The Parsimony of Attention: Modeling the 45-Minute Source and the 8-Minute Mid-Roll Threshold in the Clipper Economy

This paper examines the emerging clipping economy in digital content creation, specifically the transformation of 45-minute long-form content (podcasts, interviews, educational classes) into optimized 8-minute clips. While existing literature discusses content repurposing qualitatively, this study proposes a quantitative parsimonious model to explain the relationship. We introduce a quadratic function f(x) = -x² + 45x + 1/4, based on the principle of parsimony (Occam's Razor), which elegantly unifies three key industry numbers. The analysis shows that the vertex of the function at x = 22.5 minutes represents the Golden Mid-roll point, while its maximum value of 506.5 seconds, equivalent to 8.44 minutes, corresponds to YouTube's official threshold for mid-roll monetization. This study provides the first mathematical bridge between content psychology and platform monetization policy.