Modern Context:
In the contemporary international system, the concept of a caliphate is largely historical, and there is no widely-recognized caliphate in existence today. Most Muslim-majority countries are organized as nation-states with varying degrees of Islamic influence in their legal and political systems. These nation-states have constitutions or fundamental laws which, while they may declare Islam as the state religion and may incorporate elements of Islamic law, do not declare the state as a caliphate or appoint a caliph as a political leader.
Contemporary Interpretations:
Different Islamic political theories and movements interpret the concept of khilafah in diverse ways, and there is no universally agreed-upon model for what a modern caliphate would look like. Some Islamist movements advocate for the establishment of a caliphate as a form of Islamic governance, while many Muslims are content with various forms of governance existing in Muslim-majority countries today and do not seek the establishment of a caliphate.
Conclusion:
While the constitution of a state is indeed a defining element in determining its form of governance, the establishment of a khilafah would involve not only constitutional declarations but also widespread consensus or acceptance among the relevant Muslim communities, acknowledgment of the authority of the caliph, and adherence to Islamic principles and jurisprudence.