Update: 2017.12.11
Since no later than the giving of the Tōr•âhꞋ to MoshꞋëh on Har Sin•aiꞋ, when names are recorded by the Beit-Din in the Orthodox Jewish community they are archived in the heavenly archive. RibꞋi Yᵊhō•shuꞋa confirmed this in The Nᵊtzârim Reconstruction of Hebrew Matityâhu (NHM) 18.19f (for documentation and details see the corresponding notes): "I tell you, whatever you shall make â•surꞋ in [the Beit-Din of the Nᵊtzâr•imꞋ] on hâ-ÂrꞋëtz shall be made â•surꞋ in the Beit-Din Above…"
The Yō•khas•inꞋ recognized and included 10 categories of persons, in 3 groups of permitted intermarriage (within certain constraints), that were differentiated from the goy•
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Though the earthly scrolls were destroyed by the Romans and other oppressors—with the notable exception of both the patriarchal and matriarchal genealogies of RibꞋi Yᵊhō•shuꞋa—the names remain recorded in the Yo•khas•inꞋ in the heavenly archive Yo•khas•inꞋ – the Scroll, (family) Tree, of Life.
On the other hand, the destruction of the (physical) Yo•khas•inꞋ terminated all legitimacy of physical Ko•han•
"Herod, who also had to face a challenge to the legitimacy of his rule, forged for himself a pedigree going back to Dâ•widꞋ, after first destroying the genealogical records maintained in the Temple (according to third-century Christian historian Africanus)" ("Genealogy," EJ 7.381).
"It was not without reason that, as Hegesippus informs us, the Roman emperors Vespasian, Domitian and Trajan ordered the hunting out and execution of all who claimed Davidic descent" (Salo Wittmayer Baron, A Social and Religious History of the Jews, New York: Columbia Univ. Press, 1937, 1952,, vol. II, p. 121).
"According to Hegesippus, Vespasian, Domitian and Trajan hunted down all Jews of Davidic descent and executed them in order to extirpate the royal line on which Jews had set their hopes" (Eusebius EH iii.12 (Vespasian; ibid., iii.19-20 (Domitian; ibid., iii.32, 3-4 (Trajan); all derived from Hegesippus)." (Emil Schürer, The history of the Jewish people in the age of Jesus Christ (B.C.E. 175—135 C.E.), vol. I, edit. Geza Vermes, Fergus Millar, Matthew Black & Pamela Vermes, Edinburgh: 1973, T. & T. Clark, p. 528)
See also Eusebius EH III.xii.19-20, 32; xxxii.1-6.
With the exception of the paternal and maternal genealogies listed for RibꞋi Yᵊhō•shuꞋa in NHM (ch. 1—dating back to the Beit-Din ha-Jâ•dolꞋ), the genealogies of Beit-Dâ•widꞋ were destroyed by Herod and the Romans.
A [Ko•heinꞋ] must himself be of proven pedigree to serve in the [Beit ha-Mi•qᵊdâshꞋ] (Mid•otꞋ 5.4; Qi•dush•inꞋ 4.5). Those currently designated "[Ko•han•imꞋ]" are "presumed [Ko•han•imꞋ]," inasmuch as there is no legally sufficient proof testifying to their descent from ancient [Ko•han•imꞋ] families (see Maimonides Yad. A•sur•eiꞋ Bi•âhꞋ 20.1-2; Mâ•geinꞋ Av•râ•hâmꞋ to OH 457.2)" ("Priests and Priesthood," EJ 13.1088).
This glosses over Nᵊkhëm•yâhꞋ 7.63-65, which declares Ko•han•imꞋ lacking official Yo•khas•inꞋ to be Kha•lâl•imꞋ (profaned Ko•han•imꞋ), whom Tal•mudꞋ places on the same level as geir•imꞋ (Mish•nâhꞋ Qi•dush•inꞋ 69a-b)!!!
The genealogies of the Ko•han•imꞋ seem to have been destroyed by the Ko•han•eiꞋ hâ-RëshꞋa, to eliminate their rivals, during the Hellenization of the priesthood, long before Herod and the Romans destroyed the genealogies of Beit-Dâ•widꞋ.