Semantic Geometry & UMAP 2D
2D projection of the 3072d semantic universe: parallel sentences gravitating around the source English anchor.Semantic Geometry, 3072D Vector Embeddings & Dimensionality Reduction
| 1. Semantic Space & 3072D Embeddings | Textual anchors are projected into a continuous 3072-dimensional vector space using Google Gemini Embeddings. Rather than surface lexical matching, each sentence receives a dense coordinate encoding thematic meaning, syntactic structure, and narrative register. The authorial English original acts as the immutable center of mass. |
| 2. Cosine Similarity & Bidirectional Verification | The cosine of the angle between high-dimensional vectors measures semantic fidelity regardless of sentence length. Weighted at 40% of the hybrid verdict (0.60·Judge + 0.40·Cosine), the engine computes both direct alignment (Original ↔ Translation) and back-translation fidelity (Back-Translation ↔ Original) to ensure mathematical reversibility. |
| 3. UMAP 2D Dimensionality Reduction | Uniform Manifold Approximation and Projection (UMAP) non-linearly reduces 3072D manifold topology into a Cartesian 2D plane while strictly preserving local neighborhoods and global cluster relations. Languages carrying identical semantics cluster tightly around the source anchor, while translational divergence manifests as geometric distance. |
| 4. Polar Radar & Micro-Compass | The 2D plane is transformed into an English-centric polar coordinate system (r, θ) where the authorial source anchor sits at the origin (0, 0). The angle θ reflects the directional drift of linguistic families, while the radial distance r quantifies cosine divergence from authorial intent. |