Constitutional State Separation: A Structural Theory of Constitutional Specifications in Adaptive Systems

We study the mathematical status of the constitutional specification in adaptive systems.Most contemporary safety approaches embed behavioral constraints into model parameters,prompt conditioning, or execution mechanisms, and do not treat the constitution as an indepen-dently defined mathematical object. We propose modeling the constitution as an independentcomponent of the system state and study the structural consequences of that choice. We estab-lish two conditional results. First (Part I), under architectural assumptions in which the consti-tution is readable but not modifiable by adaptation, and under which more than one adaptivestate is compatible with a given constitution, constitutional identity is not uniquely determinedby the adaptive state; this establishes a mathematical separation between constitutional iden-tity and adaptive configuration. Second (Part II), when the constitution is represented onlythrough an embedding inside the adaptive representation and that embedding is non-injective,constitutional identity is not uniquely recoverable from the adaptive representation. The non-triviality of both results follows from explicitly stated structural assumptions rather than fromthe proofs themselves. This work does not propose an enforcement mechanism and does notaddress which constitutions are runtime-enforceable; those questions depend on the object-leveltheory developed here but lie outside its scope.