{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OPSCPBV5KLPWPRJ6QSXBYHKBJX","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":"557b3bcf0f4313332754fbcfa8e95193224b32ceb428887d2a4adb23628e6f05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-12-17T15:21:24Z","title_canon_sha256":"9e5396d2710ae9320113a8d95d124ecc988cc8af1a1986f91a70a56d38a1a3b3"},"schema_version":"1.0","source":{"id":"1412.5433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5433","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5433v1","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5433","created_at":"2026-05-18T02:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"OPSCPBV5KLPW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OPSCPBV5KLPWPRJ6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OPSCPBV5","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:edd6037cd19bb659ad1f6a3e3ae8a2ba61bc9b3ce953b13d3544ada1fcf6bc0a","target":"graph","created_at":"2026-05-18T02:31:03Z","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":"For a branched locally isometric covering of metric spaces with intrinsic metrics, it is proved that the Steiner ratio of the base is not less than the Steiner ratio of the total space of the covering. As applications, it is shown that the Steiner ratio of the surface of an isosceles tetrahedron is equal to the Steiner ratio of the Euclidean plane, and that the Steiner ratio of a flat cone with angle of $2\\pi/k$ at its vertex is also equal to the Steiner ratio of the Euclidean plane.","authors_text":"Alexandr Ivanov, Alexey Tuzhilin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-12-17T15:21:24Z","title":"Branched Coverings and Steiner Ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5433","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:cdde3dfda4154f536419f3f29440c98dad8d41ba4a6fde79223744f5c199f917","target":"record","created_at":"2026-05-18T02:31:03Z","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":"557b3bcf0f4313332754fbcfa8e95193224b32ceb428887d2a4adb23628e6f05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-12-17T15:21:24Z","title_canon_sha256":"9e5396d2710ae9320113a8d95d124ecc988cc8af1a1986f91a70a56d38a1a3b3"},"schema_version":"1.0","source":{"id":"1412.5433","kind":"arxiv","version":1}},"canonical_sha256":"73e42786bd52df67c53e84ae1c1d414df1e90b802feea411b9e413be8bbdfd2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73e42786bd52df67c53e84ae1c1d414df1e90b802feea411b9e413be8bbdfd2b","first_computed_at":"2026-05-18T02:31:03.002336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:03.002336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQfgLGrJ8OAMQdqFvrhxTR3WDYizSp/Wc+v17SXIGDm7FZ5Wk9teTxiYDjvVYUxMb73Chy+IzgXRkSfTe+g4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:03.002729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdde3dfda4154f536419f3f29440c98dad8d41ba4a6fde79223744f5c199f917","sha256:edd6037cd19bb659ad1f6a3e3ae8a2ba61bc9b3ce953b13d3544ada1fcf6bc0a"],"state_sha256":"55956e0ead41b2610554fcf7c71d8905f84cc708dc6eabb987d9faa55ab39d86"}