ARPA (now DARPA) funded a military network originally conceived for nuclear command and control.

There are two elements: (a) ARPA funded the ARPANET, a network funded by the military; (b) the network was originally conceived for nuclear command and control. True: historical sources show both, i.e. the ARPANET's own original purpose was nuclear command and control or survivable military communications. Mostly true: ARPA funded it, and its conception was substantially driven by survivable or nuclear-era military communications needs, with only a minor overstatement. Mixed: historians are genuinely divided on whether nuclear command and control was part of the ARPANET's original rationale, with credible sources on both sides. Mostly false: ARPA funded the ARPANET, but the authoritative histories (for example its planners' accounts) say it was conceived for sharing computing resources among researchers, and the nuclear-survivability idea comes from related but separate work (such as Paul Baran's work at RAND) that the claim conflates with it. False: ARPA did not fund the network, or there is no connection to military or nuclear communications at all.

Set before the research began.

1. E1 ARPANET - Wikipedia Wikipedia

   “The Advanced Research Projects Agency Network (ARPANET) was the first wide-area packet-switched network with distributed control and one of the first computer networks to implement the TCP/IP protocol suite. Both technologies became the technical foundation of the Internet. The ARPANET was established by the Advanced Research Projects Agency (now DARPA) of the United States Department of Defense.”

2. E2 ARPANET - Wikipedia Wikipedia

   “The ARPANET was not started to create a Command and Control System that would survive a nuclear attack, as many now claim. To build such a system was, clearly, a major military need, but it was not ARPA's mission to do this”

3. E3 ARPANET - Wikipedia Wikipedia

   “Later, in the 1970s, ARPA did emphasize the goal of "command and control". According to Stephen J. Lukasik, who was deputy director (1967–1970) and Director of DARPA (1970–1975):”

4. E4 [ih] When the words Internet was design to survive a nuclear war appeared for the first time? Internet Society (internet-history mailing list) · 14 February 2019

   “Larry Roberts was clear that the ARPANET was intended to support resource sharing.”

E1 confirms that the Advanced Research Projects Agency (now DARPA), part of the US Department of Defense, set up the ARPANET. That supports the funding element, since the network was established by ARPA, a Defense Department agency. However, E2 says the ARPANET "was not started to create a Command and Control System that would survive a nuclear attack". E4 records that planner Larry Roberts was clear the network was meant for resource sharing. E3 says ARPA emphasized "command and control" later, in the 1970s; together with E2 and E4, this indicates that nuclear command and control was not the network's original purpose, so the claim overstates the network's origins.