AIM Framework glossary
Data Processing Inequality
Canonical definition
The Data Processing Inequality is the information-theoretic theorem that no processing of a signal can increase the information the signal carries about its source: for any variable S, any signal X and any function g, I(S; g(X)) ≤ I(S; X). Applied to Common-Currency Integration, whose many-to-one map combines the three source signals into one Scalar, it establishes that no function of the integrated Scalar, introspection included, can recover the source decomposition the integration discarded, which is the proof of the Source Opacity Theorem.
Explanation
Once information has been thrown away, no amount of later processing can put it back. Mixing three streams into one number loses the record of how much each stream contributed, and anything that works only from the mixed number, including looking inward, inherits the loss. This general fact about information is what makes Source Opacity a mathematical necessity rather than an observation about people.
Epistemic status
Inherited (information-theoretic theorem) with Framework-Specific Application.