Module complexity 

Pillar: III. PACR field: Γ (Cognitive Split).

Computational mechanics fundamental theorem (arXiv:2601.03220): any data stream admits a unique decomposition into two inseparable projections of the same ε-machine:

S_T — statistical complexity (bits) Minimum causal-state information needed to optimally predict the stream. Rising S_T → the system is discovering learnable structure.

H_T — entropy rate (bits per symbol) Residual unpredictability that cannot be further compressed. Rising H_T → the system is encountering irreducible noise.

These two quantities are OBSERVER-DEPENDENT (the observer’s computational budget T_budget determines the ε-machine approximation order) and INSEPARABLE — removing either one from the record permanently loses information that cannot be recovered from the other.

Structs

CognitiveSplit

The cognitive split Γ = (S_T, H_T): intrinsic information structure of the processed data stream, as computed by the ε-machine approximation.