Great question. thanks for asking. Please check out https://umint.cash/ there are 2 pages on top. 1) Proof of reserves which is what we use to stabilize the sats to dollars and 2) Proof of liabilities which shows the outstanding tokens. By seeing this info in real-time you know the mint is solvent. 

Stable channel is a simple channel between a mint and a stable provider. The mint is stable while the stable provider sats goes up and down every 5 mins to balance the stable side. The history table shows how it is done. 

lmk for additional questions.