Has anyone actually produced any mathematical proof of CAP?
Great question!
This presentation, linked by the article, explains the misunderstanding: https://www.youtube.com/watch?v=Wp08EmQtP44#t=1273
The paper you are looking for is this: http://dl.acm.org/citation.cfm?id=564601
Also available here: http://webpages.cs.luc.edu/~pld/353/gilbert_lynch_brewer_pro...