Mathematical Foundations of Command
Reachability
Reachability describes whether a system can move from its current operational state to a desired future state under existing constraints and available interventions.
What It Explains
The problem this framework makes visible.
Why a formally desirable outcome may no longer be operationally attainable.
System Mechanism
How the failure forms.
The current state is identified.
The desired state is defined.
Available interventions and constraints are modeled.
Possible trajectories are evaluated.
The target is reachable only if at least one viable path remains.
Failure Signatures
What an observer would see.
Desired outcomes remaining formally stated but practically impossible
Intervention options that arrive too late
Paths blocked by accumulated constraints
Recovery plans that assume nonexistent maneuver