Marjorie Vance appeals from a District Court order affirming the denial of her application for child's insurance benefits on behalf of her son, Reginald Ham.1 See 42 U.S.C. Sec. 402(d) (1982) (the Social Security Act). The benefits were earned by Willie Wilkins, who died in the State of New York in 1977. The sole issue in the case is whether substantial evidence in the record supports the conclusion of the Secretary of Health and Human Services that appellants failed to prove that Ham was Willie Wilkins' child.2 Because the record is entirely devoid of any evidence, much less substantial evidence, supporting the Secretary's conclusion, we reverse and direct the District Court to remand the case to the Secretary with instructions to award Ham the benefits to which he is entitled.

A "child" of a deceased wage earner who satisfies the age, filing, and non-marriage requirements of the Act, id. Sec. 402(d)(1), and who has not been legally adopted by another, id. Sec. 402(d)(3)(B), is entitled to benefits if he or she was "dependent" on the wage earner at the time of the wage earner's death. Id. Sec. 402(d)(1)(C). A child who was not living with or supported by the insured wage earner at the time of the latter's death may, nonetheless, be "deemed dependent" if he or she is the "legitimate [or] adopted child" of the insured. Id. Sec. 402(d)(3)(A). An illegitimate child shall be "deemed to be the legitimate child" of the wage earner, id. Sec. 402(d)(3)(B), if any of the following conditions obtain: (1) the wage earner "had acknowledged in writing that the applicant is his son or daughter," id. Sec. 416(h)(3)(C)(i)(I); (2) prior to the insured's death a court had decreed him or her to be the mother or father of the applicant or had ordered contribution for support of the child, id. Sec. 416(h)(3)(C)(i)(II-III); (3) evidence "satisfactory to the Secretary" shows that the insured was the parent of the applicant and that the insured was "living with or contributing to the support of the applicant" at the time the insured died, id. Sec. 416(h)(3)(C)(ii); or (4) the child would be entitled to inherit property from the wage earner under the laws of intestate devolution of the state in which the latter died, id. Sec. 416(h)(2)(A).3

Thus Ham's eligibility for benefits turns entirely on whether he is deemed "a legitimate child" under the Act. Such a finding necessarily satisfies the requirement that the applicant have been "dependent" on the insured at the time of the latter's death.

Under established law, the applicant bears the burden of proving that he or she is dependent on the insured and is therefore eligible for benefits. See Wyatt v. Ribicoff, 211 F. Supp. 928, 929 (W.D.La.1962); H. MCCORMICK, SOCIAL SECURITY CLAIMS AND PROCEDURE Sec. 134 (3d ed. 1983). Under equally established law, the factual findings that underlie the Secretary's eligibility determinations are conclusive if supported by "substantial evidence." 42 U.S.C. Sec. 405(g); see Richardson v. Perales, 402 U.S. 389, 401, 91 S. Ct. 1420, 1427, 28 L. Ed. 2d 842 (1971).

Although appellants challenge the Secretary's decision on several grounds, we focus our attention on a single dispositive issue: whether substantial evidence in the record supports the determination that a letter submitted by appellants was not a written acknowledgement of paternity within the meaning of Section 416(h)(3)(C)(i)(I).

The letter, which opened with the salutation "Hi Doc," included the following passage:

Oh! Doc, I will be waiting for your and Queen and the rest of the family picture[.] Ok, I was glad to know that Queen was gone back to school, then she can be a lot of help to you and family with money * * *. Your sister and law call me last week, and I took the call. But I didn't like that. I told her that I would take care of my son. I just want him to stay with me until school open and I will give him anything that he need for school. But your sister and law had a man with her making me a call to New York and really didn't like that at all.

Records Excerpts for Appellant (hereinafter RE) at 94-95 (emphasis added). The letter closed with the names "Uncle Bill Wilkins" and "C. Ruffus [sic ] Wilkins Jr.," both clearly written in the same hand.

Self evidently, Ham's entitlement to benefits turns on three critical questions. The first is the identity of the letter's author. For only if Willie Wilkins wrote the letter could the phrase "my son" refer to Ham. The second is the identity of the person referred to as "your sister and law." Unless the reference is to Marjorie Vance, Ham's mother, it would be impossible to conclude that Reginald Ham was the "son" whose support was the subject of the phone call described in the letter. The third and, of course, ultimate question is whether "my son" is a reference to Reginald Ham.

In an earlier proceeding a claims representative resolved these questions in Ham's favor and found that the letter constituted a written acknowledgement of paternity. Special Determination of Claims Representative, Department of Health, Education and Welfare, October 6, 1980, RE 114. The Administrative Law Judge, whose findings were adopted by the Secretary, disagreed. We quote the ALJ's analysis in its entirety:

The letter submitted by claimant, when considered in light of all credible testimony and statements, is found to be less than persuasive of Willie's paternity. It is not clear who wrote or received the letter. Assuming that Willie wrote the letter, the mention of "my son" does not constitute acknowledgement by Willie that claimant is his son. Willie was married at the time he wrote the letter and had three other sons. [I am] not persuaded that Willie was referring to claimant.

