Technically

デ・ジュリ

de-juri

(based on formal (de jure) arguments, which however may be misleading)

厳密に

genmitsu ni

(based on precise facts, which however may be contrary to common misbelief or to a traditional name)

法律上の

hōritsujō no

(based on formal (de jure) arguments, which however may be misleading)