I guess you mean RippleLabs... yes, the client code is just hosted on ripple.com for convenience, you can run your own rippled to connect to and set up a webserver with the client locally too (it's what I do for example), I linked the repositories before. I'd recommend to use the tagged release versions and not bleeding edge code as it is under active development.
So if I set up a centralized webserver as you suggest, the trades will be distributed with the Ripple Labs hosted transactions?
rippled is not a webserver, you would probably deploy ripple-client on a local webserver though. Then tell the client to connect to your local server instead of the official public servers and your local rippled server needs connectivity to other rippled servers of course (just like bitcoind). I am not sure what you mean by "Ripple Labs hosted transactions".
I meant Ripple Labs generated blockchain, although there isn't a way to validate that independently. As a black box, the Ripple Labs servers just seem to be a clearinghouse of transactions similar to Liberty Reserve.
Well, just like with Bitcoin where you kinda need to use the Satoshi generated block chain, you kinda need to use the ledger chain RippleLabs started. You are free to run your own fork of course, but this has similar consequences as with Bitcoin (you'd create an Altcoin with Bitcoin rules or an alt-ledger with Ripple rules). Their validators are widely used, but not the only ones out there, so while they are currently still quite central to the network the network could very well survive without them. You can run your own validator by the way too, some people who are critical of RippleLabs would probably add yours to their UNL to have even more diversity. I might announce my own one "soonish" too, once it has a bit better hardware and runs more stable.
The bottom line is it's
not possible to verify the number of Ripple currency units in existence, in contrast to Bitcoin. You've already expressed as much:
It would be very unexpected to see that more than 100 billion XRP existed prior ....
I don't care if the system is based on balances, transactions, or lunar eclipse events. If ordinary people can't mathematically verify for themselves the number of units in existence they should be wary of investing anything into it.
I already told you how to get the total number of XRP at any ledger since 32570, here you go again:
curl -X POST -d '{ "method" : "ledger", "params" : [ { "ledger_index" : 32570 } ] }' http://s1.ripple.com:51234
You can increment ledger_index and you'll see that these header form a hashed chain (see the value in parent_hash). If you want to see total balances of all accounts so you can make sure that they add up to the number in the header this is also possible.
I'm not sure how else to explain it, but if you deal with balances it does not matter what happened before a certain point of time, it matters what the state was at a certain point and what happened since then. Any ordinary(?) person with some knwoledge about accounting can tell you that and any ordinary(?) person that is a bit interested in programming and crypto can tell you that this is also verifiable on the ledger chain.