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refactor: Remove unneeded public inputs for Root Rollup circuits #8829

@spalladino

Description

@spalladino

Double-check whether we need the following public inputs for the root rollup, and if not, remove them:

  • previous_block_hash: Should be committed to as part of the previous_archive
  • previous_archive.next_available_leaf_index: Don't we just need the root?
  • end_block_hash: Same as previous
  • end_archive.next_available_leaf_index: Same as previous
  • out_hash: Not checked anywhere in L1, also part of block header, so it's committed to as part of the archive root
  • end_timestamp: Can be derived from the end block's slot number if needed, also not checked on L1
  • end_block_number: Only used to look up the end_archive on L1, but if we know the epoch being proven, this could be derived

Also see the comments on #8704 for more context.

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