Understanding whether large language models reproduce the statistical universals that characterize human language has become a central question for digital humanities, quantitative linguistics, and the evaluation of synthetic text. Contemporary Transformer-based systems produce fluent and locally coherent output across many languages and genres. Yet fluency, grammaticality, and human preference scores do not necessarily imply that generated texts share the deeper statistical organization of human language. A model may generate plausible sentences while failing to reproduce the large-scale distributional, sequential, and informational properties documented in natural language corpora.

This project addresses that problem by extending the quantitative linguistic analysis of machine-generated text to a broader inferential framework. Natural language exhibits a set of robust statistical regularities, including Zipfian lexical frequency distributions (Zipf 1935, 1949; Piantadosi 2014), sublinear vocabulary growth described by Heaps' law (Heaps 1978; Chacoma / Zanette 2020), long-range correlations in textual sequences (Ebeling / Pöschel 1994; Altmann et al. 2012), characteristic entropy rates (Shannon 1948, 1951; Montemurro / Zanette 2011), and bursty temporal distributions of words (Altmann et al. 2009). These regularities are not merely surface effects. They reflect the interaction between lexical organization, discourse structure, redundancy, predictability, and the hierarchical organization of communication.

Previous studies have shown that neural models approximate some of these properties more successfully than simpler stochastic generators, but the evidence remains incomplete. Earlier work on recurrent and Transformer-based generators found that neural texts can reproduce aspects of long-range dependence and entropy more faithfully than Markov-chain baselines, while results for lexical scaling remain less conclusive (Lippi et al. 2019; Takahashi / Tanaka-Ishii 2019; Civico 2025). GPT-2 is therefore treated here primarily as part of the historical background and, if retained in the empirical analysis, only as a baseline for comparison with previous work. The main object of the study is the behaviour of contemporary instruction-tuned large language models.

The present study asks whether texts produced by contemporary large language models belong to the same statistical class as human texts when evaluated across several complementary dimensions. The aim is not to judge individual outputs or to assess semantic quality. Instead, the study treats human and machine-generated texts as realizations of stochastic processes and compares their statistical descriptors across languages, genres, model settings, and decoding regimes. The central question is whether similarities between human and synthetic texts reflect genuine structural convergence or only partial distributional resemblance.

The empirical design is based on a multilingual corpus of public-domain texts drawn from Project Gutenberg. The corpus covers French, Spanish, English, Italian, and German, and groups texts into three broad genres: drama, poetry, and prose. Works with unknown or ambiguous genre labels are excluded, as are books published after 2010, in order to reduce the risk of including texts produced, corrected, or substantially rephrased using neural-network tools. Each text is annotated with language, genre, century, author, title, and publication year. A standardized preprocessing pipeline removes paratextual and non-authorial material, including repository headers and footers, title pages, editorial notes, transcription credits, tables of contents, pagination artifacts, and formatting noise. This produces a cleaner historical baseline for comparison.

The synthetic corpus is generated through a matched, metadata-conditioned design rather than a continuation or paraphrase task. For each retained reference text, bibliographic metadata such as author, title, year, genre, language, and target length are converted into a structured prompt. The prompt asks the model to generate an original text consistent with the historical, literary, and linguistic context suggested by the metadata, while explicitly discouraging reproduction of known passages and overly close imitation of the author's distinctive voice. The empirical analysis will focus on the contemporary instruction-tuned models actually retained for the generation stage. For each selected reference work, synthetic texts are generated across a small number of decoding regimes, from low-stochasticity to more diverse sampling. Exact model versions, prompt identifiers, requested length, and decoding parameters are recorded in a reproducible generation manifest.

The analytical framework focuses on five families of statistical descriptors. First, lexical distributions are analysed through Zipfian scaling. Rather than relying on naive log-log regression, the study estimates the tail of the empirical frequency distribution using maximum-likelihood methods, selects the lower threshold through a Kolmogorov-Smirnov criterion, and retains the estimated tail exponent and implied Zipf exponent for each text. Second, vocabulary growth is measured through Heaps' law, estimated directly on the cumulative vocabulary-growth curve using nonlinear least squares. Third, long-range correlations are assessed with detrended fluctuation analysis, applied to character-level rank-encoded sequences. Fourth, entropy rate is estimated at the character level using a match-length estimator inspired by Lempel-Ziv and Kontoyiannis-type approaches (Kontoyiannis et al. 1998; Cover / Thomas 2006). Fifth, temporal clustering is measured through word-level burstiness based on inter-arrival times, aggregated into text-level descriptors (Goh / Barabási 2008).

The contribution of the paper lies not only in the choice of descriptors, but also in the inferential comparison of their distributions. Each text is summarized by a feature vector containing the Zipf tail exponent, the Heaps exponent, the DFA exponent, the entropy-rate estimate, and the mean burstiness index. Human and machine-generated texts are first compared through univariate tests and effect sizes for each descriptor. The analysis is then extended through regression models including group, language, model, genre, decoding parameters, and text length. Finally, the joint statistical profile of the texts is evaluated through multivariate methods such as Hotelling's T-squared test and, when feasible, MANOVA. Principal component analysis is used to visualize whether human and synthetic texts occupy overlapping or distinct regions of the resulting feature space. A scaling analysis based on truncated texts further assesses whether the estimates are stable across text lengths or affected by finite-size effects.

At the present stage, the corpus design, preprocessing protocol, generation protocol, model-selection logic, and statistical pipeline have been defined. The next step is to complete the synthetic corpora and run the full inferential comparison across language, genre, model setting, and decoding conditions. The expected contribution is methodological and substantive. Methodologically, the project provides a reproducible framework for evaluating generated text through statistical universals rather than only through local fluency or task performance. Substantively, it contributes to debates on authorship, stylistic modelling, linguistic creativity, and the epistemological status of synthetic text in digital humanities. If contemporary large language models reproduce some universals only under specific decoding conditions, or only for particular languages and genres, this would suggest that their statistical resemblance to human language is conditional rather than intrinsic. Conversely, robust convergence across descriptors and conditions would provide stronger evidence that large language models approximate not only the surface form of language, but also some of its deeper statistical organization.