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

Computer Science > Cryptography and Security [Submitted on 28 Apr 2026] The Surprising Universality of LLM Outputs: A Real-Time Verification Primitive Alex Bogdan, Adrian de Valois-Franklin 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\times (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 R^{2} = 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. Comments: 25 pages, 6 figures, 6 tables, 37 references. Code and data: this https URL Subjects: Cryptography and Security (cs.CR); Computation and Language (cs.CL) Cite as: arXiv:2604.25634 [cs.CR]   (or arXiv:2604.25634v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2604.25634 Focus to learn more Submission history From: Alex Bogdan [view email] [v1] Tue, 28 Apr 2026 13:35:31 UTC (251 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.CL References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)