def METHOD_NAME(page_or_revision, block_path, block, mapper):
    migrated = False
    child_block_name, remaining_block_path = block_path[0], block_path[1:]
    child_block = block.get(child_block_name)
    if child_block:
        migrated_value, child_migrated = migrate_block(
            page_or_revision, remaining_block_path, child_block, mapper
        )
        if child_migrated:
            block[child_block_name] = migrated_value
            migrated = True
    return block, migrated