概念网络的高阶拓扑嵌入约束与心智积累的容量上限:一个理论假说

【理论假说 / 概念框架,未经同行评议】 本文提出一个关于心智积累容量上限的理论假说。概念在脑内并不以孤立条目存储,而以加权高阶关联结构组织。本文保留并形式化三个操作概念:以概念为中心的"体积点"、由共享概念锁点锁定的相对位置、以及"三点可调、四点可调、第五点出现时至少一个距离被迫牺牲"的第五点冲突。本文把它翻译为距离几何与单纯复形的语言:用多维标度分析的应力残差刻画嵌入冲突,用 Schoenberg 判据区分可嵌入与不可嵌入的关联结构,用团复形的 Betti 数量化闭环的层级多样性,并区分 K4(其四点等距实现是三维正四面体)与平面的 C4。由此得到可被反驳的命题:心智积累的上限不在于可存储的条目数,而在于给定连接预算与可容许应力时,系统能稳定维持的高阶闭环的层级多样性。本文给出 5 条可检验推论并说明其局限;意识的主观体验、自主闭环与硬件实现不在本文范围内。 English abstract: This paper proposes a theoretical hypothesis on the capacity limit of mental accumulation. Concepts are not stored as isolated entries but as weighted higher-order relational structures. Three operational constructs from the original model are retained and formalized: the volume point, shared concept lock points, and the fifth-point conflict. The paper translates these intuitions into distance geometry and simplicial complexes: embedding conflict is expressed as stress residual in multidimensional scaling, the Schoenberg criterion separates embeddable from non-embeddable relational structures, Betti numbers of the clique complex quantify the level diversity of closed loops, and K4 (whose four equidistant points admit only a three-dimensional realisation) is distinguished from the planar C4. It yields a falsifiable claim: the limit of mental accumulation lies not in the number of storable items but in the level diversity of higher-order closed loops that a system can stably maintain under a given connection budget and stress tolerance. Five testable inferences and the limitations of the framework are given. Subjective experience, autonomous closed loops, and hardware implementation are outside the scope of this paper. 姊妹篇:第二册《自主闭环、内生评估与心智积累的物理约束:从"体积点"到类脑硬件的整合性假说》。附配套开源工具包 volume-topology。