The Disruption Index Measures Displacement Between a Paper and Its Most Cited Reference

Initially developed to capture technical innovation and later adapted to identify scientific breakthroughs, the Disruption Index (D-index) offers the first quantitative framework for analyzing transformative research. Despite its promise, prior studies have struggled to clarify its theoretical foundations, raising concerns about potential bias. Here, we show that-contrary to the common belief that the D-index measures absolute innovation-it captures relative innovation: a paper's ability to displace its most-cited reference. In this way, the D-index reflects scientific progress as the replacement of older answers with newer ones to the same fundamental question-much like light bulbs replacing candles. We support this insight through mathematical analysis, expert surveys, and large-scale bibliometric evidence. To facilitate replication, validation, and broader use, we release a dataset of D-index values for 49 million journal articles (1800-2024) based on OpenAlex.