This paper develops a geometric framework for modeling belief, 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. Beliefs are formalized as structured vectors-abstract beings-whose transmission is mediated by linear interpretation maps. A belief survives communication only if it avoids the null spaces of these maps, yielding a structural criterion for intelligibility, miscommunication, and belief death. Within this framework, I show how belief distortion, motivational drift, counterfactual evaluation, 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 belief dynamics across heterogeneous agents.

翻译：本文构建了一个几何框架，用于建模认知异构主体间的信念、动机与影响。每个主体由一个个性化价值空间表示，该向量空间编码了主体解释与评估意义的内在维度。信念被形式化为结构化向量——抽象存在体——其传递通过线性解释映射进行中介。信念只有在避免落入这些映射的零空间时才能在交流中存续，从而为可理解性、误解与信念消亡提供了结构性判据。在此框架内，我展示了信念扭曲、动机漂移、反事实评估以及相互理解的局限性如何从纯代数约束中产生。核心结论——“无零空间领导条件”——将领导力表征为表征可达性的属性，而非说服或权威。更广泛而言，该模型解释了抽象存在体在穿越多样化认知几何结构时如何传播、变异或消失。该论述通过将意义保存建立在结构兼容性而非共享信息或理性的基础上，统一了概念空间、社会认识论与人工智能价值对齐领域的洞见。我认为，这种认知几何视角阐明了人类与人工系统中影响的认知边界，并为分析异构主体间的信念动力学提供了通用基础。