What Is the Scope of Pikuach Nefesh (Can I File a Death Penalty Appeal on Shabbat)?

I am an attorney currently working on a death penalty appeal on behalf of a convicted client. We have a brief in the case due on a Friday, and I lined up assistance from non-Jewish colleagues in case the brief isn’t ready when Shabbat starts. Was that necessary here, given that I am trying to prevent an execution and save a life? Are there any circumstances in which it would be permissible to work on a death penalty case on Shabbat?

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Music featured in this episode: Heavy Weight by White Noise Maker