As used in this section, the term “beneficiary” means only a surviving spouse entitled to benefits at the time of death (see § 725.212), or a miner. An individual will be considered to be the child of a beneficiary if:
(a) The courts of the State in which the beneficiary is domiciled (see § 725.231) would find, under the law they would apply, that the individual is the beneficiary's child; or
(b) The individual is the legally adopted child of such beneficiary; or
(c) The individual is the stepchild of such beneficiary by reason of a valid marriage of the individual's parent or adopting parent to such beneficiary; or
(d) The individual does not bear the relationship of child to such beneficiary under paragraph (a), (b), or (c) of this section, but would, under State law, have the same right as a child to share in the beneficiary's intestate personal property; or
(e) The individual is the natural son or daughter of a beneficiary but is not a child under paragraph (a), (b), or (c) of this section, and is not considered to be the child of the beneficiary under paragraph (d) of this section if the beneficiary and the mother or the father, as the case may be, of the individual went through a marriage ceremony resulting in a purported marriage between them which but for a legal impediment (see § 725.230) would have been a valid marriage; or
(f) The individual is the natural son or daughter of a beneficiary but is not a child under paragraph (a), (b), or (c) of this section, and is not considered to be the child of the beneficiary under paragraph (d) or (e) of this section, such individual shall nevertheless be considered to be the child of the beneficiary if:
(1) The beneficiary, prior to his or her entitlement to benefits, has acknowledged in writing that the individual is his or her son or daughter, or has been decreed by a court to be the parent of the individual, or has been ordered by a court to contribute to the support of the individual (see § 725.233(e)) because the individual is his or her son or daughter; or
(2) Such beneficiary is shown by satisfactory evidence to be the father or mother of the individual and was living with or contributing to the support of the individual at the time the beneficiary became entitled to benefits.