PAGR: Proof-Carrying Algebraic-Geometric Retrieval: A Quiver-, Provenance-, and Sheaf-Theoretic Framework for Grounded LLM Retrieval

תקציר מקורי באנגליתarXiv:2609.06127v1 Announce Type: cross Abstract: Retrieval-augmented generation is usually formulated as a statistical information-retrieval problem. Graph-based variants add relational structure, but the mathematical status of that structure is often left underspecified. Three distinct questions tend to be conflated: which statements are certified as knowledge, which latent representations are useful for retrieval, and which multi-hop compositions are semantically admissible. We propose Proof-Carrying Algebraic-Geometric Retrieval (PAGR), a framework that separates these questions mathematically. Its symbolic layer is a many-sorted relational theory generated by a typed quiver, path equations, and positive Horn inclusions. A quiver representation assigns inner-product spaces to entity ty