Hi - I'm Chris from the Money View symposium. I thought I'd check in on your work.
Mind if I criticise your use of a couple of phrases related to equity? I hope not, because I'm doing it now... :-) I think there's a crucial conceptual point here.
"Beta carries [$10 of] equity against this exposure". Beta doesn't have any exposure. It has a (debt) asset, which may or may not involve Beta being paid in future. The worst that can happen is that Beta gets nothing. Beta's $10 equity liability means that, on the assumption that Beta is paid the $10 it is owed by Alpha, it will ultimately give that $10 to its owners.
"Alpha also holds $9 in assets, supported by equity." Again, equity doesn't support anything. It is a note in the accounts that the difference between its $19 of assets and its $10 of liabilities is owed to Alpha's owners.
I think the source of confusion is the thinking that led to the (IMO awful) uses and sources of funds model. The underlying assumption is that every economic action is part of a transaction with an equal and opposite transfer of money. So if a Walmart offers a customer a $5 voucher as a goodwill gesture because they didn't like the flavour of some cheese they bought there, that counts as a *source of funds* for Walmart, even though that doesn't make any sense at all. The underlying assumption is that the customer bought a $5 voucher with $5 of cash.
You get the same with equity. Normally, a firm gains equity when its owners transfer money to the firm. It's the money (the asset) which supports the firm, not the equity. Equity represents the fact that the firm owes that money to the owners.
All in all, I think it's really important to keep in mind that there can be individual economic actions (assignment [tangible/debt], issuance, set-off and novation) which are not part of a transaction. They transfer some of one party's (raw) net worth to the other.