Despite extensive research on scientific disruption, two questions remain: why disruption has declined amid growing knowledge, and why disruptive work receives fewer and delayed citations. One way to address these questions is to identify an intrinsic, paper-level property that reliably predicts disruption and explains both patterns. Here, we propose a novel measure, knowledge independence, capturing the extent to which a paper draws on references that do not cite one another. Analyzing 114 million publications, we find that knowledge independence strongly predicts disruption and mediates the disruptive advantage of small, onsite, and fresh teams. Its long-term decline, nonreproducible by null models, provides a mechanistic explanation for the parallel decline in disruption. Causal and simulation evidence further indicates that knowledge independence drives the persistent trade-off between disruption and impact. Taken together, these findings fill a critical gap in understanding scientific innovation, revealing a universal law: Knowledge independence breeds disruption but limits recognition.