Do I need to appoint a local representative?

Short answer: Usually your organization does, not Cyber Crucible. Several regimes require entities outside the country that process residents' personal data to appoint a local representative — and since Cyber Crucible normally acts as a processor, that obligation sits with you as the controller. 
 How the roles divide 
 
 Cyber Crucible as processor (normal case): you, as controller, designate the local representative. Cyber Crucible cooperates fully with local compliance obligations. 
 Cyber Crucible as controller (unusual): if it processed personal data for its own purposes, it would provide a local representative in the relevant jurisdiction. 
 
 Saudi Arabia's PDPL Article 33 is the clearest example of this requirement, but similar provisions appear across the GDPR-derived family. 
 On controller registration 
 Some regimes require certain controllers to register with the supervisory authority — typically public bodies, entities whose main activity is processing personal data, or those handling high-risk sensitive data. 
 Cyber Crucible's core business is cybersecurity software rather than general personal data handling, so it does not fall into those categories. Registration rules are monitored and compliance would follow if the role or activities changed.