{"paper":{"title":"Adelic Loop Groups and Perfectoid Analogies: Factorization and Holomorphic Bundles on the Adelic Projective Line","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Alberto Verjovsky","submitted_at":"2026-07-11T19:11:03Z","abstract_excerpt":"We develop a theory of adelic loop groups on the universal one-dimensional solenoid (S^1_{\\mathbb Q}=(\\mathbb R\\times\\widehat{\\mathbb Z})/\\mathbb Z_{\\mathrm{diag}}), the compact abelian group whose Pontryagin dual is (\\mathbb Q) rather than (\\mathbb Z). We introduce the adelic projective line (\\mathbb{CP}^1_{\\mathbb Q}), its ring of Laurent--Puiseux series, and holomorphic vector bundles defined by solenoidal clutching data. We prove that its Picard group is naturally isomorphic to the additive group (\\mathbb Q).\n  The paper establishes a scalar Wiener--Birkhoff factorization theorem, a matrix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10447","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10447/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}