Cycle Decomposition Identity

Definition

The fundamental decomposition of institutional behaviour into aligned and misaligned components. This is the cycle analogue of orthogonal decomposition in functional analysis—every capital function splits into mission-aligned and fragility-driven parts.

Formula

Example

A hospital's capital behaviour decomposes into A(K) (equipment-cycle matched) and E(K) (budget-cycle driven). The decomposition reveals exactly how much behaviour serves mission versus fragility.

Source

OAIA Section 3.3