This paper examines whether the availability of post-quantum digital signature algorithms alone is sufficient to support a coherent migration of Bitcoin under its existing protocol semantics. Rather than evaluating cryptographic constructions or governance mechanisms, the analysis focuses on structural constraints arising from Bitcoin’s definitions of ownership, validity, and consensus as originally specified by Nakamoto. By holding core assumptions fixed, including signature-defined ownership, immutable ledger history, and independent node validation, the paper characterizes a protocol-semantic constraint showing that certain migration objectives cannot be simultaneously satisfied without modifying underlying consensus semantics. The analysis is non-temporal, does not assume the existence of a cryptographically relevant quantum computer, and does not propose migration mechanisms or policy prescriptions.