I wondered if citrus aurantifolia 'Pursha' was the same as Persian lime too. It seems unlikely Persian/Tahiti/Bearss lime would be part of any cross since it does not produce viable pollen and since, as stated by Dr. Manners on this forum, it produces less than 1 seed per 1000 fruit. I don't read French very well but I found this and maybe it will help.
La limette douce de Rome ou Pursha (Citrus lmetta « Pursha »).
C'est probablement un hybride entre la limette et l'orange ou entre la limette et le chinotto (orange amère à feuilles de myrte). Il figure comme un arbuste à frondaison irrégulière, aux feuilles elliptiques, à l'apex pointu, d'une couleur vert foncé, brillant ; son pédoncule est légèrement ailé. Ses fleurs blanches et très odorantes fleurissent sans interruption, du printemps à l'automne. Ses fruits sont globuleux et creusés aux extrémités ; l'écorce n'adhère pas à la pulpe, qui est aigre-douce et savoureuse. Le citrus limetta « Pursha" est apprécié également comme plante ornementale.
Here's the English version that I found after I already posted.
The sweet lime from Rome, or Pursha (Citrus Lime Pursha)
It is probably a hybrid of the lime and the orange or of the lime and the myrtle-leaved orange. The plant consists of bushes with an irregular foliage, elliptical, dark green leaves with a pointed apex; the petiole is slightly winged. The flowers, which blossom continuously from spring to autumn, are white and very fragrant. The fruit are globular and with a depression at the poles; the peel is not sticking to the pulp, which is sweet and sour and tasty. The Citrus Lime Pursha is also appreciated as ornamental plant.
Here is a link that indicates a different cross.
http://www.citrusvariety.ucr.edu/citrus/purshalime_chinotto.html