The correct option is At least half of the State Legislatures..
Explanation
Article 368 of the Indian Constitution lays down the procedure for amending the Constitution. While some provisions can be amended by a simple majority of Parliament (outside the scope of Article 368), others require a special majority. To protect the federal equilibrium, provisions affecting the federal structure require an even more rigid procedure involving state participation.
Detailed Analysis:
For amendments that seek to change the federal provisions of the Constitution, the procedure prescribed under the proviso to Article 368(2) must be followed. This requires:
- Special Majority of Parliament: A majority of the total membership of each House and a majority of not less than two-thirds of the members of that House present and voting.
- Ratification by States: The amendment must be ratified by the Legislatures of at least one-half of the States by a simple majority.
Examples of such federal provisions include:
- Election of the President and its manner.
- Extent of the executive power of the Union and the States.
- Supreme Court and High Courts.
- Distribution of legislative powers between the Union and the States (Seventh Schedule).
- Representation of States in Parliament.
- Article 368 itself.
Therefore, ratification is required from at least half of the State Legislatures, not all or one-third. The Supreme Court does not participate in the ratification process.
Key Takeaway:
Amendments altering the federal structure of the Constitution are "entrenched" and require a Special Majority of Parliament plus ratification by at least 50% of the State Legislatures.