Quai Research Accepted to AFT 2026: Optimal Reward Allocation via Proportional Splitting

We're excited to share that "Optimal Reward Allocation via Proportional Splitting" has been accepted to the Advances in Financial Technologies (AFT) 2026 conference at the London School of Economics in London, one of just 36 submissions selected from 185. AFT 2026 takes place October 6 through 9.

Developed with Common Prefix, the paper introduces Proportional Reward Splitting (PRS), a reward mechanism designed to strengthen proof-of-work systems against strategies such as selfish mining. Congratulations to authors Lukas Aumayr, Zeta Avarikioti, Dimitris Karakostas, Karl Kreder, and Shreekara Shastry!

This isn't theory waiting on adoption. PRS is already running on Quai Network as workshares.

The problem: mining is winner-take-all

In Bitcoin, mining works like a lottery. Millions of machines race to find one winning hash, a single machine wins the whole block reward, and every near miss earns nothing. That design creates two problems.

First, small miners can't handle the feast-or-famine income, so they hand their hashpower to big mining pools just to get steady pay. Over time, a few pools end up controlling most of the network.

Second, it opens the door to manipulation. The most famous attack, called selfish mining, was published just three years after Bitcoin launched. A large miner secretly holds back blocks it finds, then releases them at the right moment to erase competitors' work and collect more than its fair share. Researchers have shown this works in Bitcoin for miners well below half the network.

Both problems trace back to the same root: the protocol only counts winning blocks, so it has a very blurry picture of who is actually doing the work.

The idea: count the near misses too

The paper's fix is to make that picture sharp. Alongside full blocks, the protocol accepts workshares: proofs of work that are built exactly like blocks but meet an easier difficulty bar. Because the bar is lower, workshares show up far more often than blocks, and who finds them is a running sample of who holds the mining power. It's the difference between guessing an election from one vote and running a proper poll.

With that sample in hand, Proportional Reward Splitting changes how each block's reward is paid out. Instead of the block finder taking everything, the reward at each height is divided among the block and the workshares published around it, in proportion to the work each miner proved. If you contribute 5% of the network's work, you collect about 5% of the rewards. Every time.

What the researchers found

The team analyzed PRS two ways: with formal math, and with simulations that pit an optimal attacker against each reward scheme (Bitcoin's, FruitChains, and plain Reward Splitting) under realistic settings.

• Honesty becomes the best strategy. The math shows PRS is an equilibrium: no miner can earn more by deviating from the protocol, so publishing your work immediately is always the smart move. An earlier scheme called FruitChains proved this too, but only with confirmation windows so long they'd take days in practice. PRS holds up at the short windows real blockchains actually use.
• Selfish mining becomes uncompetitive. In the simulations, an attacker needs more than 38% of all mining power before any manipulation strategy beats honest mining, versus 35% for the next best scheme. And even a 38% attacker only collects about 38% of rewards under PRS, compared with 40% under Reward Splitting and over half under Bitcoin's rules.
• Double spending and censorship get harder too. The paper tests each scheme against double-spend attacks and censorship attacks. PRS is the strongest option across most attacker sizes, and it beats plain Reward Splitting in every scenario tested.
• The cost is modest. The catch to sampling more workshares is that someone has to store them. The paper measures this tradeoff directly: against realistic attackers, estimating mining power to within about 3% costs a few hundred kilobytes per block. A fair, attack-resistant payout system for the price of some storage.

What this means for Bitcoin and other proof of work currencies

Nothing about PRS is specific to Quai. It's a reward design any proof of work chain could adopt, and the paper measures it directly against the reward rules Bitcoin uses today.

Read that way, the results are a diagnosis of the status quo. Under winner-take-all payouts, a large miner can profit by manipulating which blocks get published, and the paper's simulations show an attacker with 38% of hashpower collecting more than half of all rewards under Bitcoin's rules. The same variance problem is what pushed most of Bitcoin's hashrate into a handful of pools. These are not flaws in proof of work itself. They are flaws in how the rewards are divided.

That is the encouraging part. Proof of work security does not have to come bundled with jackpot economics. A chain that counts near misses and pays proportionally keeps the same energy-backed security while disincentivizing selfish mining and removing the need for pools. For Bitcoin, changing the reward rule would take a hard fork, so adoption there is a long conversation. For other proof of work currencies, the blueprint is now published, peer reviewed, and running in production.

The authors also point to what comes next: extending proportional splitting to DAG-based ledgers, and exploring whether the same ideas could work in proof of stake, where each participant's power is already known exactly.

Already live on Quai

Quai Network implements this research today. Miners on Quai produce workshares automatically while hunting for blocks; near misses get included in upcoming blocks and paid their share of the reward instead of being thrown away. With a block every five seconds and several workshares alongside each one, the network pays out constantly, which is why solo mining on Quai stays practical without pools.

For more on how workshares run in production, read The Next Evolution in Proof of Work: Quai Network's Workshares.

Read the paper

• Optimal Reward Allocation via Proportional Splitting on arXiv
• AFT 2026 conference details, October 6 through 9 at the London School of Economics
• PoEM: Proof of Entropy Minima, the Quai consensus research PRS builds on
• go-quai on GitHub, where the workshare logic lives in open source

We're thrilled to see this work recognized at AFT and already in action on Quai.