  Practical data analysis involves many implicit or explicit assumptions about
the good behavior of the data, and excludes consideration of various
potentially pathological or limit cases. In this work, we present a new general
theory of data, and of data processing, to bypass some of these assumptions.
The new framework presented is focused on integration, and has direct
applicability to expectation, distance, correlation, and aggregation. In a case
study, we seek to reveal faint structure in financial data. Our new foundation
for data encoding and handling offers increased justification for our
conclusions.
