The distribution of powers between the Centre (Union government) and the States is the factor that determines that the Indian Constitution is federal.

The Indian Constitution establishes a federal system of government, where powers are divided between the central government and the state governments. The distribution of powers is outlined in the Constitution itself, specifying the areas of governance for which each level of government is responsible.

Under the Indian Constitution, there are three lists that delineate the powers of the Centre and the States:

1. Union List: This list includes subjects on which only the central government has the authority to legislate and make laws.

2. State List: This list consists of subjects on which only the state governments have the power to legislate and make laws.

3. Concurrent List: This list includes subjects on which both the central and state governments can legislate and make laws. However, in case of a conflict, the central law prevails.

This distribution of powers between the Centre and the States reflects the federal nature of the Indian Constitution. It allows for both levels of government to have autonomy and legislative authority in their respective domains.

The other options mentioned in the question, such as a written and rigid Constitution, an independent judiciary, and the vesting of residuary powers with the Centre, are important aspects of the Indian Constitution, but they do not specifically determine its federal character.