The challenges focused solely on claims that he was born in Canada. NOBODY even hinted that his father's citizenship status might be an issue. As to paper trail, it was widely reported in 1880 that Irish father was born in Ireland yet NOBODY even bothered to ask if he was a citizen. Why? You have only two ways to explain this. Either voters in 1880 were ignorant trusting sheeple when compared to today's voters (IMHO, the opposite is true) or they did not see his father's citizenship as an issue that was even worth talking about.
I'm willing to put my money where my mouth is. Are you? I'll bet that not a single person ever challenged Arthur on this issue (e.g. his father's citizenship status) from 1880 (when he ran for veep) to 1885 when he left office?
How do you intend to prove that?
Are you advocating that there should be no two citizen parent requirement for eligibility? If so, why?