{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LWH7X3DSWYMI4SCPLOAR3GPLPM","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":"fee84f514a289aee7324b1e935a36a2cf814ffe6e5099710987307fbb8bfd82e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-09T19:08:14Z","title_canon_sha256":"3fc9b0afb75803fd678533a6238e4d0027111c9e12dfb4cae106f702e4b6a1be"},"schema_version":"1.0","source":{"id":"1307.2542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2542","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2542v2","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2542","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"LWH7X3DSWYMI","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LWH7X3DSWYMI4SCP","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LWH7X3DS","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:74a6b883ef53885e49bd0e658e440a3c7edb739a0aca6f26a09e7df2f903198e","target":"graph","created_at":"2026-05-18T03:17:56Z","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":"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","authors_text":"Marco Freibert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-09T19:08:14Z","title":"Calibrated and parallel structures on almost Abelian Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2542","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":"sha256:01f326958946f5a669e0708611d3025be75c9d051039ec682835f558140092e6","target":"record","created_at":"2026-05-18T03:17:56Z","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":"fee84f514a289aee7324b1e935a36a2cf814ffe6e5099710987307fbb8bfd82e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-09T19:08:14Z","title_canon_sha256":"3fc9b0afb75803fd678533a6238e4d0027111c9e12dfb4cae106f702e4b6a1be"},"schema_version":"1.0","source":{"id":"1307.2542","kind":"arxiv","version":2}},"canonical_sha256":"5d8ffbec72b6188e484f5b811d99eb7b3cde84be1320491f020f17f2ae50aa91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d8ffbec72b6188e484f5b811d99eb7b3cde84be1320491f020f17f2ae50aa91","first_computed_at":"2026-05-18T03:17:56.208248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:56.208248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZPEt3hELHUnCHEc5U1f/PC+/fBirx6W0oFAgugui3TFM7+c/aWQSnuK5FHRY8x6/NPKVgoldSS9pbH/BoYjMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:56.208748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01f326958946f5a669e0708611d3025be75c9d051039ec682835f558140092e6","sha256:74a6b883ef53885e49bd0e658e440a3c7edb739a0aca6f26a09e7df2f903198e"],"state_sha256":"020b30788d882cc43a865d47e6ee84b372f04e17985bf593e55c5effcb482191"}