As a USA 501(c)(3) the OpenAI non-profit has to file a tax return each year with the IRS. One of the required fields on that tax return is to “Briefly describe the organization’s mission or most significant activities”—this has actual legal weight to it as the IRS can use it to evaluate if the organization is sticking to its mission and deserves to maintain its non-profit tax-exempt status.
The evolution of OpenAI’s mission statement (Simon Willison)
He has some commentary in his blog over the changes each year, or you can read the gist he created directly: https://gist.github.com/simonw/e36f0e5ef4a86881d145083f759bcf25/revisions