Does anyone know of any proof which says that convergence can be guaranteed without a block reward? I would like to hear more detail because it's my gut feeling that it cannot.
I am working on it for a white paper.
Details are upthread.
We've covered the issues upthread, perhaps not to your satisfaction.
Let me reiterate again that the math you cited from Meni Rosenfeld was incomplete and thus incoherent. I explained that the same probabilistic guarantees can be obtain by increasing the number of confirmations rather than increasing the block reward.
The Nash equilibrium in an unprofitable PoW design (which doesn't require there is necessarily no block reward but rather just that the block reward is less than profitable at the current difficulty) is that payers want their transactions to be included in the longest-chain, thus they will send their PoW shares towards confirming blocks which honor the LCR.
In my design, the amount of electricity that secures the coin is sensibly insignificant relative to the value of transactions since each transaction includes a PoW share.