Task-Relative Failure of Representational Equivalence: How a Representation Adequate for One Task Can Fail Another Without Changing

This conceptual paper introduces Task-Relative Failure of Representational Equivalence, the constraint that a fixed representation can preserve the distinctions required by one task while merging a distinction required by another. A representation can therefore remain unchanged while its adequacy changes with the use made of it. The claim requires a specific collision: two cases that the new task must handle differently receive the same representation. Missing detail alone does not establish failure. The assessment standard is task-relative adequacy, requiring renewed examination of which distinctions a representation preserves when it is reused under different demands. The paper relates the constraint to rounding error in numerical computation and uses the 1991 Patriot missile battery failure at Dhahran to examine the task-dependent consequences of limited precision. The discussion considers how prolonged operation and faster targets altered the consequences of accumulated timing error. Part of the Equivalence and Interchangeability series within On Human Modeling, the paper offers questions for evaluating reuse, identifying who authorizes it, and examining who bears its consequences. Its framework can inform human–AI research on whether summaries, classifications, and model outputs preserve the distinctions required when they are reused for a different task.