{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GCV2JSPSBWJN5YQMW2KL3Q4XEM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a81f26361c4b04efa30d75d84b9c5adb4a52c592e549d95688b890f45c60b9ad","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-11T00:41:21Z","title_canon_sha256":"af61a713af5f31b9b630ec3af27075a2c1534dfd538d5e1f19a7794a219f082b"},"schema_version":"1.0","source":{"id":"1212.2261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2261","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2261v1","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2261","created_at":"2026-05-18T03:38:45Z"},{"alias_kind":"pith_short_12","alias_value":"GCV2JSPSBWJN","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GCV2JSPSBWJN5YQM","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GCV2JSPS","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:cb34461a032dab150325cfa541edcc5d77909ef01a976816cd21db065bd3cdc9","target":"graph","created_at":"2026-05-18T03:38:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce coG_2-vector fields, coRochesterian 2-forms and coRochesterian vector fields on manifolds with a coclosed G_2-structure as a continuous of work from [15], and we show that the spaces of coG_2-vector fields and of coRochesterian vector fields are Lie subalgebras of the Lie algebra of vector fields with the standard Lie bracket. We also define a bracket operation on the space of coRochesterian 2-forms associated to the space of coRochesterian vector fields and prove, despite the lack of a Jacobi identity, a relationship between this bracket and so-called coG_2-morphisms.","authors_text":"Albert J. Todd, Sema Salur","cross_cats":["hep-th","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-11T00:41:21Z","title":"Diffeomorphisms of 7-Manifolds with Coclosed G_2-Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2261","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:abd1c1519a659f11376e29cef9a616f154cad99471363cd8651ec5236a354c3e","target":"record","created_at":"2026-05-18T03:38:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a81f26361c4b04efa30d75d84b9c5adb4a52c592e549d95688b890f45c60b9ad","cross_cats_sorted":["hep-th","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-12-11T00:41:21Z","title_canon_sha256":"af61a713af5f31b9b630ec3af27075a2c1534dfd538d5e1f19a7794a219f082b"},"schema_version":"1.0","source":{"id":"1212.2261","kind":"arxiv","version":1}},"canonical_sha256":"30aba4c9f20d92dee20cb694bdc3972330afd65d8179892ad650368c75d4f8e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30aba4c9f20d92dee20cb694bdc3972330afd65d8179892ad650368c75d4f8e9","first_computed_at":"2026-05-18T03:38:45.483996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:45.483996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G4acUjRw38zdcIWMN0mf5R0HdrrKGrKQ1gdNwooP0lTnqHYQZE/Wo2iCdVSnF8WIp6gDZ+/785UokiQjGoa2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:45.484836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abd1c1519a659f11376e29cef9a616f154cad99471363cd8651ec5236a354c3e","sha256:cb34461a032dab150325cfa541edcc5d77909ef01a976816cd21db065bd3cdc9"],"state_sha256":"8d1c9eb8131e513e0ef7ecc23f4af302386bc7aded3040871dc5aae05679f0b7"}