Hmm, an interesting perspective. First, to be clear, most of these proposals are "self-verifying" so to speak, so the question doesn't arise (i.e. proof of burn, proof of work and aut-ct). Specifically for a payment though, like ecash, I imagined it as "user has N entry point relays, relays talk to each other" and the latter is a matter of relationship between relays. I suspect that's how it works today. Relay X just blocks relay Y when it sees it sending a bunch of objectionable spam, otherwise they choose to cooperate. As for relays behaving adversarially because they might be in economic competition, that could be a good point, I'm not sure.

How about backing Nostr events (or pubkeys) with timelocked fidelity bonds as an alternative/addition to proof-of-burn? This seems to mitigate the perverse incentive you mention at the end of your paper: > "Interestingly, this proposal creates an incentive for Bitcoin miners to spam unprotected Nostr relays, in order to force users to pay for their posts." With a bond, the cost is capital lock-up rather than a per event sacrifice, so miners don’t receive the "attention fee" itself (only normal on-chain transaction fees). And the bond is still globally verifiable by anyone with a Bitcoin node. The math on how bonds could be valued compared to burns is explained here: >

Gist

Financial mathematics of joinmarket fidelity bonds

Financial mathematics of joinmarket fidelity bonds - financial-mathematics-of-joinmarket-fidelity-bonds.md

(Although, if bonds were per event, I suspect the quadratic factor should be removed. However, if bonds are per pubkey for sybil resistance the quadratic factor makes sense.) To avoid UTXO bloat, I suspect a notary could aggregate many small user timelocks into a single on-chain bond UTXO using an Ark-like construction, while still giving each user a unilateral exit path after the timelock if the notary stops cooperating. I'm unsure about the details though.