What does responsibility for a task after writing the technical specification mean to you?

Responsibility for the task after writing the technical specification (TS) includes:

• Monitoring compliance of implementation with TS requirements
• Participating in clarifying and refining the TS as needed
• Coordinating interactions between the development team and stakeholders
• Ensuring timely resolution of arising questions and issues
• Checking work results, testing, and acceptance
• Providing knowledge transfer and documentation for support

That is, responsibility does not end with writing the TS, but continues until the successful implementation and support of the solution.