[qqii]

Using a bloom filter as a distributed hash means you're edging quite close to a blockchain, the only question your schema now has is consensus - how is work examined for trustworthiness? What prevents network spam?

I haven't puzzled it though but intuitively it feels like you wouldn't be able to achieve the "same validity" (aka you'd have a weaker set of guarentees) without the liveness of a blockchain like system. Whether you agree with what threshold of validity is acceptable is a different matter.