Operator Composition Calculator
Compose Δ and Λ operators algebraically
Decoupling Operator
Separates mission from fragility sources (political, fiscal, donor, leadership cycles)
Alignment Operator
Synchronizes resource flows with beneficiary lifecycle needs
Operator Strength Configuration
How completely does your design decouple from fragility sources?
How well do resource flows align with beneficiary cycles?
Composition Results
Decoupled Alignment
First decouple from fragility, then align with mission cycles
Aligned Decoupling
First align with mission, then decouple from fragility
Repeated Decoupling
Applying decoupling twice
Repeated Alignment
Applying alignment twice
Property Verification
Commutativity Check
Does Δ ∘ Λ = Λ ∘ Δ in your design?
In general, these operators do NOT commute. Order matters.
Idempotence Check
Does applying Δ twice give the same result as once?
A well-designed decoupling operator should be idempotent.
Completeness Check
Does Δ decouple from ALL four fragility sources?
Partial decoupling leaves residual vulnerability.
Coherence Check
Does Λ align with the FULL beneficiary lifecycle?
Partial alignment creates timing gaps.
Key Insight from OAIA Theory
The order of operator composition matters. Applying Δ ∘ Λ (decoupling first, then alignment) typically produces more robust institutional designs than Λ ∘ Δ. This is because protected alignment is more stable than aligned protection—you want to eliminate fragilities before optimizing resource flows.