Table of Contents
- 1 Introduction
- 2 Hashrate Externalities
- 3 Targeted Nakamoto - A Mechanism Design Perspective
- 4 The Model
- 5 The Targeted Block Reward Policy
- 6 Strategic Effects of Block Adjustment Policy
- 7 Monetary Neutrality
- 8 Conclusion
- 9 Original Analysis
- 10 Technical Details
- 11 Code Implementation
- 12 Future Applications
- 13 References
1 Introduction
Proof-of-Work (PoW) blockchain cryptocurrencies like Bitcoin require the application of computing power by miners to operate the network. Miners assemble blocks and compete to solve a puzzle set by the code. The number of puzzle guesses (one hash per guess) a mining computer makes in a specified interval of time is its hashrate, which consumes electricity.
1.1 Balancing Competing Risks
Bitcoin faces two conflicting existential risks: currently, high mining energy consumption invites political backlash; in the future, reductions in miner rewards will cause hashrate to decline, lowering the cost of an attack. Targeted Nakamoto balances these concerns by guiding hashrate towards a chosen target.
1.2 Links to code and web API
Kristian Praizner wrote the code for the hashrate control algorithm and implemented it on an API that is a companion to this paper.
1.3 Related Literature
The paper builds on existing research in blockchain mechanism design and Bitcoin protocol improvements, citing works on PoW optimization and network security models.
1.4 The research question and design constraints
How to design a protocol that maintains Bitcoin's security while reducing its environmental impact, without breaking monetary neutrality or creating new attack vectors.
1.5 Roadmap
The paper proceeds by analyzing hashrate externalities, presenting the Targeted Nakamoto mechanism, modeling its effects, and discussing implementation considerations.
2 Hashrate Externalities
Mining activity creates two key externalities: network security (positive) and carbon emissions (negative). Higher hashrate increases security but also increases energy consumption.
2.1 Dependencies
Hashrate depends on block rewards, electricity costs, and mining hardware efficiency. The relationship follows: $H = f(R, C_e, E)$ where $H$ is hashrate, $R$ is block reward, $C_e$ is electricity cost, and $E$ is hardware efficiency.
2.2 Network Security
Network security cost decreases with hashrate: $S_c = \frac{k}{H}$ where $S_c$ is security cost and $k$ is a constant. Higher hashrate makes 51% attacks more expensive.
3 Targeted Nakamoto - A Mechanism Design Perspective
Targeted Nakamoto is a protocol that incentivizes miners to home hashrate in on the minimum cost range by capping block rewards when above target and imposing a block reward floor when below.
3.1 Key Building Blocks of Targeted Nakamoto
The protocol uses adjustable block rewards, difficulty-based triggers, and monetary neutrality mechanisms to maintain system integrity while controlling hashrate.
3.2 An overview of the mechanism design of the protocols
The design follows incentive-compatible principles where miners are economically motivated to maintain hashrate near the target level without central coordination.
4 The Model
The mathematical model formalizes the relationship between hashrate, block rewards, and network parameters to predict system behavior under the proposed protocol.
4.1 The puzzle difficulty signal of hashrate
Network difficulty $D$ serves as a proxy for hashrate: $D \propto H$. The protocol uses difficulty measurements to trigger reward adjustments when $D$ deviates from target $D_t$.
4.2 Mining equilibrium
Mining equilibrium occurs when $R \times P_s = C_e \times E \times H$ where $P_s$ is probability of solving the puzzle. The protocol adjusts $R$ to maintain $H$ near optimal level.
5 The Targeted Block Reward Policy
The core innovation: a dynamic block reward policy that adjusts based on current hashrate relative to target levels.
5.1 The block reward adjustment allocations
When hashrate exceeds target: $R_{actual} = R_{base} - \Delta R$. When hashrate falls below target: $R_{actual} = R_{base} + \Delta R$.
5.2 The puzzle difficulty signal and policy switch points
Policy triggers activate when $|D - D_t| > \delta$ where $\delta$ is the tolerance threshold. Adjustment magnitude: $\Delta R = \alpha |D - D_t|$ with $\alpha$ as sensitivity parameter.
5.3 Policy to control hashrate
The control algorithm uses proportional-integral feedback to minimize oscillations and maintain stable hashrate around the target level.
6 Strategic Effects of Block Adjustment Policy
The policy creates predictable economic incentives that guide miner behavior toward the socially optimal hashrate level.
