{"paper":{"title":"The geometry-first formulation of gauge theory is not equivalent to the symmetry-first one","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"physics.hist-ph","authors_text":"Henrique Gomes","submitted_at":"2026-07-27T16:56:47Z","abstract_excerpt":"This paper argues that the geometry-first and symmetry-first formulations of gauge theory are not equivalent. They differ in three respects. First, the geometry-first formulation---in which gauge groups arise as automorphism groups of structured fundamental vector bundles---admits fewer theories when its generating structures are restricted to finite tensorial data. Charged theories with additive structure group $\\mathbb{R}$ have no such presentation. Second, even when a symmetry-first theory has a geometry-first presentation, its principal bundle and matter bundles do not determine which stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24901","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/2607.24901/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"}