{"paper":{"title":"Cyclic source pairings for Penrose--Sparling non-Hausdorff twistor spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.RT"],"primary_cat":"math.DG","authors_text":"Ioannis P. Zois","submitted_at":"2026-06-02T09:41:00Z","abstract_excerpt":"We introduce noncommutative geometry techniques in order to reinterpret the Penrose--Sparling non-Hausdorff twistor space of the anti-self-dual Coulomb field by means of an explicit etale gluing groupoid and its convolution algebra.\n  This algebraic model keeps track of both the identified open part and the two non-separated copies of the source quadric.\n  We compute two kinds of Chern--Connes pairings. The strict tangent-module analogue, obtained from \\([T_{\\mathbb R}\\CP^3\\otimes\\C]\\), vanishes because \\[ \\operatorname{ch}_3(T^{1,0}\\CP^3)+ \\operatorname{ch}_3(T^{0,1}\\CP^3)=0. \\] By contrast, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04054","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/2606.04054/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"}