[ethresear.ch] [Privacy] Private Stablecoin on Ethereum

In the buy protocol (Section 4.4), the transition from uncirculated protocol inventory (pa_P) to a circulating user note (cmx_out) relies on off-chain coordination between the ramp and the operator before the relayer submits the atomic transaction to ReserveVault.

Could you confirm if my understanding of this flow is accurate: the user provides pa_U to the ramp, the ramp generates cmx_out and signs BuyAuth, the operator spends the inventory note using ask_P and pairs the dummy note, and finally the relayer submits the bundle?

Related to this coordination, I have two technical questions:

1. Since the ramp generates cmx_out (with rho = nf_D) and signs BuyAuth, while the operator holds ask_P to spend the inventory note, can multiple independent ramps interact with a single operator instance concurrently? If so, how does the protocol prevent inventory note contention where two purchase bundles attempt to spend the same uncirculated protocol note in the same block?

2. If the operator becomes temporarily unavailable to counter-sign the inventory spend after the ramp has already signed BuyAuth and handed the note plaintext to the user, the user’s on-chain credit is delayed until BuyAuth expires. Is there a mechanism for the ramp to pre-custody signed inventory batches, or must every buy transaction require live interactive signing from the operator?