Contracting IBM to build Gemini's computer

Today we are talking about computers in space! 1964 saw the launch of Gemini I, the first spacecraft to carry an onboard computer. The aptly named Gemini Guidance Computer was responsible for guidance, navigation, and safe reentry. Built by IBM it weighed in at a tiny 59 pounds. For 1960's technology there just isn't any comparison to make, it was an amazingly small machine. What secrets does it hold? Did IBM crack some secret code to build such a tiny computer?

https://www.ibiblio.org/apollo/Gemini.html - Overview of the Gemini Guidance Computer

https://history.nasa.gov/computers/ch1-1.html - Official NASA History

https://www.ibiblio.org/apollo/Documents/GeminiProgrammingManual.pdf - How the thing was programmed