6.1 Stability of Miner Equilibrium
Analysis shows the system converges to stable equilibrium where marginal security benefit equals marginal environmental cost.
6.2 Dynamic Adjustment of Hashrate
Simulations demonstrate hashrate responds to reward adjustments within 2-3 difficulty adjustment periods, showing rapid convergence to target.
7 Monetary Neutrality
Monetary neutrality is maintained by proportional adjustments in spending potential among UTXO holders, offsetting the additions and subtractions to the block reward.
7.1 The Targeted Monetary Policy
The protocol uses UTXO set adjustments to ensure total monetary supply remains unchanged despite block reward variations: $\sum UTXO_{value} = constant$.
8 Conclusion
Targeted Nakamoto represents a promising approach to balancing Bitcoin's security needs with environmental concerns, providing a framework for sustainable PoW blockchain operation.
9 Original Analysis
一针见血：Targeted Nakamoto attempts to solve Bitcoin's fundamental sustainability paradox, but the implementation complexity may outweigh its theoretical benefits. This is another academic solution searching for a real-world problem.
逻辑链条：The paper's core argument follows a clean economic logic: hashrate creates security benefits and environmental costs → optimal hashrate minimizes total cost → protocol adjustments can guide miners to this optimum. However, the chain breaks at implementation. Like many mechanism design papers (similar to the elegant but impractical ideas in early CycleGAN research), the mathematical beauty doesn't translate to blockchain reality. The assumption that miners will passively accept reward manipulations ignores the competitive dynamics that drive Bitcoin mining.
亮点与槽点：The monetary neutrality mechanism is genuinely innovative - using UTXO adjustments to offset reward changes shows deep understanding of Bitcoin's architecture. This surpasses simpler proposals like Ethereum's early difficulty bombs. However, the proposal suffers from the same central planning pitfalls that Bitcoin was designed to avoid. Setting the "optimal" hashrate requires exactly the kind of subjective judgment that decentralized systems eliminate. The Cambridge Bitcoin Electricity Consumption Index shows Bitcoin currently consumes ~100 TWh annually - who gets to decide what the "right" number should be?
行动启示：For developers: study the UTXO adjustment mechanism for other applications, but avoid the central planning aspects. For miners: prepare for more sophisticated reward structures emerging. For researchers: focus on less intrusive solutions like renewable energy integration. The Bitcoin community should view this as an interesting thought experiment rather than a practical upgrade path. As the Bitcoin Core development process has shown (reference: Bitcoin Improvement Proposals governance model), elegant academic solutions rarely survive contact with Bitcoin's conservative upgrade philosophy.
10 Technical Details
The protocol uses a control theory approach with the fundamental equation: $H_{t+1} = H_t + \beta(R_t - C(H_t))$ where $\beta$ is adjustment speed, $R_t$ is current reward, and $C(H_t)$ is mining cost function. The optimal hashrate $H^*$ solves: $\min_H [\alpha \cdot SecurityCost(H) + (1-\alpha) \cdot EnvironmentalCost(H)]$ where $\alpha$ is the security-emission tradeoff parameter.
11 Code Implementation
function calculate_reward_adjustment(current_difficulty, target_difficulty):
deviation = current_difficulty - target_difficulty
if abs(deviation) > THRESHOLD:
adjustment = -SENSITIVITY * deviation
return adjustment
return 0
def update_utxo_set(block_reward_change, utxo_set):
total_adjustment = block_reward_change * BLOCK_INTERVAL
adjustment_factor = 1 + (total_adjustment / utxo_set.total_value)
for utxo in utxo_set:
utxo.value *= adjustment_factor
return utxo_set12 Future Applications
The mechanism could be adapted for other PoW blockchains facing similar sustainability challenges. Potential applications include: Ethereum Classic, Litecoin, and emerging industrial blockchain platforms. The UTXO adjustment technique could also be used for implementing monetary policy in central bank digital currencies.
13 References
- Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System
- Cambridge Centre for Alternative Finance (2023). Cambridge Bitcoin Electricity Consumption Index
- Buterin, V. (2014). Ethereum White Paper
- Aronoff, D. (2025). Targeted Nakamoto: A Bitcoin Protocol to Balance Network Security and Carbon Emissions
- Zhu et al. (2017). Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks (CycleGAN)