{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O3YM6NZJGX5QNETLOAWN4KZXP5","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":"dcbc0e9731a39f70051d1c2c40e96e2d4698a550d5e63985687c06db54a7d737","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-02T11:24:39Z","title_canon_sha256":"c555e9eb7326355ccc6b7bac97341066d2ff433c4c40d47d4c057c69b6756e60"},"schema_version":"1.0","source":{"id":"1407.0523","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0523","created_at":"2026-05-18T02:47:15Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0523v2","created_at":"2026-05-18T02:47:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0523","created_at":"2026-05-18T02:47:15Z"},{"alias_kind":"pith_short_12","alias_value":"O3YM6NZJGX5Q","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O3YM6NZJGX5QNETL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O3YM6NZJ","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:3d6116c1faf0699da5140f78d94b7a503e880d1050ca04dfe8fdd2615915a36c","target":"graph","created_at":"2026-05-18T02:47:15Z","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":"Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric which is in some way far from being biinvariant, in a sense made explicit in terms of Tricerri and Vanhecke's homogeneous structures. The semisimple and solvable cases are studied. We extend to the general case, Kowalski-Tricerri's and Bieszk's classifications of connected and simply-connected unimodular cyclic metric Lie groups for dimensions less than or equal to five.","authors_text":"Jose Antonio Oubina, Jose Carmelo Gonzalez-Davila, P. M. Gadea","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-02T11:24:39Z","title":"Cyclic metric Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0523","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":"sha256:4b415685601735c5cffda6c2214caf05b8ea0bc07bda03cd6d3a9e660ffe1448","target":"record","created_at":"2026-05-18T02:47:15Z","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":"dcbc0e9731a39f70051d1c2c40e96e2d4698a550d5e63985687c06db54a7d737","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-02T11:24:39Z","title_canon_sha256":"c555e9eb7326355ccc6b7bac97341066d2ff433c4c40d47d4c057c69b6756e60"},"schema_version":"1.0","source":{"id":"1407.0523","kind":"arxiv","version":2}},"canonical_sha256":"76f0cf372935fb06926b702cde2b377f603d273b4ef5180062e0d731de2dd7e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76f0cf372935fb06926b702cde2b377f603d273b4ef5180062e0d731de2dd7e7","first_computed_at":"2026-05-18T02:47:15.136088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:15.136088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AMpA0LhT27kvbO/9kAIbU4NDh2pkN6U+LH9CBDgPr8KumTtSqVkbqOJdTcWcx3i4noKAHRHhANm027c8PV4eDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:15.136695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0523","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b415685601735c5cffda6c2214caf05b8ea0bc07bda03cd6d3a9e660ffe1448","sha256:3d6116c1faf0699da5140f78d94b7a503e880d1050ca04dfe8fdd2615915a36c"],"state_sha256":"dcad4c27c495253811a95acb473b1f6d36922299ab750c240d7ee4cad2216cf1"}