Compare his equation with my math explanation, and you see that Peter's conceptualization employs the average orphan rate for everyone when everyone chooses the same propagation time. The average orphan rate reflects the systemic waste of hashrate due to conflicts over which block to build the next block on. But the key point is that this waste is shared by all miners, so it isn't a cost because the difficulty readjusts commensurately, i.e. the overall profit in the system is determined by the difficulty relative to total block rewards. Peter's conceptual mistake is that it is the relative advantages that miners have over each other that determines relative profitability and this is why the cost of block space doesn't go to 0 when debasement rate goes to 0.
It appears that Peter Rizun has not only acknowledged this issue in his paper but he also made other important caveats as well, such as that the block reward must be some positive value.
Quote
We made three important simplifying assumptions in this paper: (1) we assumed the
probability of orphaning a block was well characterized by a single parameter that represented
the time between when a miner had solved a block and when his solution had been
communicated and accepted by his peers, (2) in Sections 7 to 9, we assumed that this time
parameter had a lower bound, in part, due to the capacity of the channels used to communicate
the solutions and by the coding gain with which they could be compressed, as described by the
Shannon-Hartley theorem, and (3) we ignored the costs a miner bears when he commits
transactions to a block beyond those due to orphaning. These simplifications bring up
questions that deserve further study:
(1) The time it takes to propagate information to the other miners is not in general
constant across the network, while the mempool is largely homogenous. This
suggests that, assuming equal hashing costs, miners who can propagate their block
solutions faster will earn a larger surplus. Relatedly, recent evidence also suggests that
miners may begin mining prior to fully receiving and validating new blocks.
(2) Imagine the existence of a mining cartel, interconnected with high-capacity relay
channels and committed to standardized mempool policies (to facilitate dense
compression of block solutions). Such a cartel could greatly reduce the time required
to propagate solutions to its other members. Do we expect such cartels to form and
what might be their effect?
(3) When a miner accepts a transaction that increases the set of unspent outputs (UTXO),
he takes on a liability equal to the present value of the cost of storing those new
outputs indefinitely far into the future. Is a healthy fee market expected to emerge that
charges users the true cost of expanding Bitcoin’s UTXO set?
We conclude by noting that the analysis presented in this paper breaks down when the
block reward falls to zero. It suggests that the cost of block space is zero; however, this would
suggest zero hash power, which in turn would suggest that transactions would never be mined
and, paradoxically, that no block space would be produced. Happily, questions about the
post-block reward future can be explored at a leisurely pace, as we have a quarter-century
before it begins to become a reality. Into the distant future then, a healthy transaction fee
market is expected to exist without a block size limit.
probability of orphaning a block was well characterized by a single parameter that represented
the time between when a miner had solved a block and when his solution had been
communicated and accepted by his peers, (2) in Sections 7 to 9, we assumed that this time
parameter had a lower bound, in part, due to the capacity of the channels used to communicate
the solutions and by the coding gain with which they could be compressed, as described by the
Shannon-Hartley theorem, and (3) we ignored the costs a miner bears when he commits
transactions to a block beyond those due to orphaning. These simplifications bring up
questions that deserve further study:
(1) The time it takes to propagate information to the other miners is not in general
constant across the network, while the mempool is largely homogenous. This
suggests that, assuming equal hashing costs, miners who can propagate their block
solutions faster will earn a larger surplus. Relatedly, recent evidence also suggests that
miners may begin mining prior to fully receiving and validating new blocks.
(2) Imagine the existence of a mining cartel, interconnected with high-capacity relay
channels and committed to standardized mempool policies (to facilitate dense
compression of block solutions). Such a cartel could greatly reduce the time required
to propagate solutions to its other members. Do we expect such cartels to form and
what might be their effect?
(3) When a miner accepts a transaction that increases the set of unspent outputs (UTXO),
he takes on a liability equal to the present value of the cost of storing those new
outputs indefinitely far into the future. Is a healthy fee market expected to emerge that
charges users the true cost of expanding Bitcoin’s UTXO set?
We conclude by noting that the analysis presented in this paper breaks down when the
block reward falls to zero. It suggests that the cost of block space is zero; however, this would
suggest zero hash power, which in turn would suggest that transactions would never be mined
and, paradoxically, that no block space would be produced. Happily, questions about the
post-block reward future can be explored at a leisurely pace, as we have a quarter-century
before it begins to become a reality. Into the distant future then, a healthy transaction fee
market is expected to exist without a block size limit.
