This paper develops a geometric framework for modeling concepts, motivation, and influence across cognitively heterogeneous agents. Each agent is represented by a personalized value space, a vector space encoding the internal dimensions through which the agent interprets and evaluates meaning. Evaluative concepts are formalized as structured vectors, abstract beings, whose transmission is mediated by linear interpretation maps. An abstract being survives communication only if it avoids the null spaces of these maps, yielding a structural criterion for intelligibility, miscommunication, and concept death. Within this framework, I show how conceptual distortion, motivational drift, and the limits of mutual understanding arise from purely algebraic constraints. A central result, the No-Null-Space Leadership Condition, characterizes leadership as a property of representational reachability rather than persuasion or authority. More broadly, the model explains how abstract beings can propagate, mutate, or disappear as they traverse diverse cognitive geometries. The account unifies insights from conceptual spaces, social epistemology, and AI value alignment by grounding meaning preservation in structural compatibility rather than shared information or rationality. I argue that this cognitive-geometric perspective clarifies the epistemic boundaries of influence in both human and artificial systems, and offers a general foundation for analyzing conceptual dynamics across heterogeneous agents.

翻译：本文构建了一个几何框架，用于模拟认知异质性智能体之间的概念、动机与影响过程。每个智能体被表征为一个个性化价值空间——即编码其内部维度的向量空间，该空间决定了智能体解读与评估意义的方式。评价性概念被形式化为结构化向量（抽象存在），其传递过程由线性解释映射介导。抽象存在仅在避开这些映射的零空间时才能成功传播，从而为可理解性、沟通误差及概念消亡提供了结构性判据。在此框架下，本文展示了概念扭曲、动机漂移及相互理解的局限性如何源于纯粹的代数约束。核心结论“无零空间领导条件”将领导力界定为表征可达性的属性，而非说服力或权威性。更广泛而言，该模型解释了抽象存在如何在跨越不同认知几何结构时进行传播、突变或消亡。通过将意义保存奠基于结构相容性（而非共享信息或理性），本研究统一了概念空间、社会认识论及人工智能价值对齐等领域的洞见。本文论证了这一认知几何视角能阐明人类与人工系统中影响力的认知边界，并为分析异质性智能体间的概念动力学提供通用基础。