# The Surprising Universality of LLM Outputs: A Real-Time Verification Primitive

arXiv: https://arxiv.org/abs/2604.25634 · HTML: https://mlsanity.com/paper/2604.25634/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [SummaC: Re-Visiting NLI-based Models for Inconsistency Detection in Summarization](https://mlsanity.com/paper/2111.09525/) (2021)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Understanding Factuality in Abstractive Summarization with FRANK: A Benchmark for Factuality Metrics](https://mlsanity.com/paper/2104.13346/) (2021)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Lookback Lens: Detecting and Mitigating Contextual Hallucinations in Large Language Models Using Only Attention Maps](https://mlsanity.com/paper/2407.07071/) (2024)
- [Your Large Language Models Are Leaving Fingerprints](https://mlsanity.com/paper/2405.14057/) (2024)
- [Learned Hallucination Detection in Black-Box LLMs using Token-level Entropy Production Rate](https://mlsanity.com/paper/2509.04492/) (2025)
- [LLM-Generated Natural Language Meets Scaling Laws: New Explorations and Data Augmentation Methods](https://mlsanity.com/paper/2407.00322/) (2024)
- [Modeling the Unigram Distribution](https://mlsanity.com/paper/2106.02289/) (2021)
- [The Geometry of Truth: Layer-wise Semantic Dynamics for Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2510.04933/) (2025)
- [FDLLM: A Dedicated Detector for Black-Box LLMs Fingerprinting](https://mlsanity.com/paper/2501.16029/) (2025)
- [HalluField: Detecting LLM Hallucinations via Field-Theoretic Modeling](https://mlsanity.com/paper/2509.10753/) (2025)

## Built on by (most cited first, 3 of 3)

- [RAILS: Verification-Native Clearing For Agentic Commerce](https://mlsanity.com/paper/2606.08790/) (2026)
- [Machine Psychometrics: A Mathematical Psychology of Artificial Intelligence](https://mlsanity.com/paper/2605.23952/) (2026)
- [Lost in Sampling: Assessing Lexical Reachability in LLMs via the Word Coverage Score (WCS)](https://mlsanity.com/paper/2605.27268/) (2026)

## Abstract (arXiv)

We report a striking statistical regularity in frontier LLM outputs that enables a CPU-only scoring primitive running at 2.6 microseconds per token, with estimated latency up to 100,000× (five orders of magnitude) below existing sampling-based detectors. Across six contemporary models from five independent vendors, two generation sizes, and five held-out domains, token rank-frequency distributions converge to the same two-parameter Mandelbrot ranking distribution, with 34 of 36 model-by-domain fits exceeding R2 = 0.94 and 35 of 36 favoring Mandelbrot over Zipf by AIC. The shared family does not collapse the models into statistical duplicates. Fitted Mandelbrot parameters remain cleanly separable between models: the cross-model spread in q (1.63 to 3.69) exceeds its per-model bootstrap standard deviation (0.03 to 0.10) by more than an order of magnitude, yielding tens of standard deviations of separation per few thousand output tokens. Two capabilities follow. First, statistical model fingerprinting: text from a vendor-delivered LLM can be tested against its claimed model family without cryptographic watermarks or access to model internals, supporting provenance verification and silent-substitution audits. Second, a model-agnostic reference distribution for black-box output assessment, from which we derive a single-pass scoring primitive that composes with model log probabilities when available and degrades to a rank-only mode usable on closed APIs. Pilot results on FRANK, TruthfulQA, and HaluEval map where the primitive helps (lexical anomalies, unsupported entities) and where it structurally cannot (reasoning errors in domain-appropriate vocabulary). We position the primitive as a first-pass triage layer in compound evaluation stacks, not as a replacement for sampling-based or source-conditioned verifiers.