Every founding scientific discovery opens one door. In doing so it makes other doors invisible — not because they do not exist, but because the framework built from the founding observation redefines what counts as a question worth asking. This paper introduces the Foundational Remainder: the portion of a founding observation that the founder's framework rendered permanently invisible to subsequent workers. A four-step methodology is proposed for identifying and mining the Foundational Remainder of any established scientific framework. Historical case studies — Newton's gravity, Faraday's electromagnetic induction, Darwin's natural selection — are examined to demonstrate the method. The paper argues that the next generation of scientific breakthroughs is more likely to emerge from the Foundational Remainder of existing frameworks than from incremental progress within them.