Data Processing Inequality
Processing cannot increase mutual information about the source
The data processing inequality (Claude Shannon; standard in 1948 communication theory): for any Markov chain X → Y → Z,
I(X ; Z) ≤ I(X ; Y)
Processing cannot increase mutual information between an output and the original source — only preserve or decrease it. This is the formal proof that the L0–L3 ladder is not arbitrary: a L2 artifact has at most the same I with ground truth as its inputs; in practice, less after probabilistic or lossy steps.
Strict inequality holds when information is genuinely lost — every non-invertible transform (including logical inference from concrete L0s), every η < 1 probabilistic step, every aggregation that discards detail, every inconsistent cross-stream join.
Corpus stance
A1 — adopted on this site: Formal content of Why Atomicity Matters and What Information Theory Says.