What serves as a "parent" document that represents a contract between the developer and the client?

It is the SRS document or the Software Requirement Specification.

Explanation:

The parent document that serves as a contract between the client and the developer is the SRS document, and it contains all the details related to software that needs to be developed. The clients let the business analyst know all about the software he wants the software development company to develop, and the business analyst then write the SRS document covering all the requirements, and this forms the contract details and is shared in between the developer and the client if the developer is working independently, and in between the company and the client if the developer is working for certain company.