去中心化的代价，双重支付：地理去中心化不变式带来的延迟下限与最小补贴
The Price of Decentralization, Paid Twice: A Latency Floor and a Minimal Subsidy from a Geographic Decentralization Invariant
- Ryonix Labs Inc.（Ryonix Labs 公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明地理去中心化必然导致延迟下限和激励补贴，且两者成恒定比例，通过Solana实测数据验证了中心化风险。
AI中文摘要：
延迟感知的验证者选择——通过投票权重、领导权或快速法定人数成员资格来奖励低网络延迟的验证者——已知会促使验证者共置，从而侵蚀拜占庭容错所假设的地理故障独立性。我们给这种张力一个尖锐的、与协议无关的形式。若一个权益配置称为(rho,gamma)-去中心化的，即不存在半径rho的区域内持有超过gamma比例的权益，我们证明对于法定人数阈值beta>gamma，每个提议者的beta-法定人数提交延迟至少为rho——与协议无关——且在平面中最小值为恰好rho*sqrt(beta/gamma)。我们的主要结果将这个几何下限与激励下限耦合：在具有真实法定人数延迟奖励的位置选择博弈中，中心化作为超临界O(2)对称性破缺分岔出现，而维持去中心化目标需要大小为Theta(c*rho/sqrt(gamma))的反集中补贴——去中心化被支付两次，一次在延迟中，一次在激励中，且比例恒定。我们数值验证了每一项声明，并在实测地理数据上验证：在RIPE-Atlas延迟矩阵上的719个验证者的Solana普查中，验证者中本聪系数为19，但地理中本聪系数为1-2。我们明确范围：下限是基础的；贡献在于延迟-补贴耦合。
英文摘要：
Latency-aware validator selection---rewarding validators for low network latency through voting weight, leadership, or fast-quorum membership---is known to push validators to co-locate, eroding the geographic fault-independence that Byzantine fault tolerance assumes. We give this tension a sharp, protocol-agnostic form. Calling a stake configuration (rho,gamma)-decentralized if no radius-rho region holds more than a gamma fraction of stake, we prove that for quorum threshold beta>gamma every proposer's beta-quorum commit latency is at least rho---independent of the protocol---and in the plane the minimum is exactly rho*sqrt(beta/gamma). Our main result couples this geometric floor to an incentive one: in a location-choice game with the true quorum-latency reward, centralization arises as a supercritical O(2)-symmetry-breaking bifurcation, and sustaining a decentralization target costs an anti-concentration subsidy of magnitude Theta(c*rho/sqrt(gamma))---decentralization is paid twice, in latency and in incentives, in a constant ratio. We verify every claim numerically and on measured geography: a 719-validator Solana census on a RIPE-Atlas latency matrix has validator Nakamoto coefficient 19 but geographic Nakamoto 1--2. We are explicit about scope: the floor is elementary; the contribution is the latency--subsidy coupling.
