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I (User:SnowFire) sent a letter to the Biblioteca Nacional to confirm the public domain status of the work (as Encyclopedia Britannica did not credit an author nor give a date of publication; I wrote a letter to them, too, but they only referred me to BN.). The body of their response:

en respuesta a su petición de fecha 23 de octubre, le comunicamos que la litografía del retrato de Juan de Padilla no presenta problemas de derecho de autor para su uso.

Referente a los datos del retrato que manda son los siguientes: la signatura de nuestros fondos es IH/6829-2; Busto en ovalo. Inscripción en una banderola debajo del retrato que pone "Juan de Padilla decapitado en Villalar el 24 de abril de 1522" S. Llanta lo dibujó y litografió. Litografía de J. Donón.

My translation to English:

In response to your question of October 23rd, we can tell you that the lithograph of Juan de Padilla does not present copyright problems for use.

Referring to the details of the work that you asked are the following: the signature of our (purchase?) is IH/6829-2; (it's a) bust in an oval. Inscribed on the banderole beneath the work is "Juan de Padilla was decapitated in Villalar the 24th of April in 1522." It's drawn and lithographed on the rim. The lithograph is by J. Donón.