Claim: Once block rewards turn 0 (when bitcoin exceeds its issuance limit), to make it uneconomical for block producers to engage in a double spend attack, the average transaction fees must amount to 8.3%.
Source: BIS  Beyond the doomsday economics of cryptocurrencies in proof of work  https://www.bis.org/publ/work765.pdf
Background/Assumptions:
 Bank for International Settlements (BIS) is a central bank owned by 60 central banks around the world, and aims to enforce monetary and financials stability globally  it regularly releases research papers on matters that they deem relevant to their cause.`
 In January 2019, they released a paper titled, “BIS  Beyond the doomsday economics of cryptocurrencies in proof of work” which discussed the economics how bitcoin achieves “payment finality”  a gurantee that a payment will not be reversed, especially unethically  a critical attribute that enforces trust in payment systems
 As part of the discussion, the paper presents a model to showcase that a double spending attack, which repudiates payment finality, can be profitable, and therefore only under certain conditions can the double spend attack be prevented, and the reliability of the payment system be enforced. These conditions are important for a user of bitcoin payemnt system as they need to be aware of the rules under which the system can be deemed as reliable
 One such condition they propose is that, once block rewards cease, the average transaction fees (average transaction cost as a percentage of transaction amount) must amount to 8.3% (under certain set of assumptions) to make it uneconomical for block producers to engage in a double spend attack,
I will argue that the condition used to derive transaction amount, which assumes that dishonest miner can double spends all transactions in the block (irrespective of whether if he/she owns all private keys in that block), is incorrect  these do not generally negate the overall conclusions of the paper, but rather only generate incorrect numbers for transaction fees needed to prevent double spend attacks  this can present an overly negative view for bitcoin payment system. A range of assumptions have been laid out in the paper to support this claim  i present only relevant assumptions below, and analyse those which can be deemed as incorrect.
Analysis
To come to the conclusion, the paper presents the equlibrium conditiions that must exist in bitcoin market. In particular:

Equilibrium condition for honest miners: If we assume mining process is competitive, miners will continue to mine until they break even, and the average expenses of computational work equal block rewards plus transaction fees (i.e., revenues from mining)
 Equation 1

Equilibrium condition for disincentiving double spend attacks from dishonest miner: This requires a bit more context. A user of the bitcoin system would would want to prevent double spend attacks if they wish to deem the payment system is reliable. Miners can engage in double spend attacks by investing in enough computational power such that they are mining on the longest chain (the mechanics of why this is this the case are relayed in the paper), and will continue to attack as long as the benefits of attacking outweigh the gains.

The benefits to a miner from engaging in a double spend attack are 1) the amount of bitcoin double spent and 2) the mining revenues (block rewards + transaction fees) gained from validating the block which had the double spend transaction.
 Equation 2

Conversely, the cost of an attack are the cost of electricity consumed in generating substantial computational power (to be able to present the longest chain), and the potential loss in value realised if bitcoin price falls following a double spend attack. Assuming the the equipment generating computational power can be rented:
 Equation 3

Since the dishonest miner must also compete with other miners, we must assume that , in the event of an attack, the cost of computational power must be at least equal to cost born by other miners to break even, and hence equations 1 and 3 must hold at the same time. Inserting Equation 1 into 3 makes it:
 Equation 4

Finally, a miner is disincentivised from attacking if Cost>Gain. If we rearrange equations 2 and 4, this means:
 Equation 5
The above illustrates that the total mining revenues (which are the transaction fees, when block rewards become 0)
gained by honest miners (i.e., the cost of forgery) must be sufficiently high to discourage dishonest miners from investing in rented equipment to out compete them.

Rearranging above equation further, and taking some addtional minor assumptions, Equation 5 can be allow us to focus on the transaction fees as a percentage of transaction amounts needed to sustain double spend attacks:
 Equation 6

Assuming some values about above parameters then allows the paper to conclude that the right hand side of above equation, which is being defined as the average transaction fees, needs to be greater that 0.083 (8.3%) to make it greater than the gain from an attack, and thereby to make it uneconomical for a dishonest miner to double spend.
Challenge: In this above equation, to qualify the right hand side of the equation as “average transaction fees”, one must that assume the amount double spent is equal to the amount of all bitcoins in the “dishonest” block (i.e., the block which has a double spend transaction). However:
 Successfully completing a double spend attack will require other miners to form consensus around the dishonest miners chain.
 Formation of consensus around a blockchain requires all the miners to firstly agree that the transactions in the block are all valid even before they check that chain is the longest.
 A transaction will be deemed valid if, at a minimum, the underlying bitcoins are being spent by the owners of those bitcoins (those who own private keys).
 If a dishonest miner attempts to double spend transactions using bitcoins to which he/she does not have private keys, the transaction will be rejected by all other miners even if the amount of computational work performed on it is greater than the rest (i.e., even if it were the “longest chain”)
 To successfully complete a double spend attack, a rational dishonest miner, therefore, will only attempt to double spend transactions in the block to which he has a private key, which may be a small proportion of the total transactions in the block.
The average transaction fee in above equation should therefore be defined as percentage of transaction fees a percentage of amount that was double in the “dishonest” block, as opposed to total amount in the “dishonest” block
Status: Challenge Claim  50 CRED