Occasionally the term “weak subjectivity period” pops up in Eth2 discussions. It’s a weird concept that you can usually just watch fly by and not miss too much. But when you’re talking about how to sync an existing Eth2 chain it becomes quite important. Probably the best resource for it is Vitalik’s post: Proof of Stake: How I Learned to Love Weak Subjectivity I’ve struggled to get my head around it and why it matters so am writing up my current understanding. There is almost certainly at least one mistake in here somewhere…

So what is the weak subjectivity period? It’s the period that a client can be offline for and when it comes back online be able to completely reliably process blocks to get to the consensus chain head. For proof of work you can always do this, but not for proof of stake. To see why not, let’s look at an example.

Say we have an Eth2 network chugging away. Once 2/3 of those validators have attested to a particular epoch it’s considered finalised and no re-orgs can change it. In order to finalise two conflicting epoch’s you’d need at least 1/3 of validators to sign conflicting attestations but doing so is a slashable offence so there’s a very strong economic incentive to not do that. That incentive is essentially what crypto-economics are all about, whether you’re talking PoW or PoS it’s not that it’s mathematically impossible to break the chain, but that it costs you more money than anyone is willing or able to spend.

At this point it sounds like you should be able to just process blocks reliably, confirm the attestations and signatures all line up and it all works out. What’s the catch?

The catch is that validators can withdraw their staked funds and stop being a validator. There are limits on how fast those withdrawals can happen but once the money is out the economic incentive to not misbehave is gone. Critically despite the validator having withdrawn the money, they still have their private key and can sign things – with no staked funds anymore they can’t be slashed for it. Nodes fully sync’d to the chain know they are no longer a validator and reject those signatures but nodes further behind don’t yet have that information and see the signature as valid.

So, if we have 1/3 of validators which have withdrawn their stake, if my node is far enough back on the chain to have not seen the withdrawal of any of those nodes, then 1/3 of the validators you currently think are valid have no incentive to be honest and can sign any blocks or attestations with complete impunity and potentially form a chain which conflicts with the finalised state but is otherwise entirely valid. They can feed you those blocks to lead you down the wrong chain.

However if your node was further along the chain to see one or more of those validators exit, you’d reject their attestations leaving less than 1/3 of the validators as dishonest and allowing you to reliably reach the real chain head.

So the weak subjectivity period is essentially how far behind your node can be before 1/3 of validators can have exited without you knowing about it. Once you fall behind more than that, you need to confirm the chain you want to sync to out of band.