{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7J6ETJL5B6TNA4CTN2G2EYFKDS","short_pith_number":"pith:7J6ETJL5","schema_version":"1.0","canonical_sha256":"fa7c49a57d0fa6d070536e8da260aa1cb2b86530481f05e8005e3e6d29aa31cf","source":{"kind":"arxiv","id":"1410.7903","version":2},"attestation_state":"computed","paper":{"title":"Half-flat structures inducing Einstein metrics on homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alberto Raffero","submitted_at":"2014-10-29T08:49:27Z","abstract_excerpt":"In this paper, we consider half-flat $SU(3)$-structures and the subclasses of coupled and double structures. In the general case we show that the intrinsic torsion form $w_1^-$ is constant in each of the two subclasses. We then consider the problem of finding half-flat structures inducing Einstein metrics on homogeneous spaces. We give an example of a left invariant half-flat (non coupled and non double) structure inducing an Einstein metric on $S^3\\times S^3$ and we show there does not exist any left invariant coupled structure inducing an ${\\rm Ad}(S^1)$-invariant Einstein metric on it. Fina"},"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":"1410.7903","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T08:49:27Z","cross_cats_sorted":[],"title_canon_sha256":"ddc3197e8129eb49924e7d6392c30e4e71d2d6b85b4f99dd70da9850abd47519","abstract_canon_sha256":"e977b045a1ebb1e88a6b4a9cd442f21f729d0a8fc05fbb1035059515c624a76a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:16.579064Z","signature_b64":"uSWRS3wYy32Ad+BKYnVE+wBF8AFC4ATbWE/aJNMg5LCx4x+g6tqIgGYBnJxS0Ayl70KLXY4MCWhmwwKPNR9FCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa7c49a57d0fa6d070536e8da260aa1cb2b86530481f05e8005e3e6d29aa31cf","last_reissued_at":"2026-05-18T02:19:16.578348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:16.578348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Half-flat structures inducing Einstein metrics on homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alberto Raffero","submitted_at":"2014-10-29T08:49:27Z","abstract_excerpt":"In this paper, we consider half-flat $SU(3)$-structures and the subclasses of coupled and double structures. In the general case we show that the intrinsic torsion form $w_1^-$ is constant in each of the two subclasses. We then consider the problem of finding half-flat structures inducing Einstein metrics on homogeneous spaces. We give an example of a left invariant half-flat (non coupled and non double) structure inducing an Einstein metric on $S^3\\times S^3$ and we show there does not exist any left invariant coupled structure inducing an ${\\rm Ad}(S^1)$-invariant Einstein metric on it. Fina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7903","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.7903","created_at":"2026-05-18T02:19:16.578452+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.7903v2","created_at":"2026-05-18T02:19:16.578452+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7903","created_at":"2026-05-18T02:19:16.578452+00:00"},{"alias_kind":"pith_short_12","alias_value":"7J6ETJL5B6TN","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"7J6ETJL5B6TNA4CT","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"7J6ETJL5","created_at":"2026-05-18T12:28:19.803747+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/7J6ETJL5B6TNA4CTN2G2EYFKDS","json":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS.json","graph_json":"https://pith.science/api/pith-number/7J6ETJL5B6TNA4CTN2G2EYFKDS/graph.json","events_json":"https://pith.science/api/pith-number/7J6ETJL5B6TNA4CTN2G2EYFKDS/events.json","paper":"https://pith.science/paper/7J6ETJL5"},"agent_actions":{"view_html":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS","download_json":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS.json","view_paper":"https://pith.science/paper/7J6ETJL5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.7903&json=true","fetch_graph":"https://pith.science/api/pith-number/7J6ETJL5B6TNA4CTN2G2EYFKDS/graph.json","fetch_events":"https://pith.science/api/pith-number/7J6ETJL5B6TNA4CTN2G2EYFKDS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS/action/storage_attestation","attest_author":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS/action/author_attestation","sign_citation":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS/action/citation_signature","submit_replication":"https://pith.science/pith/7J6ETJL5B6TNA4CTN2G2EYFKDS/action/replication_record"}},"created_at":"2026-05-18T02:19:16.578452+00:00","updated_at":"2026-05-18T02:19:16.578452+00:00"}