Thanks to research done in 2005 by Mike Sebastian, we know of 9 patents granted to Texas Instruments, all of which describe both the hardware and software of the TI-57 in surprising detail.
Of these 9 patents, the first 8 were filed on October 27, 1976, and the last was filed on March 23, 1979. The issue dates are in the same order as the patent numbers, with the first issue date being almost one and a half years later (March, 7, 1978).
I’ve compared a few of these patent texts to each other. Using 4,125,901 as an arbitrary baseline, I compared it to the first patent in the list (4,078,251), and aside from the introductory text and claims, the vast majority of the text and diagrams are identical, with most differences being either typist mistakes or OCR quirks.
I should add that the text for all of the patents above came from Google, although I apparently could have obtained the same full-text results from the U.S. Patent and Trademark Office as well, since all these patents were issued after 1976.
The back of every TI-57 also mentions these patents:
THIS PRODUCT AND ITS COMPONENTS ARE PROTECTED BY ONE OR MORE OF THE FOLLOWING U.S. PATENTS AND OTHER PATENTS PENDING: 3819921 3955181 3904863 3987416 3921142 3988604 3932846 3989939 3934233 3991305 3952174 3991306 3855577 4014013 4005293