Which of the following statements are correct regarding the jurisdiction of the Supreme Court of India?

A.Original jurisdiction extends to any dispute between the Government of India and one or more States or between the Government of India and any State or States on one side and one or more States on the other or between two or more States.

B.Appellate Jurisdiction extends when the Union plus some States are one side and some other States on the other side of the dispute.

C.Under Articles 129 and 142 of the Constitution, the Supreme Court has been vested with the power to punish for contempt of court.

D.As of now, the International Commercial Arbitration cannot be initiated in the Supreme Court.

The correct option is A and C only.

Let us analyze each statement step-by-step to understand the jurisdiction of the Supreme Court of India:

1. Statement A is correct:
Under Article 131 of the Constitution of India, the Supreme Court has exclusive original jurisdiction in any dispute:
- Between the Government of India (Union) and one or more States.
- Between the Government of India and any State or States on one side and one or more other States on the other side.
- Between two or more States.
Thus, Statement A accurately describes the original jurisdiction of the Supreme Court.

2. Statement B is incorrect:
A dispute involving the Union and some States on one side and other States on the other side falls under the Original Jurisdiction of the Supreme Court (pursuant to Article 131), not its Appellate Jurisdiction. Appellate jurisdiction deals with appeals against judgments from lower courts (like High Courts).

3. Statement C is correct:
Article 129 of the Constitution of India establishes the Supreme Court as a "court of record" and explicitly grants it the power to punish for contempt of itself. Additionally, Article 142(2) provides the Supreme Court with the power to make orders for the investigation or punishment of any contempt of itself. Therefore, the Supreme Court has the authority to punish for contempt under these articles.

4. Statement D is incorrect:
Under Section 11 of the Arbitration and Conciliation Act, 1996, in matters of International Commercial Arbitration, applications for the appointment of an arbitrator can be made to the Supreme Court of India (specifically to the Chief Justice of India or their designate). Thus, International Commercial Arbitration procedures can be initiated in the Supreme Court.

Conclusion:
Since only statements A and C are correct, the correct choice is A and C only.