CVPD at QIAS 2026: RAG-Guided LLM Reasoning for Al-Mawarith Share Computation and Heir Allocation

Islamic inheritance (Ilm al-Mawarith) is a multi-stage legal reasoning task requiring the identification of eligible heirs, resolution of blocking rules (hajb), assignment of fixed and residual shares, handling of adjustments such as awl and radd, and generation of a consistent final distribution. The task is further complicated by variations across legal schools and civil-law codifications, requiring models to operate under explicit legal configurations. We present a retrieval-augmented generation (RAG) pipeline for this setting, combining rule-grounded synthetic data generation, hybrid retrieval (dense and BM25) with cross-encoder reranking, and schema-constrained output validation. A symbolic inheritance calculator is used to generate a large high-quality synthetic corpus with full intermediate reasoning traces, ensuring legal and numerical consistency. The proposed system achieves a MIR-E score of 0.935 and ranks first on the official QIAS 2026 blind-test leaderboard. Results demonstrate that retrieval-grounded, schema-aware generation significantly improves reliability in high-precision Arabic legal reasoning tasks.