Operator Non-Commutativity

Definition

The fundamental property that domain alignment operators almost never commute. This means the order of applying alignment transformations matters—health-then-budget differs from budget-then-health—and explains why cross-sector coordination fails structurally.

Formula

Example

Science-grant non-commutativity: applying A_science (2-5 year throughput) then A_gov (1-year grants) destroys research alignment. The grant cycle cannot be undone by subsequent scientific alignment attempts.

Source

OAIA Section 6.3