{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:V5T5HDJ6Q6PR42ZIFKZFH6Y5MM","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":"eb90770e2c9b3d8b988065a72ad6bb4cde44ffa7a7e36eb250f134aafff5ebe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T10:02:01Z","title_canon_sha256":"8bc8f3be2bfcfe6b929a80a331622000637fd53c6996f8826544ffab9f926f43"},"schema_version":"1.0","source":{"id":"1411.5814","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5814","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5814v2","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5814","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"V5T5HDJ6Q6PR","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"V5T5HDJ6Q6PR42ZI","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"V5T5HDJ6","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:ea2e0577671a8bac654385bdfc89024ac5b75381b5d4c0af8edaa04dbc7b2df6","target":"graph","created_at":"2026-05-18T02:32:21Z","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":"We study topological structures of the sets $(0,1/2)^3 \\cap \\Omega$ and $(0,1/2)^3 \\setminus \\Omega$, where~$\\Omega$ is one special algebraic surface defined by a symmetric polynomial in variables $a_1,a_2,a_3$ of degree~$12$. These problems arise in studying of general properties of degenerate singular points of dynamical systems obtained from the normalized Ricci flow on generalized Wallach spaces. Our main goal is to prove the connectedness of $(0,1/2)^3 \\cap \\Omega$ and to determine the number of connected components of $(0,1/2)^3 \\setminus \\Omega$.\n  Key words and phrases: Riemannian metr","authors_text":"N.A. Abiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T10:02:01Z","title":"On topological structure of some sets related to the normalized Ricci flow on generalized Wallach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5814","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:e03161e7aa6f918182a8e5404a49f0cdacb6d12b69c512f3540f799d11b91eff","target":"record","created_at":"2026-05-18T02:32:21Z","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":"eb90770e2c9b3d8b988065a72ad6bb4cde44ffa7a7e36eb250f134aafff5ebe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T10:02:01Z","title_canon_sha256":"8bc8f3be2bfcfe6b929a80a331622000637fd53c6996f8826544ffab9f926f43"},"schema_version":"1.0","source":{"id":"1411.5814","kind":"arxiv","version":2}},"canonical_sha256":"af67d38d3e879f1e6b282ab253fb1d6310355455916f677f2fef69866cc7c2d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af67d38d3e879f1e6b282ab253fb1d6310355455916f677f2fef69866cc7c2d9","first_computed_at":"2026-05-18T02:32:21.520474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:21.520474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XUcvex6okIgiao1Qmv5fZtKK+1wU2EmnkuBI96qwS35Lzmz3YTePWyAFY7aF+SFSplib0FwCgDyru3jHVct2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:21.520844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5814","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e03161e7aa6f918182a8e5404a49f0cdacb6d12b69c512f3540f799d11b91eff","sha256:ea2e0577671a8bac654385bdfc89024ac5b75381b5d4c0af8edaa04dbc7b2df6"],"state_sha256":"ee884333fbf9b68f73d07cead9664c2512307f997d05b19fa422f715f204c42c"}