{"paper":{"title":"Specific PDEs for Preserved Quantities in Geometry. I. Similarities and Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Edward Anderson","submitted_at":"2018-09-06T15:30:23Z","abstract_excerpt":"We provide specific PDEs for preserved quantities $Q$ in Geometry, as well as a bridge between this and specific PDEs for observables $O$ in Physics. We furthermore prove versions of four other theorems either side of this bridge: the below enumerated sentences. For the generic geometry - in the sense of it possessing no generalized Killing vectors, i.e.\\ continuous geometrical automorphisms - the $P$ form a smooth space of free functions over said geometry. If a geometry possesses the corresponding type of Killing vectors, the $P$ must Lie-brackets commute with `sums-over-points of the automo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02045","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}