RNG exploitability analysis assuming pure RANDAO-based main chain

In addition to a possible additional “buffer” lookahead, does this introduce a grinding attack because of shard-to-main-chain synchronisation? That is, the concept of “5 blocks ago” is subjective from the point of view of the shards

Ah sorry, to be clear, by “5 blocks ago” I actually mean “the start of the previous period”. The shards always know what the main chain period is, because the DAG structure enforces it (the first shard block in a given period needs to reference the main chain block hash at the start of that period). That said, if we don’t have this tight linking, then I would be inclined to say, just set up a separate RANDAO in each shard. RANDAOs are not exactly complex or expensive to set up and maintain, so there’s not that much of a loss from this.