{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:WIKARWATZZQMLFZO5YBYBDBNRU","short_pith_number":"pith:WIKARWAT","schema_version":"1.0","canonical_sha256":"b21408d813ce60c5972eee03808c2d8d2f149efaa864ed6f0b0664504071065a","source":{"kind":"arxiv","id":"math/0305124","version":5},"attestation_state":"computed","paper":{"title":"Some remarks on G_2-structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Robert L. Bryant","submitted_at":"2003-05-08T15:07:28Z","abstract_excerpt":"This article consists of some loosely related remarks about the geometry of G_2-structures on 7-manifolds and is partly based on old unpublished joint work with two other people: F. Reese Harvey and Steven Altschuler. Much of this work has since been subsumed in the work of Hitchin \\cite{MR02m:53070} and Joyce \\cite{MR01k:53093}. I am making it available now mainly because of interest expressed by others in seeing these results written up since they do not seem to have all made it into the literature.\n  A formula is derived for the scalar curvature and Ricci curvature of a G_2-structure in ter"},"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":"math/0305124","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2003-05-08T15:07:28Z","cross_cats_sorted":[],"title_canon_sha256":"04e4964f05e25bc0eeba06e18c99a475ff5c7bf85f365e65a090bbb8b5192bd0","abstract_canon_sha256":"9372be1b22726a4f576487279bef1b4ff0a52f6cd7837952062df828d3833a78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:18:05.622649Z","signature_b64":"8BhJavMeDS/qJriTs5zTKCRL+fE4dRf3GgHmo61nAcfk6gMqIqSv4Qao5/6sr0U4+QWS3X0h6mwlVTNpb85MAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b21408d813ce60c5972eee03808c2d8d2f149efaa864ed6f0b0664504071065a","last_reissued_at":"2026-07-05T10:18:05.622157Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:18:05.622157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some remarks on G_2-structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Robert L. Bryant","submitted_at":"2003-05-08T15:07:28Z","abstract_excerpt":"This article consists of some loosely related remarks about the geometry of G_2-structures on 7-manifolds and is partly based on old unpublished joint work with two other people: F. Reese Harvey and Steven Altschuler. Much of this work has since been subsumed in the work of Hitchin \\cite{MR02m:53070} and Joyce \\cite{MR01k:53093}. I am making it available now mainly because of interest expressed by others in seeing these results written up since they do not seem to have all made it into the literature.\n  A formula is derived for the scalar curvature and Ricci curvature of a G_2-structure in ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305124","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0305124/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0305124","created_at":"2026-07-05T10:18:05.622222+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0305124v5","created_at":"2026-07-05T10:18:05.622222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305124","created_at":"2026-07-05T10:18:05.622222+00:00"},{"alias_kind":"pith_short_12","alias_value":"WIKARWATZZQM","created_at":"2026-07-05T10:18:05.622222+00:00"},{"alias_kind":"pith_short_16","alias_value":"WIKARWATZZQMLFZO","created_at":"2026-07-05T10:18:05.622222+00:00"},{"alias_kind":"pith_short_8","alias_value":"WIKARWAT","created_at":"2026-07-05T10:18:05.622222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2403.16661","citing_title":"Dynamics of Cayley Forms","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2405.15408","citing_title":"Four-dimensional Riemannian geometry via 2-forms","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06800","citing_title":"$G_2$ flux compactifications","ref_index":27,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU","json":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU.json","graph_json":"https://pith.science/api/pith-number/WIKARWATZZQMLFZO5YBYBDBNRU/graph.json","events_json":"https://pith.science/api/pith-number/WIKARWATZZQMLFZO5YBYBDBNRU/events.json","paper":"https://pith.science/paper/WIKARWAT"},"agent_actions":{"view_html":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU","download_json":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU.json","view_paper":"https://pith.science/paper/WIKARWAT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0305124&json=true","fetch_graph":"https://pith.science/api/pith-number/WIKARWATZZQMLFZO5YBYBDBNRU/graph.json","fetch_events":"https://pith.science/api/pith-number/WIKARWATZZQMLFZO5YBYBDBNRU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU/action/storage_attestation","attest_author":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU/action/author_attestation","sign_citation":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU/action/citation_signature","submit_replication":"https://pith.science/pith/WIKARWATZZQMLFZO5YBYBDBNRU/action/replication_record"}},"created_at":"2026-07-05T10:18:05.622222+00:00","updated_at":"2026-07-05T10:18:05.622222+00:00"}