Osgood Box
The "Osgood Box" was a device given to Osgood and her Zygon duplicate by the Doctor to use if the ceasefire between humans and Zygons broke down after a peace treaty was arranged. The two Osgoods recorded a brief video explaining the Osgood Box and its abilities before one of them was murdered by Missy. (TV: The Zygon Invasion)
Initially, one Osgood box- a red box- was revealed to exist, supposedly with the ability to either save the Zygons or destroy them. This Osgood Box was kept within the Black Archive under the Tower of London. However, inside the Archive, an identical blue box was revealed with the red box. In reality, two Osgood Boxes existed, named after the fact there were two Osgoods who guarded watch over them.
Both boxes contained two buttons inside them, hidden underneath a lid. The buttons were labeled "truth" and "consequences" in all capital letters accordingly. Pressing them would allegedly cause an event to take place as safeguards or countermeasures against either humans or Zygons. The red box would either release Z-67 gas into the Earth's atmosphere which would turn Zygon biology inside-out, or detonate the nuclear warhead underneath the Archive, which would wipe out most of London. The blue box would either send out a signal that would disable their ability to shapeshift for at least an hour and revert them to their true forms, exposing their alien nature to all, or send out a signal that permanently prevented them from changing back from the human forms or other disguises that they assumed.
However, neither of the boxes posed a threat at all, merely being empty objects with superficial buttons made to appear threatening through clever deception and misinformation. The Osgood Boxes were simply framing devices used by the Doctor to demonstrate a "scale model of war", as no matter what decision the parties made who used the boxes, they would never know for sure what the impact of their actions would be or who would potentially have their lives shattered. The Twelfth Doctor was able to use them to persuade Bonnie to stop a rebellion and stop Kate Stewart from taking drastic actions against the Zygons.
The Doctor needed to rely on the memory-wiping devices in the Black Archive to make the Osgood Boxes serve their purpose to their fullest, and he set them off with his sonic sunglasses each time the experiment failed. It took the Doctor sixteen tries to get Bonnie to see reason while Kate, who may or may not have made the right choice, while Kate noted they could not forget what the boxes really were after being opened but was never the wiser to the memory wipes. (TV: The Zygon Inversion)
Appearance and abilities
The designs and functions of the Osgood Boxes were directly inspired by that of the Moment, as the Doctor had once faced a decision to use the dangerous weapon to end the Last Great Time War at the expense of innocent Gallifreyan lives. Like the moral dilemma with the Moment, the moral dilemma with the Osgood Boxes was resolved through Clara Oswald having an influence in some way over the conflict. (TV: The Zygon Inversion)
Behind the Scenes
The Osgood Boxes can be compared to the Schrodinger's cat experiment in that it was impossible to know what would happen from using them until opening them and learning they were harmless. However, while it would normally only be possible to do this experiment just once due to remembering what one saw, the Doctor went to such lengths as to erase the memories of those who used the boxes when they failed to meet his expectations and forcibly manipulated the results of the experiment until he got a desired response from both subjects involved.
