Auditing Creativity in Large Language Models: Value, Semantic Diversity, and Generation Budgets

Assessments of language-model creativity can change when evaluation moves from distinct wording to distinct ideas, excludes low-value outputs, or accounts for how a system generates and selects candidates. This paper develops a mathematical audit of these changes, building on established distinctions among quality, novelty, and diversity. A distributional ledger separates reference-relative novelty, externally assessed value, semantic diversity conditional on value, and generation and selection budgets. Exact finite-distribution results characterize reward tilts, sequence and token temperature, likelihood-based judging, and filtering versus ranking. The entropy derivative retains a covariance with the base log-probability: alignment can diversify or concentrate outputs even while divergence from the base increases. Preservation and contrastive cancellation results identify their assumptions and the additional identification requirements needed for deployment. A reproducible secondary analysis examines 132,000 released NoveltyBench responses from six models, two generation conditions, and two prompt sets. The complete paired analysis retains 131,520 responses. At ten candidates and a quality-score threshold of seven, in-context generation increases the mean number of semantic groups whose first representative qualifies by 4.63 on curated prompts and 1.70 on WildChat, with paired prompt-bootstrap intervals of [4.15, 5.11] and [1.56, 1.84]. Qualification reduces the corresponding unfiltered coverage gains by approximately 28 percent and 37 percent. Some descriptive model rankings change, while positive coverage gains persist across thresholds and after excluding judge-model name overlaps. Released judgments, representative-only scoring, and unequal context costs limit interpretation; no new human validation, historical-originality measurement, or causal alignment claim is made. Controlled numerical checks verify the mathematical implementation, and a prospective protocol specifies the evidence still needed. The contribution is an intervention audit and an empirical demonstration of measurement sensitivity, rather than a new creativity taxonomy or a universal creativity score.