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第三方干预是维护公平规范的重要机制，但个体在执行规范时并非一视同仁，而是表现出显著的群体差异。本研究通过两个实验，探讨错误信念心理理论 (False Belief Theory of Mind, FB ToM) 如何影响4～6岁儿童 (n = 212, Mage = 5.57 ± 0.54岁, 107名男孩) 在分配双方来自同一群体 (分配者和接受者均为内群体成员，以及分配者和接受者均为外群体成员)，及分配双方来自不同群体情境下的第三方干预行为及其行为原因。结果发现：通过 FB ToM 任务的儿童表现出显著的规范边界敏感性，会减少对纯外群体情境下不公分配的第三方干预；在双方均为外群体情境中，通过 FB ToM 的儿童的第三方干预行为显著少于未通过 FB ToM 的儿童。当互动中存在内群体成员时，通过 FB ToM 的儿童的第三方干预显著多于其在不包含内群体成员情境中的第三方干预。原因分析表明，这种第三方干预的减少并非出于对外群体的冷漠或忽视公平，而是出于对规范适用范围的区分。研究表明，错误信念心理理论促使儿童形成情境敏感的规范边界意识：更严格维护涉及内群体成员的共享规范，更克制介入外群体内部情境。因此，心理理论的发展可能帮助儿童从应用普遍公平原则，转向基于群体边界的规范执行，从而更好地完成社会化进程。

人工智能（AI）正从算法工具向自主智能体演进，标志着“智能文明”这一新型文明形态的兴起。文章从文明演化的大历史视角，梳理了从语言、文字到人工智能的智能爆炸演化序列，揭示了智能文明对个体心智、社会关系、价值实践与生产方式的深层重构，分析了思想社会、人机混合体、制度对齐等全球前沿态势及其在社交、教育、科研、医学、企业管理和社会治理等领域的发展前景。在此基础上，文章进一步探讨智能文明的文化维度与文明互鉴可能，指出中华文明中的和合、共生理念为构建包容性智能文明治理框架提供了独特资源；同时，智能文明也带来劳动力替代、算法权力集中和认知主体性侵蚀等严峻挑战。最后，文章提出以制度对齐为核心，通过制度创新、理论建构、多元文化评测和国际合作，推动建立包容、公正、可持续的智能文明新秩序。

Given a symmetric simple random walk $(X_n)_{n \ge 0}$, the family of all symmetric simple random walks $(Y_n)_{n \ge 0}$ adapted to the filtration of $(X_n)_{n \ge 0}$ was studied in Collevecchio et al. (2022). In particular, the authors established necessary and sufficient conditions under which the suitably normalized two-dimensional process $((X_n, Y_n))_{n \ge 0}$ converges weakly to a two-dimensional Brownian motion. When this occurs, we say that the random walk $(Y_n)_n$ is normal (with respect to $(X_n)_n$). In this paper, we investigate whether a "randomly selected" $(Y_n)_{n \ge 0}$ is normal. We consider a very general randomization procedure and look at both the quenched and annealed settings.

Jin, Milojević, Tomon and Zhang established a powerful recursive estimate relating the positive eigenvalues of a graph whose least eigenvalue is small in absolute value. We establish a refinement of this result, yielding improved estimates across spectral graph theory and discrepancy theory, and for Chowla's cosine problem. Recent results of Janzer, Tomon and Yip allow us to directly transfer least eigenvalue estimates to the corresponding surplus estimates. Using these tools, we fully resolve a conjecture of Räty, Sudakov and Tomon. We show that, for an $n$-vertex graph $G$ with least eigenvalue $λ_n$ and surplus $\operatorname{sp}(G)$, if $G$ is $ε$-far from all disjoint unions of cliques, then $|λ_n|\geq Ω_ε(n^{1/4})$ and $\operatorname{sp}(G)\geq Ω_ε(n^{5/4})$. Furthermore, we show that when $G$ is $n^{-o(1)}$-far from all disjoint unions of cliques, we have $|λ_n|\geq n^{1/4 - o(1)}$ and $\operatorname{sp}(G)\geq n^{5/4 - o(1)}$. Finally, we show that the surplus of a $K_t$-free graph with $m$ edges is at least $m^{0.614 - o(1)}$ as $m$ tends to infinity.

We describe construction of gravitationally dressed observables in de Sitter (dS) space, to leading non-trivial order in Newton's constant. We show that for an underlying field theory observable to be "gravitationally dressable," it must be dS invariant. If it satisfies this condition, its gravitational dressing can be constructed in terms of certain Green functions, by solving the condition that the dressed observable commute with the constraints. We provide a construction of the Green functions relevant for dressing observables lying on a time-symmetric slice. A simple example of a dS invariant observable is an operator creating a two-particle state of scalars. In the large mass limit, the particles are shown to be antipodally located, and the dressing of this operator (or corresponding state) can be explicitly constructed. Its behavior is diagnosed by certain correlators involving this state, and we check explicitly that these correlators then reproduce a linearized version of the Schwarzschild-dS solution. The underlying dS-invariant observables may be thought of as relational, and we argue can be generalized to include systems with properties of observers, which then could be likewise gravitationally dressed. We also briefly describe how such dressed observables can be related to alpha vacua, and discuss other questions regarding a more complete construction and role of such operators.