[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-273643-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-273643-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","linguistic-holonomy-and-statistical-watermarks-inner-geometry-of-meaning-preserving-transformations","Linguistic Holonomy and Statistical Watermarks - Inner Geometry of Meaning-Preserving Transformations","","Statistical watermarks for language models rely on the freedom of the signifier, selecting tokens with near-equivalent meaning. This dependence makes the watermark fragile under transformations that alter textual form while preserving content. Prior work evaluates robustness only through endpoint statistics via semantic similarity between original and rewritten texts. This study shows the endpoint statistic is incorrect and proves a canonical factorization of the holonomy invariant into an endpoint part and a stabiliser holonomy that the detector cannot perceive, yielding an exact residual identity and a decay law based on survived seeding windows.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/linguistic-holonomy-and-statistical-watermarks-inner-geometry-of-meaning-preserving-transformations/273643/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/linguistic-holonomy-and-statistical-watermarks-inner-geometry-of-meaning-preserving-transformations/273643.png","ImageObject",300,407,{"name":42,"@type":43},"Miles","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-04","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",11,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the main idea behind statistical watermarks in language models?","Question",{"text":63,"@type":64},"They watermark text by restricting generation to a secret, key-dependent subset of tokens, so detection relies on the presence of tokens belonging to that subset.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why does evaluating robustness only by endpoint semantic similarity fail?",{"text":68,"@type":64},"Because the paper proves the relevant invariant factorizes, and a holonomy component in the stabilizer of the initial state is invisible to the detector; thus endpoint-only statistics miss essential structure.",{"name":70,"@type":61,"acceptedAnswer":71},"What does the detector residual identity show about edits?",{"text":72,"@type":64},"The residual statistic is proportional to the number of positions whose seeding window remains intact, leading directly to a decay law as an independent-edit corollary.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},273643,1789472349,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145,"preview_page_count":4},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","arXiv : 2608 . 19369v 1 [cs .CL] 19 Aug 2026  \nLinguistic Holonomy and Statistical Watermarks: Inner Geometry of Meaning-Preserving Transformations  \nDaniele Corradetti  \nGrupo de Física Matemática, Instituto Superior Técnico  \nAv. Rovisco Pais, 1049-001 Lisboa, Portugal  \nDepartamento de Matemática, Universidade do Algarve  \nCampus de Gambelas, 8005-139 Faro, Portugal  \n[danielecorradetti@tecnico.ulisboa.pt](danielecorradetti@tecnico.ulisboa.pt)  \nAbstract  \nStatistical 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;  \nthe 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.  \nThe 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.  \n1 Introduction and Motivation  \nWhen Raymond Queneau published his Exercices de style in 1947, inspired by Bach’s Art of Fugue, he wrote the same trivial anecdote ninety-nine times. A man is jostled on a bus; two hours later a friend advises him to move a button on his overcoat. Nothing else happens. What varies is everything else: the register, the tense, the person, the alphabet, the sonnet form, the language of a mathematician. The content is held fixed by fiat, and the form is allowed to move as far as it can. Queneau took himself to be doing something intrinsically geometric, and named an early version of the work Dodécaèdre ; the intuition, as was argued in [4], is not casual at all.  \nEighty years later the same operation has acquired an adversarial use. Since 2 August 2026 the outputs of at least one major language model carry a machine-readable mark, in response to the transparency obligations of Article 50 of the European AI Act [1] . The published description of such marks is careful: the mark does not change meaning, quality or readability, it survives copying and light editing, and it is stated to be lost under paraphrase, heavy editing, translation and mixing with other text. Whoever wishes to remove the mark, then, is being invited to perform an Exercice de style. The question of how much of the mark survives such an exercise is the subject of this article.  \nPreprint.  \n\n| Family | Mechanism | Context h | Output law | What an edit destroys |\n| --- | --- | --- | --- | --- |\n| Green list [7] | logit bias | ≥ 1 | perturbed | token and its h predecessors |\n| Unigram [15] | logit bias | 0 | perturbed | the token alone |\n| Exponential [10, 2] | sampling rule | ≥ 0 | exact | token and seeding context |\n| Tournament [5] | sampling rule | ≥ 1 | exact | token and seeding context |\n| Semantic [6] | sentence partition | — | perturbed | the sentence embedding |\n\nTable 1: Synoptic table of the families of text watermarks. The last column is the one that matters for this article: in every family except the Unigram scheme, an edit damages not only the position it touches but every position t","cbCaimSIIE8BBWqS","https://ap.wps.com/l/cbCaimSIIE8BBWqS","pdf",397470,15,"English","# Abstract\n## Introduction and Motivation\n## The Landscape\n## Against These Constructions stands a Literature of Attacks\n## The Gap","[{\"question\":\"What is the main idea behind statistical watermarks in language models?\",\"answer\":\"They watermark text by restricting generation to a secret, key-dependent subset of tokens, so detection relies on the presence of tokens belonging to that subset.\"},{\"question\":\"Why does evaluating robustness only by endpoint semantic similarity fail?\",\"answer\":\"Because the paper proves the relevant invariant factorizes, and a holonomy component in the stabilizer of the initial state is invisible to the detector; thus endpoint-only statistics miss essential structure.\"},{\"question\":\"What does the detector residual identity show about edits?\",\"answer\":\"The residual statistic is proportional to the number of positions whose seeding window remains intact, leading directly to a decay law as an independent-edit corollary.\"}]","Linguistic Holonomy and Statistical Watermarks - Inner Geometry of Meaning-Preserving Transformations | PDF",38]