Retrieval-Assisted Scalar Grounding for Natural-Language Optimization: A Diagnostic Study

Abstract Retrieval and structural checks can make natural-language optimization outputs appear usable even when numerical grounding—assigning textual quantities to model parameters—is incomplete. We examine this diagnostic gap through three questions: fixed-catalog schema identification, the validity of coverage/type readiness as a numerical check, and the mechanisms underlying grounding outcomes. On 331 queries from NLP4LP, a benchmark for natural-language linear and mixed-integer linear programming, and 335 schema documents, term frequency–inverse document frequency retrieval and a pretrained dense encoder identify the target schema for 301 and 313 queries. Lexical grounding with multiplicative-word extraction passes coverage/type readiness on 265 queries, but only seven meet the complete stored-reference scalar-tolerance criterion: 2.64% of ready outputs. A mutually exclusive residual partition distinguishes retrieval, coverage, type, and numerical failures. Six grounding procedures under fixed retrieval yield between seven and 46 complete successes, with candidates, scoring, abstention, and decoding changing together. A separate 49-query assignment study with fixed candidates and scores improves exact slot counts without increasing the five whole-instance tolerance successes, limiting attribution to search. The methodological contribution is joint reporting of retrieval, readiness, and complete scalar agreement with explicit assistance, denominators, and evidence boundaries. Reference-derived inventories and benchmark exposure restrict the findings to assisted grounding. Supplementary relationship judgments and author contrasts assisted by artificial intelligence illustrate semantic limits without establishing accuracy. A versioned public release supports saved-record reanalysis; missing historical predictions and restricted originals prevent full experimental reproduction.