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The article is mathematically unsound and provides no proof or model whatsoever of what they claim.

I am a little surprised that it just provides a simulated model; Yahoo ran a famous experiment which does exactly what demonstrates his point about randomness and media success being only weakly correlated with success: "Experimental Study of Inequality and Unpredictability in an Artificial Cultural Market" http://www.princeton.edu/~mjs3/salganik_dodds_watts06_full.p..., Salganik et al 2006; Salganik & Watts 2009, http://www.princeton.edu/~mjs3/salganik_watts09.pdf "Web-Based Experiments for the Study of Collective Social Dynamics in Cultural Markets"; http://cultural-science.org/FeastPapers2008/AlexBentley1Bp.p... ; "Leading the Herd Astray: An Experimental Study of Self-fulfilling Prophecies in an Artificial Cultural Market" https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3785310/ , Salganik & Watts 2008.

Great links! I agree with the general truth of the phenomenon described & your references do a much better job demonstrating this.

I think it's meant more as a thought experiment than an actual formal proof.