Will there be a way verify the integrity of
I’m thinking of something that look like what’s in Helios.
The paper.
Now maybe i should ask the same question to my government about fiat money. 
Approximately. Although this may improve as algorithms to measure it improve
As long as you are using a SAFE wallet then yes 
Helios is interesting, must look into it more when I have time.
I bet that you (@dirvine) will prefer the HVZK (Honest Verifier Zero Knowledge) part more than the server architecture.
Who’s writing the SAFEbet Dapp? 
Sorry but you will never have more time 
just hard choice to make… but i wish you many more great revealing moment!
It seems to me that your are algorithmically tracking a mutable probabilistic distributed creature. 
Can the creation and destruction of safecoin be just stored as immutable fact on the network?
I think auditability (the total number of safecoins) needs to exist. We need to be able to point people to the fact that the system is doing exactly what it says it’s doing in regards to creating, burning/absorbing (or whatever we are calling the process of network payments going back into the max possible total) coins. We need this for market cap and trust that we never go over the max.
What kind of algorithms might exist for this?
This can only be estimated by sampling and using statistics to calculate things like % of issued Safecoin. I don’t know what the precision or metrics will turn out to be.
If it isn’t behaving, you will see it show up pretty quickly as inflation. That may be enough.