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

arXiv · AI, language, vision and robotics · article · Sep 5, 2026 · UTC

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 relation

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