# Linguistic Holonomy and Statistical Watermarks: Inner Geometry of Meaning-Preserving Transformations

arXiv: https://arxiv.org/abs/2608.19369 · HTML: https://mlsanity.com/paper/2608.19369/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Watermarking generated content and models, one of 12 directions in LLM safety and security.
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Placed in

- LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/)

## Builds on (most cited first, 11 of 11)

- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [Paraphrasing evades detectors of AI-generated text, but retrieval is an effective defense](https://mlsanity.com/paper/2303.13408/) (2023)
- [Can AI-Generated Text be Reliably Detected?](https://mlsanity.com/paper/2303.11156/) (2023)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [Provable Robust Watermarking for AI-Generated Text](https://mlsanity.com/paper/2306.17439/) (2023)
- [Undetectable Watermarks for Language Models](https://mlsanity.com/paper/2306.09194/) (2023)
- [On the Reliability of Watermarks for Large Language Models](https://mlsanity.com/paper/2306.04634/) (2023)
- [Mark My Words: Analyzing and Evaluating Language Model Watermarks](https://mlsanity.com/paper/2312.00273/) (2023)
- [No Free Lunch in LLM Watermarking: Trade-offs in Watermarking Design Choices](https://mlsanity.com/paper/2402.16187/) (2024)
- [Linguistic Loops and Geometric Invariants as a Way to Pre-Verbal Thought?](https://mlsanity.com/paper/2503.23311/) (2025)
- [Chainwash: Multi-Step Rewriting Attacks on Diffusion Language Model Watermarks](https://mlsanity.com/paper/2605.05503/) (2026)

## Abstract (arXiv)

Statistical watermarks for language models live in the freedom of the signifier: they choose among tokens that are nearly equivalent in meaning, and they are therefore eroded by exactly those transformations which move the form of a text while leaving its content in place. The literature measures such transformations by their endpoint, through the semantic similarity between the original and the rewritten text. We show that the endpoint is the wrong statistic. Adapting the formalism of linguistic loops, we prove that the invariant of a chain of meaning-preserving transformations factorises canonically into an endpoint part and a holonomy in the stabiliser of the initial state, the second of which the semantic deficit cannot see; the loop rotation is parallel transport on the unit sphere of the embedding space, so that the analogy with the Wilson loop becomes a theorem rather than a figure of speech. On the side of the detector we prove an exact identity: the residual statistic is proportional to the number of positions whose seeding window survived intact, from which the decay law ρh+1 follows as the independent-edit corollary. The identity has a disconcerting consequence, which we confirm to three decimal places: at one and the same retention rate the surviving signal may be one half of the original, one quarter of it, or exactly nothing, according only to where the edits fall.