. 42 U.S.C. §§ 416(h)(2)(A), (C). Jones sought to establish an entitlement to benefits for her 11-year-old son, Brandon Jones, by the last two of these methods--proof of paternity under state intestate statute (§ 416(h)(2)(A)), and paternity plus support (§ 416(h)(3)(C)(ii)). The Social Security Administration turned down her application on the ground that she had proved neither paternity nor support. The district court upheld the denial of benefits.

Claxton was domiciled in Missouri, and Missouri's intestate succession statute requires, so far as bears on this case, clear and convincing evidence of paternity. Mo.Ann.Stat. § 474.060(2). But that is all that the statute requires; unlike the method of establishing entitlement that we are calling "paternity plus support," there is no requirement of proving that the father ever provided any support to the child. Proof of paternity is easier under the "paternity plus support" method than under the Missouri statute, because proof by a preponderance of evidence is all that is required under the former method, and that is, of course, a lesser burden than proof by clear and convincing evidence. Brown v. Bowen, 847 F.2d 342, 345-46 (7th Cir.1988); Imani v. Heckler, 797 F.2d 508, 511-12 (7th Cir.1986). Oddly, we cannot find a case that holds that a preponderance of the evidence is all that the paternity plus support method requires; nor does the Social Security Act, or the regulations under it, prescribe a standard of proof, although the Act does make clear that the claimant for benefits bears the burden of persuasion. 42 U.S.C. § 405(g). But we have no doubt that preponderance of the evidence is the proper standard, as it is the default standard in civil and administrative proceedings, Steadman v. SEC, 450 U.S. 91, 101 n. 21, 101 S. Ct. 999, 1007 n. 21, 67 L. Ed. 2d 69 (1981); see also Director v. Greenwich Collieries, 512 U.S. 267, ----, 114 S. Ct. 2251, 2257-58, 129 L. Ed. 2d 221 (1994), and no reason for a different standard in paternity-plus-support cases has been suggested or occurs to us. On the contrary, the fact that proof of support is required as well as proof of paternity is an argument for a lower standard of proof than under statutes that require proof of paternity by clear and convincing evidence but require no evidence at all of support.

The administrative law judge got this wrong; he required proof of paternity by clear and convincing evidence under both the paternity and the paternity-plus-support methods. He compounded his error by equating "clear and convincing" to "beyond a reasonable doubt." These are serious errors. While Jones indeed failed to prove Claxton's paternity beyond a reasonable doubt, the evidence of his paternity is very strong and might well be found to have satisfied the clear and convincing standard, and, all the more, the preponderance standard. It is undisputed that Claxton (who was married to, and had children by, another woman) was having an affair with Jones when she became pregnant with Brandon. In 1981, after she became pregnant, she moved to California to be with her mother. Brandon was born, and shortly afterward Claxton visited him and the mother in California and bought clothes, groceries, and other items for him. At Claxton's urging, the mother moved with the baby back to St. Louis and the two of them lived in an apartment over Claxton's grocery store. Claxton saw Brandon, and bought him clothes and toys, from time to time. In 1989 or 1990, Cynthia Jones moved with her son to Illinois. Claxton died in 1991 without having seen either Cynthia or Brandon, or provided any financial or other tangible assistance to Brandon, after their move to Illinois. Brandon testified at the benefits hearing that Claxton had told him that he was his father and that he believed it.

Claxton's widow, testifying against paternity, speculated that if her husband had given money or goods to Brandon it was purely because of the disinterested generosity for which he was known. She did not testify that her husband was not Brandon's father--only that he didn't know whether he was or not, and speculated that her husband's brother, or perhaps one of the employees of the grocery store, might be Brandon's father--might have impregnated Jones when they were living in the apartment above the store. But Brandon had already been born when he and his mother returned from California and moved into the apartment.

Although the administrative law judge's determination that Claxton was not the father cannot stand, because he applied the wrong standard of proof and the error is not harmless, we cannot reverse the determination that Jones has failed to establish entitlement by the state intestate statute method. The reason is that she has abandoned her reliance on this method in this court. E.g., Harris v. City of Marion, 79 F.3d 56, 59 (7th Cir.1996); Griman v. Makousky, 76 F.3d 151, 153 (7th Cir.1996); Doherty v. City of Chicago, 75 F.3d 318, 326 (7th Cir.1996). Although her main brief contains a couple of references to the administrative law judge's having applied the wrong standard to determining paternity under the state intestate statute, the statute is not cited in either of her briefs; the statement of the issues presented does not mention the statute; and the only request for relief is that we remand for a redetermination of paternity under the preponderance of the evidence standard, a standard applicable to the "paternity plus support" method of establishing entitlement to child insurance benefits but not to the state intestate statute method. At argument, one of the judges said that he had a problem with the administrative law judge's handling of the state intestate method, even though Jones's lawyer did not: "I know you don't [have a problem with it], I do," the judge said. Jones's lawyer agreed that the administrative law judge had misapplied the Missouri statute, but she did not request relief from that error. The appellee's lawyer, when his turn to speak came, stated that the state intestate method was not involved in the appeal, and Jones's lawyer did not challenge this statement in her rebuttal.

