3. IRCP Algorithm and Implementation

The IRCP algorithm implements the mathematical framework through a neural architecture that learns inverse mappings while enforcing conservation constraints. The algorithm consists of five main components: 1. **Embedding Encoder**: Maps text to semantic embeddings 2. **Measure-Preserving Transform**: Implements φ: U×V → V×U 3. **Coordinate Predictor**: Maps embeddings to 4D coordinates 4. **Inverse Attention Mechanism**: Implements A'(C') dynamics 5. **Conservation Constraint Enforcer**: Maintains mathematical properties We utilize a frozen SentenceTransformer model (all-MiniLM-L6-v2) as the base encoder: **Rationale**: Pre-trained embeddings provide semantic understanding while frozen weights ensure stability during inverse learning. Where: - **L_coord**: Coordinate prediction accuracy - **L_consistency**: Embedding-coordinate consistency - **L_conservation**: Conservation constraint satisfaction - **L_attention**: Attention mechanism regularization - **L_topology**: Ring topology preservation