N.Y. CVP Law § 3033

§ 3033. Contracts to submit; enforcement of submission. 1. Any written\ncontract, otherwise valid under the substantive law, to submit any\nexisting or future controversy to the court pursuant to section 3031 is\nvalid and enforceable and shall be construed as an implied consent of\nthe parties to the jurisdiction of the supreme court of this state to\nenforce it pursuant to the procedures of rule 3036, and to enter\njudgment thereon, and shall constitute a waiver by the parties of the\nright to trial by jury.\n 2. If the parties to a dispute arising under a contract to submit a\ncontroversy to the court under section 3031 are unable to agree on a\nstatement of claims and defenses and relief sought pursuant to that\nsection, the court on motion shall settle the terms of the statement.\nIn deciding the motion the court shall consider and determine any\nquestions as to the existence of the contract or its validity or the\nfailure of any party to perform it. If a substantial issue of fact be\nraised as to the making of the contract or submission or the failure to\ncomply therewith, the court or judge shall proceed to trial of such\nissue without a jury, unless either party should demand a jury trial.\n