How do you know summary entries are valid if order doesn't matter?
I.e. "we have 10 customers as of this date" can become immediately invalid if a new entry is appended afterwards with a date before that summary entry (i.e. because it was on a peer which hadn't yet sent it)
Realistically, you never store summaries in the log. Instead, you store what it took to calculate them. So you won't store "we have 10 customers on this date with this range" but instead store "we found these 10 customers on this date with this range". This assumes you can store infinite sized lists in your log, but realistically, this is never a concern if you can keep your time windows small enough. Then, you periodically do a reconciliation and log corrections (look for entries not summarized -- easily done via a bloom filter which can tell you what entries are definitely NOT in your set) over a longer period.
For example, we had a 28-day reconciliation period at one company I worked at (and handled over 120 million events per day). If you appended an event earlier than 28 days prior, it was simply ignored. This very rarely happened, but allowed us to fix bugs with events for up to 28 days.
IME you have to be willing to recalculate the summaries up to some kind of consistency window.
Yes you may be changing history and you may have a business reason not to address that revision immediately (you've already billed them?) - but the system can still learn it made a mistake and fix it (add activity from Jan 30 evening that comes in late to the Feb bill?)
I.e. "we have 10 customers as of this date" can become immediately invalid if a new entry is appended afterwards with a date before that summary entry (i.e. because it was on a peer which hadn't yet sent it)