{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WPO2GCGXUGARY3CGVJ46B4JMBJ","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":"36427c56664ae862a5a3057c2137f65a9b2a77676a87b5b1b062382869ff7e07","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-26T09:19:10Z","title_canon_sha256":"ae8deffb1e5101b2786bb26e69f50c0931a22745987949c12b0f9bfa21d0a4c6"},"schema_version":"1.0","source":{"id":"1804.09951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09951","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09951v2","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09951","created_at":"2026-05-18T00:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"WPO2GCGXUGAR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WPO2GCGXUGARY3CG","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WPO2GCGX","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:850bea891a2563a2dfa1f28c4cc7330d36142246ba561a3234899371c4126fc1","target":"graph","created_at":"2026-05-18T00:03:24Z","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 the notion of complex $G_2$ manifold $M_{\\mathbb C}$, and complexification of a $G_2$ manifold $M\\subset M_{\\mathbb C}$. As an application we show the following: If $(Y,s)$ is a closed oriented $3$-manifold with a $Spin^{c}$ structure, and $(Y,s)\\subset (M, \\varphi)$ is an imbedding as an associative submanifold of some $G_2$ manifold (such imbedding always exists), then the isotropic associative deformations of $Y$ in the complexified $G_2$ manifold $M_{\\mathbb C}$ is given by Seiberg-Witten equations.","authors_text":"Selman Akbulut, Ustun Yildirim","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-26T09:19:10Z","title":"Complex $G_2$-manifolds and Seiberg-Witten Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09951","kind":"arxiv","version":2},"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":"sha256:6429a9d427f4a671c1eba2988d249607aa9f03a25bafb173d82bc1f77e2f7200","target":"record","created_at":"2026-05-18T00:03:24Z","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":"36427c56664ae862a5a3057c2137f65a9b2a77676a87b5b1b062382869ff7e07","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-26T09:19:10Z","title_canon_sha256":"ae8deffb1e5101b2786bb26e69f50c0931a22745987949c12b0f9bfa21d0a4c6"},"schema_version":"1.0","source":{"id":"1804.09951","kind":"arxiv","version":2}},"canonical_sha256":"b3dda308d7a1811c6c46aa79e0f12c0a787ad104fd7156baeef2a2dce7ae8756","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3dda308d7a1811c6c46aa79e0f12c0a787ad104fd7156baeef2a2dce7ae8756","first_computed_at":"2026-05-18T00:03:24.527378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:24.527378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqjUkbyzmKOz9qPRF9NMJ8TQ1gHgfD9qHgzuvi4WOy1BNr3fzCKu3v5TADl/08I5/+ugkua9TObSIQqrWdqiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:24.527821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6429a9d427f4a671c1eba2988d249607aa9f03a25bafb173d82bc1f77e2f7200","sha256:850bea891a2563a2dfa1f28c4cc7330d36142246ba561a3234899371c4126fc1"],"state_sha256":"2b205181a0b46ad46d4b1891d8aabf70fb8a5afab42fc792e472aea8858aff59"}