Although an argument that an appellant has waived an issue can itself be waived, e.g., Wilson v. Kelkhoff, 86 F.3d 1438, 1445 (7th Cir.1996); Jeppesen v. Rust, 8 F.3d 1235, 1237 (7th Cir.1993); Fagan v. Washington, 942 F.2d 1155, 1157 (7th Cir.1991), that did not happen here. On the contrary, the government stated in its appellee's brief (and repeated, as we have noted, at the argument) that Jones "concedes that the 'state alternative' [what we are calling the state intestate statute method of establishing entitlement to child insurance benefits] does not apply" and "instead" is claiming entitlement under the "paternity plus support" section of the child insurance benefits statute. Jones filed a reply brief but did not take issue with these statements in the government's brief, just as she did not at argument. It is true that the government's brief defends the administrative law judge's finding that Jones had not established that Claxton was her son's father, but the issue of paternity is relevant to paternity plus support as well as to the state intestate statute, so the government's discussing it cannot be taken as a tacit acknowledgment that the intestate statute method was still in the case.

Jones's lawyer may have made a tactical decision to confine her appeal to the paternity plus support method because it is easier to prove paternity under that method. She may have believed that even if she could obtain a fresh determination of paternity under the Missouri statute, the administrative law judge would not have found paternity established by clear and convincing evidence. Whatever the lawyer was thinking, we cannot grant relief on a ground so thoroughly waived, since none of the exceptions to the waiver doctrine are applicable. See, e.g., Association of Community Organizations for Reform Now (ACORN) v. Edgar, 56 F.3d 791, 796-98 (7th Cir.1995). The government had no reason to think that the Missouri statute was still in the case, and therefore made no effort to meet an argument based on that statute--an argument not made.

Under the paternity plus support method of establishing entitlement to child insurance benefits, Jones had to prove not only that Claxton was Brandon's father, but also that Claxton was contributing to the child's support when he died, 42 U.S.C. § 416(h)(3)(C)(ii), and that the support was "regular and substantial." 20 C.F.R. § 404.366(a)(2). She cannot prove either. Until a year or two before his death, Claxton provided intermittent support to Brandon, but it could hardly be described as regular and substantial. It was not regular; and no effort was made to establish that it was substantial. After Brandon and his mother moved to Illinois, at least one year and possibly two years before Claxton's death, Claxton provided zero support to Brandon. Jones says that it was not his fault; that he wanted to; that he tried but failed to find out where she and Brandon were living. This would be relevant to a temporary interruption, see 20 C.F.R. § 404.366(a)(2), but we do not think that the statute can reasonably be interpreted to be satisfied by zero support. Remember that there are many different methods of establishing entitlement to child insurance benefits; if each is to be watered down to nothing, the statute will place no limitations on such entitlements.

Some courts relativize "substantial" to the resources of the putative father. E.g., Parker v. Schweiker, 673 F.2d 160 (6th Cir.1982); Jones v. Harris, 629 F.2d 334 (4th Cir.1980) (per curiam). None, however, has gone so far as to equate substantial to zero because the father's resources are zero or, as in this case, because circumstances beyond his control prevent him from devoting any of his resources to his child's support. Even the Sixth Circuit, the leader in relativizing, has held that the father must provide some support. Chester v. Secretary of Health & Human Services, 808 F.2d 473, 476 (6th Cir.1987); Young v. Secretary of Health & Human Services, 787 F.2d 1064, 1070 (6th Cir.1986); see also Wolfe v. Sullivan, 988 F.2d 1025, 1028 (10th Cir.1993). Our court has held the same thing, Schaefer v. Heckler, 792 F.2d 81, 86-87 (7th Cir.1986), emphasizing that the statute is not to be gutted by reference to the financial wherewithal of the father. Bennemon v. Sullivan, 914 F.2d 987 (7th Cir.1990). Sporadic support will not do, however exiguous the father's resources, because the purpose of federal child insurance benefits is not to benefit minor children as such but, as the Supreme Court pointed out in Mathews v. Lucas, 427 U.S. 495, 507-08, 514-15, 96 S. Ct. 2755, 2763-64, 49 L. Ed. 2d 651 (1976), to replace the support that the child would have received from his father had the father not died. Bennemon v. Sullivan, supra, 914 F.2d at 990-91; Trammell v. Bowen, 819 F.2d 167, 169 (7th Cir.1987); see also Mornes v. Chater, 91 F.3d 1403, 1404-05 (10th Cir.1996). Every father whose parental rights have not been terminated (as by the lawful adoption of the child by another person) has a legal duty to support his child, Ind.Code § 35-46-1-5; 1 Homer H. Clark, Jr., The Law of Domestic Relations in the United States § 5.4, p. 317 (2d ed. 1987), but the reality is of course different and many fathers, especially of children born out of wedlock, do not support their children. The fact that Brandon Jones is probably the child of Ivory Claxton is not by itself proof or even strong evidence that if Claxton had lived he would have supported the child. He had terminated support, at best intermittent, well before he died.

Because Jones has failed to satisfy the "support" requirement of the "paternity plus support" method of establishing entitlement, and has waived the issue whether she proved paternity under the Missouri intestacy statute, we must affirm the denial of benefits despite the administrative law judge's erroneous handling of the paternity issue.

AFFIRMED.