{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:C43NWQH6FUBU2PK2EMAOHXO57U","short_pith_number":"pith:C43NWQH6","schema_version":"1.0","canonical_sha256":"1736db40fe2d034d3d5a2300e3ddddfd34f13fd93d60cdb589018ca60398818b","source":{"kind":"arxiv","id":"1503.08350","version":1},"attestation_state":"computed","paper":{"title":"Quaternionic Heisenberg groups as naturally reductive homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ana Cristina Ferreira, Ilka Agricola, Reinier Storm","submitted_at":"2015-03-28T21:06:33Z","abstract_excerpt":"In this note, we describe the geometry of the quaternionic Heisenberg groups from a Riemannian viewpoint. We show, in all dimensions, that they carry an almost $3$-contact metric structure which allows us to define the metric connection that equips these groups with the structure of a naturally reductive homogeneous space. It turns out that this connection, which we shall call the canonical connection because of its analogy to the $3$-Sasaki case, preserves the horizontal and vertical distributions and even the quaternionic contact structure of the quaternionic Heisenberg groups. We focus on t"},"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":"1503.08350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-28T21:06:33Z","cross_cats_sorted":[],"title_canon_sha256":"d70ea8afe7760d350cf331d2d2895518925086ba0d39bdb57f5baa148fb51d3e","abstract_canon_sha256":"719279f5b8976e2bd2b154a3886eede839aefc0494952be33754b8e579e28b22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:02.550497Z","signature_b64":"hL5qgho58RC6cS9qcipEhA72qKJjc0utZXr3n62IOM9YMv8LdVZkwUlId7ahjuPZQRhrWBdO4Ol7gu/99p9FAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1736db40fe2d034d3d5a2300e3ddddfd34f13fd93d60cdb589018ca60398818b","last_reissued_at":"2026-05-18T01:29:02.549956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:02.549956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quaternionic Heisenberg groups as naturally reductive homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ana Cristina Ferreira, Ilka Agricola, Reinier Storm","submitted_at":"2015-03-28T21:06:33Z","abstract_excerpt":"In this note, we describe the geometry of the quaternionic Heisenberg groups from a Riemannian viewpoint. We show, in all dimensions, that they carry an almost $3$-contact metric structure which allows us to define the metric connection that equips these groups with the structure of a naturally reductive homogeneous space. It turns out that this connection, which we shall call the canonical connection because of its analogy to the $3$-Sasaki case, preserves the horizontal and vertical distributions and even the quaternionic contact structure of the quaternionic Heisenberg groups. We focus on t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08350","kind":"arxiv","version":1},"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":"1503.08350","created_at":"2026-05-18T01:29:02.550024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08350v1","created_at":"2026-05-18T01:29:02.550024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08350","created_at":"2026-05-18T01:29:02.550024+00:00"},{"alias_kind":"pith_short_12","alias_value":"C43NWQH6FUBU","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C43NWQH6FUBU2PK2","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C43NWQH6","created_at":"2026-05-18T12:29:14.074870+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/C43NWQH6FUBU2PK2EMAOHXO57U","json":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U.json","graph_json":"https://pith.science/api/pith-number/C43NWQH6FUBU2PK2EMAOHXO57U/graph.json","events_json":"https://pith.science/api/pith-number/C43NWQH6FUBU2PK2EMAOHXO57U/events.json","paper":"https://pith.science/paper/C43NWQH6"},"agent_actions":{"view_html":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U","download_json":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U.json","view_paper":"https://pith.science/paper/C43NWQH6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08350&json=true","fetch_graph":"https://pith.science/api/pith-number/C43NWQH6FUBU2PK2EMAOHXO57U/graph.json","fetch_events":"https://pith.science/api/pith-number/C43NWQH6FUBU2PK2EMAOHXO57U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U/action/storage_attestation","attest_author":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U/action/author_attestation","sign_citation":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U/action/citation_signature","submit_replication":"https://pith.science/pith/C43NWQH6FUBU2PK2EMAOHXO57U/action/replication_record"}},"created_at":"2026-05-18T01:29:02.550024+00:00","updated_at":"2026-05-18T01:29:02.550024+00:00"}