{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:G25WVGMAHAETQP7J45V5J6U5PN","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":"3017d2107575081bd5e5d7f82107509cf798beedf572370666e0b124b8e873f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-15T18:54:38Z","title_canon_sha256":"51f6d05db98aac8eba1c656fa9fcc745727000b8c3f9b0480db2be33fa6cee07"},"schema_version":"1.0","source":{"id":"1904.07288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.07288","created_at":"2026-05-17T23:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1904.07288v1","created_at":"2026-05-17T23:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07288","created_at":"2026-05-17T23:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"G25WVGMAHAET","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"G25WVGMAHAETQP7J","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"G25WVGMA","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:4795f45cacdb2bdde6248d7f920b73e81ac4f62891fd85499cbc75ba14ef65c4","target":"graph","created_at":"2026-05-17T23:48:29Z","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 consider solvable hypersurfaces of the form $N \\exp(\\R H)$ with induced metrics in the symmetric space $M = SL(3,\\C)/SU(3)$, where $H$ a suitable unit length vector in the subgroup $A$ of the Iwasawa decomposition $SL(3,\\C) = NAK$. Since $M$ is rank $2$, $A$ is $2$-dimensional and we can parametrize these hypersurfaces via an angle $\\alpha \\in [0,\\pi/2]$ determining the direction of $H$. We show that one of the hypersurfaces (corresponding to $\\alpha = 0$) is minimally embedded and isometric to the non-symmetric $7$-dimensional Damek-Ricci space. We also provide an explicit ","authors_text":"Gerhard Knieper, John R. Parker, Norbert Peyerimhoff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-15T18:54:38Z","title":"Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07288","kind":"arxiv","version":1},"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:c8c0ca5138bf67e07b83a02db693529a1fdd075030f580b892c1d8cc4cdd5d3f","target":"record","created_at":"2026-05-17T23:48:29Z","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":"3017d2107575081bd5e5d7f82107509cf798beedf572370666e0b124b8e873f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-15T18:54:38Z","title_canon_sha256":"51f6d05db98aac8eba1c656fa9fcc745727000b8c3f9b0480db2be33fa6cee07"},"schema_version":"1.0","source":{"id":"1904.07288","kind":"arxiv","version":1}},"canonical_sha256":"36bb6a99803809383fe9e76bd4fa9d7b72d77eed4e4f275302987c5160180e2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36bb6a99803809383fe9e76bd4fa9d7b72d77eed4e4f275302987c5160180e2c","first_computed_at":"2026-05-17T23:48:29.063493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:29.063493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BvtgzbHDixUGQ33CDuxqoT3M7LBfm14CMSNSyw3M8tLg2IWDQLyjG9zZz4DftwVmt25ZEAJ5/yckhErC6tNkDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:29.064068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.07288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8c0ca5138bf67e07b83a02db693529a1fdd075030f580b892c1d8cc4cdd5d3f","sha256:4795f45cacdb2bdde6248d7f920b73e81ac4f62891fd85499cbc75ba14ef65c4"],"state_sha256":"ce881780d764c1046e4364e051673d479e0705e3b34845cf1c2114002b8d1986"}