{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LWH7X3DSWYMI4SCPLOAR3GPLPM","short_pith_number":"pith:LWH7X3DS","schema_version":"1.0","canonical_sha256":"5d8ffbec72b6188e484f5b811d99eb7b3cde84be1320491f020f17f2ae50aa91","source":{"kind":"arxiv","id":"1307.2542","version":2},"attestation_state":"computed","paper":{"title":"Calibrated and parallel structures on almost Abelian Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marco Freibert","submitted_at":"2013-07-09T19:08:14Z","abstract_excerpt":"In this article, we determine the seven-dimensional almost Abelian Lie algebras which admit calibrated or parallel G_2-/G_2^*-structures. Along the way, we show that certain well-established curvature restrictions for calibrated and parallel G_2-structures are not valid in the G_2^* case. In more detail, we provide the first example of a Ricci-flat calibrated G_2^*-structure on a compact manifold whose holonomy is not contained in G_2^*. Moreover, we get examples of non-flat parallel G_2^*-structures on almost Abelian Lie algebras g. We give a full classification of these G_2^*-structures if g"},"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":"1307.2542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-09T19:08:14Z","cross_cats_sorted":[],"title_canon_sha256":"3fc9b0afb75803fd678533a6238e4d0027111c9e12dfb4cae106f702e4b6a1be","abstract_canon_sha256":"fee84f514a289aee7324b1e935a36a2cf814ffe6e5099710987307fbb8bfd82e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:56.208748Z","signature_b64":"ZPEt3hELHUnCHEc5U1f/PC+/fBirx6W0oFAgugui3TFM7+c/aWQSnuK5FHRY8x6/NPKVgoldSS9pbH/BoYjMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d8ffbec72b6188e484f5b811d99eb7b3cde84be1320491f020f17f2ae50aa91","last_reissued_at":"2026-05-18T03:17:56.208248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:56.208248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Calibrated and parallel structures on almost Abelian Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marco Freibert","submitted_at":"2013-07-09T19:08:14Z","abstract_excerpt":"In this article, we determine the seven-dimensional almost Abelian Lie algebras which admit calibrated or parallel G_2-/G_2^*-structures. Along the way, we show that certain well-established curvature restrictions for calibrated and parallel G_2-structures are not valid in the G_2^* case. In more detail, we provide the first example of a Ricci-flat calibrated G_2^*-structure on a compact manifold whose holonomy is not contained in G_2^*. Moreover, we get examples of non-flat parallel G_2^*-structures on almost Abelian Lie algebras g. We give a full classification of these G_2^*-structures if g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2542","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":"1307.2542","created_at":"2026-05-18T03:17:56.208325+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2542v2","created_at":"2026-05-18T03:17:56.208325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2542","created_at":"2026-05-18T03:17:56.208325+00:00"},{"alias_kind":"pith_short_12","alias_value":"LWH7X3DSWYMI","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LWH7X3DSWYMI4SCP","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LWH7X3DS","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.11316","citing_title":"Torsion-free $H$-structures on almost Abelian solvmanifolds","ref_index":563,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM","json":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM.json","graph_json":"https://pith.science/api/pith-number/LWH7X3DSWYMI4SCPLOAR3GPLPM/graph.json","events_json":"https://pith.science/api/pith-number/LWH7X3DSWYMI4SCPLOAR3GPLPM/events.json","paper":"https://pith.science/paper/LWH7X3DS"},"agent_actions":{"view_html":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM","download_json":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM.json","view_paper":"https://pith.science/paper/LWH7X3DS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2542&json=true","fetch_graph":"https://pith.science/api/pith-number/LWH7X3DSWYMI4SCPLOAR3GPLPM/graph.json","fetch_events":"https://pith.science/api/pith-number/LWH7X3DSWYMI4SCPLOAR3GPLPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM/action/storage_attestation","attest_author":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM/action/author_attestation","sign_citation":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM/action/citation_signature","submit_replication":"https://pith.science/pith/LWH7X3DSWYMI4SCPLOAR3GPLPM/action/replication_record"}},"created_at":"2026-05-18T03:17:56.208325+00:00","updated_at":"2026-05-18T03:17:56.208325+00:00"}