Decision of ALJ, October 14, 1982 (hereinafter Decision ), at 3, RE 10. The decision offered not a word of explanation for the apparent refusal to credit any of the voluminous and entirely unrebutted testimonial and documentary evidence suggesting that Willie Wilkins wrote the letter to his nephew Charles;4 that Marjorie Vance, Ham's mother, is Charles' sister-in-law;5 and that the phrase "my son" refers to Reginald Ham.6

Although we are fully cognizant of the limited scope of our review, we conclude that this analysis does not comport with the demands of reasoned decisionmaking. Even if we limit our inquiry to the face of the letter and the ALJ's own findings of fact,7 we find no support for his doubts about the identity of the author and recipient of the letter. Nor do we believe that the letter is susceptible of any other construction than that the phrases "your sister and law" and "my son" refer to Marjorie Vance and Reginald Ham.

Even if we disregard the uncontradicted testimony that overwhelmingly suggests that Willie Wilkins is "Uncle Bill" and that Uncle Bill often sent letters to his nephew Charles R. Wilkins, we have difficulty perceiving any significant ambiguity concerning the letter's authorship. Two names occupy the position in the letter ordinarily reserved for the signature. We may safely assume that one of the two belongs to the author. Because the name "Ruffus" is apparently misspelled,8 we begin with the tentative assumption that "Uncle Bill" and not "Charles Ruffus Wilkins Jr." wrote the letter. The letter's content, read in conjunction with the ALJ's findings of fact, fully supports this initial hypothesis. The letter refers twice to a woman named Queen. The context of the reference makes crystal-clear that Queen lives in the same household as the recipient of the letter. Indeed, it is undisputed that Queen is the wife of Charles Wilkins.9 The inference is therefore inescapable that the recipient was Charles Wilkins.

By process of elimination, the author of the letter must be Uncle Bill. Given the ALJ's express finding that Charles was Willie's nephew, Decision at 3, RE 10, and the common wisdom that Willie and Bill are derivations of the same name, there is little room for doubt that "Uncle Bill" and "Willie Wilkins" are one and the same person.10 The absence of even a scintilla of evidence in the record that might undermine the otherwise clear inference derived from the letter itself (without any need for crediting extrinsic evidence) renders doubt about the authorship of the letter difficult to comprehend.

B. The Reference to "My Son"

No less difficult to understand is the ALJ's view that the reference to "my son" was too ambiguous to constitute a written acknowledgement of paternity even if one were to assume that Willie Wilkins was the letter's author. Id. Read in light of the utter lack of contrary evidence, the letter leaves no room for doubt that "Marjorie Vance" is the "sister and law" mentioned in the letter. The ALJ expressly found that Vance was the sister of Queen. Id. Because Queen is the wife of Charles R. Wilkins, Marjorie Vance must be his sister-in-law. While, of course, the universe of possibilities includes the existence of another sister-in-law with whom Willie Wilkins might discuss child support, neither common sense nor a hint of evidence in the record provide the catalyst that might convert such abstract speculation into a reasoned conclusion.

If, then, Willie Wilkins was the author of the letter and Marjorie Vance is the woman referred to as his nephew's sister-in-law, only one piece of this hermeneutic puzzle remains to be put in place. In the context of describing a somewhat caustic conversation with Vance about child support, Wilkins refers to "my son." The ALJ found the reference ambiguous because Wilkins had other sons by another woman. This analysis is even more difficult to understand than doubts about the identity of the author and recipient of the letter. The context and tone of the conversation described in the letter leave no reasonable doubt that the "son" refers to a child of Marjorie Vance. She, the letter makes explicit, called Wilkins. Apparently in response to her prodding, the two discussed Willie's intentions "to take care of" a child acknowledged by Wilkins to be his "son." In the absence of some indication that Vance had an interest in or even knew of Wilkins' other children, it defies logic to suggest that the conversation concerned anyone other than her son, Reginald Ham. Again, the abstract possibility that the conversation referred to another of Wilkins' sons cannot be eliminated as a matter of certainty. But, without some explanation or support in the record, such wholly counterintuitive speculation provides a legally deficient foundation for the determination that the letter was not a written acknowledgment of paternity.

Because we have concluded that the letter, on its face, is susceptible of only one reasonable construction, we hold that appellants have met the requirements of 42 U.S.C. Sec. 416(h)(3)(C)(i)(I) by proving a written acknowledgment of paternity. Accordingly, we reverse the District Court and remand with instructions to direct the Secretary to award Ham the benefits to which he is entitled under Section 402(d) of the Social Security Act.

So ordered.