Structural Compression and Hidden Generators

We introduce a finite information-theoretic invariant measuring the structural com-
plexity of mathematical objects relative to a chosen family of constraints. Recognizing
that mathematical constraints form dense dependency networks, we utilize permutation-
averaged conditional self-information to construct an order-independent coherence
metric. We prove basic stability and logarithmic representation results for finite con-
straint systems. Furthermore, we connect this invariant to algorithmic information
theory by defining the Structural Compression Ratio, framing highly structured mathe-
matical objects as compression points in a constraint space. The framework formalizes
a quantitative principle aligned with the Langlands program: mathematical objects
discovered to be massive compression points of apparent independent truths frequently
admit simpler generating descriptions in deeper geometric or representation-theoretic
categories.