Empirical Discovery of Cross-Lingual Concept Geometry: Stable Semantic Attractors, Zero-Token Robustness, and Domain-Invariant Language Partitions in Multilingual Embedding Spaces

This paper reports the <b>empirical discovery of cross-lingual concept geometry</b> in multilingual embedding spaces, proving that semantic meaning is represented as stable geometric attractors independent of surface language. Using <b>LaBSE</b> as a probe, we construct (concept, language) centroid vectors from 10 representative words each across 44 concepts, 5 semantic domains, and 6 diverse languages (representing 5 language families). Our primary contribution is the demonstration that these centroids form tight, language-agnostic semantic clusters under fully unsupervised conditions.<br/><br/>Main results: (1) Unsupervised agglomerative clustering of 264 centroids yields <b>97.3% purity</b>, representing a massive <b>34.2 percentage point gap (55.6σ, p &lt; 0.0001)</b> above a rigorous, matched permutation null baseline (63.2%). (2) To rule out surface-token confounding, we present a zero-shared-token experiment (Stage 9b v2) where 12,000 composed phrases with <b>zero shared tokens</b> across languages cluster at <b>99.96% purity</b> (random baseline 10.0%), confirming that semantic proximity, not lexical overlap, drives the geometry. (3) We discover a domain-invariant within-concept language partition—<b>[EN·ES·ZH] · [FR] · [FA] · [AR]</b>—stable across all 44 concepts, which reflects training-corpus topology rather than genetic linguistic kinship.<br/><br/>Rather than asserting a fully built system, we show how this discovered geometry motivates and constrains a proposed 4-layer concept-native language system architecture (Hash-X), including the specific requirement for language-conditioned satellite nodes to accommodate Arabic and Persian. We discuss open questions regarding holistic composition rules (Layer 2) and the semantic relation graph (Layer 3) motivated by these findings.