{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YYVMZ6XFE4GYTJ6RGZ7CMYQTD5","short_pith_number":"pith:YYVMZ6XF","schema_version":"1.0","canonical_sha256":"c62accfae5270d89a7d1367e2662131f44ce2830f99ef8e7c5a583945e7e760e","source":{"kind":"arxiv","id":"2606.29659","version":1},"attestation_state":"computed","paper":{"title":"Integral Gauss formula and the Poisson equation for the $G_2$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Artem Pulemotov, Stepan Hudecek, Timothy Buttsworth","submitted_at":"2026-06-28T23:59:54Z","abstract_excerpt":"We produce a formula, analogous to the Gauss-Codazzi equation, which relates the geometry of a $G_2$-structure and its Hodge Laplacian to the geometry of the induced $SU(3)$-structure on an embedded hypersurface. As an application, we obtain necessary conditions for the solvability of the Poisson equation for (not necessarily closed) $G_2$-structures in a neighbourhood of this hypersurface. Next, we prove that our conditions are sufficient in the cohomogeneity one setting, assuming the symmetry group is compact and simple."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.29659","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-06-28T23:59:54Z","cross_cats_sorted":[],"title_canon_sha256":"9b45e4a059bd9ab02c9c003476e68eb4fe6117096e55ee9ffc1ca6e393030c7d","abstract_canon_sha256":"688513a583468af130ff8d85fa1001f2e8afd22ae83d532f323104e72a3978ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:29.248104Z","signature_b64":"7XUqhuehibJ5sSVr2Q/4Ni6065sSfOWtvmx5REP9tHm3ExVr5YbCfAC7xS2r1R9p+/ylrt6BfohQtHgMGwg+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c62accfae5270d89a7d1367e2662131f44ce2830f99ef8e7c5a583945e7e760e","last_reissued_at":"2026-06-30T02:17:29.247552Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:29.247552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integral Gauss formula and the Poisson equation for the $G_2$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Artem Pulemotov, Stepan Hudecek, Timothy Buttsworth","submitted_at":"2026-06-28T23:59:54Z","abstract_excerpt":"We produce a formula, analogous to the Gauss-Codazzi equation, which relates the geometry of a $G_2$-structure and its Hodge Laplacian to the geometry of the induced $SU(3)$-structure on an embedded hypersurface. As an application, we obtain necessary conditions for the solvability of the Poisson equation for (not necessarily closed) $G_2$-structures in a neighbourhood of this hypersurface. Next, we prove that our conditions are sufficient in the cohomogeneity one setting, assuming the symmetry group is compact and simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29659","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/2606.29659/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.29659","created_at":"2026-06-30T02:17:29.247637+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29659v1","created_at":"2026-06-30T02:17:29.247637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29659","created_at":"2026-06-30T02:17:29.247637+00:00"},{"alias_kind":"pith_short_12","alias_value":"YYVMZ6XFE4GY","created_at":"2026-06-30T02:17:29.247637+00:00"},{"alias_kind":"pith_short_16","alias_value":"YYVMZ6XFE4GYTJ6R","created_at":"2026-06-30T02:17:29.247637+00:00"},{"alias_kind":"pith_short_8","alias_value":"YYVMZ6XF","created_at":"2026-06-30T02:17:29.247637+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5","json":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5.json","graph_json":"https://pith.science/api/pith-number/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/graph.json","events_json":"https://pith.science/api/pith-number/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/events.json","paper":"https://pith.science/paper/YYVMZ6XF"},"agent_actions":{"view_html":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5","download_json":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5.json","view_paper":"https://pith.science/paper/YYVMZ6XF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29659&json=true","fetch_graph":"https://pith.science/api/pith-number/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/graph.json","fetch_events":"https://pith.science/api/pith-number/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/action/storage_attestation","attest_author":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/action/author_attestation","sign_citation":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/action/citation_signature","submit_replication":"https://pith.science/pith/YYVMZ6XFE4GYTJ6RGZ7CMYQTD5/action/replication_record"}},"created_at":"2026-06-30T02:17:29.247637+00:00","updated_at":"2026-06-30T02:17:29.247637+00:00"}