Based on the provided knowledge sources, I can offer some insights into your question about inviting a user to sign in using the OIDC method in Kratos and setting traits according to Jsonnet mapping. However, the information available doesn't directly address the concept of user invitations in Kratos. Regarding the OIDC method and trait mapping: 1. Kratos supports social sign-in (including OIDC) providers, which can be configured to map user data to identity traits using Jsonnet [Social sign-in data mapping](https://www.ory.sh/docs/kratos/social-signin/data-mapping#write-a-jsonnet-data-mapper). 2. When a user signs in for the first time using an OIDC provider, the Jsonnet data mapper can be used to map the claims returned by the provider to the identity traits in Kratos [End-to-end GitHub example](https://www.ory.sh/docs/kratos/social-signin/data-mapping#end-to-end-github-example). 3. The Jsonnet mapper allows you to define how the data from the OIDC provider should be mapped to the identity traits in Kratos. This mapping is applied when the user authenticates, including their first login [Social sign-in data mapping](https://www.ory.sh/docs/kratos/social-signin/data-mapping#write-a-jsonnet-data-mapper). However, the knowledge sources don't provide specific information about an invitation system for OIDC users in Kratos. The typical flow involves configuring the OIDC provider, setting up the Jsonnet mapper, and then allowing users to sign in directly through the configured provider. If you need to implement an invitation system, you might need to explore custom solutions or additional features that are not covered in the provided knowledge sources. For the most accurate and up-to-date information on implementing such a feature, I recommend consulting the official Ory documentation or reaching out to the Ory community for guidance.

I understand your concern about enabling the registration flow in Kratos. However, based on the provided knowledge sources, I don't have specific information about creating users on the fly without enabling the registration flow in Kratos. The available information primarily focuses on standard registration and login flows, including social sign-in methods like OIDC. The knowledge sources indicate that Kratos typically uses the registration flow for creating new users, including those signing in with OIDC providers for the first time [Registration with Google, Facebook, GitHub, ..., OpenID Connect / OAuth 2.0](https://www.ory.sh/docs/kratos/self-service/flows/user-registration#registration-with-google-facebook-github--openid-connect--oauth-20). Unfortunately, the provided knowledge sources don't contain information about alternative methods for creating users without enabling the registration flow. This seems to be a specific use case that isn't covered in the available documentation. Given your requirements, you might need to explore custom solutions or reach out to the Ory community or support channels for more specific guidance on how to achieve user creation without enabling the registration flow. They may be able to provide insights into advanced configurations or alternative approaches that aren't documented in the provided knowledge sources. I apologize that I couldn't provide a more direct solution to your specific need. If you have any other questions about Ory that I might be able to help with based on the available information, please feel free to ask.