{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2SV5LYM5HQPDYAEBZ22IZIH4JK","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":"c62bf636c74da9e4b0581afab181f4af76453b56759760d19d9cca58131e79fc","cross_cats_sorted":["math.CO","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-10T00:37:06Z","title_canon_sha256":"5d203144d08bef543cfbd719f788aa2e9ead3aa0f4454ac0aef2e25e33f4cafc"},"schema_version":"1.0","source":{"id":"1803.03728","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03728","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03728v3","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03728","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"2SV5LYM5HQPD","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2SV5LYM5HQPDYAEB","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2SV5LYM5","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:bc75532d1c2d3351c90d3004619ae8f8e24f64501c4c7199046eda0c564cccbf","target":"graph","created_at":"2026-05-17T23:53:06Z","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 prove that a geodesic net with three boundary (= unbalanced) vertices on a non-positively curved plane has at most one balanced vertex. We do not assume any a priori bound for the degrees of unbalanced vertices. The result seems to be new even in the Euclidean case. We demonstrate by examples that the result is not true for metrics of positive curvature on the plane, and that there are no immediate generalizations of this result for geodesic nets with four unbalanced vertices.","authors_text":"Fabian Parsch","cross_cats":["math.CO","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-10T00:37:06Z","title":"Geodesic nets with three boundary vertices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03728","kind":"arxiv","version":3},"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":"sha256:1da763226e46de55137f475ce91017e3fd4ef4f3c35762a8dd964abfb471d293","target":"record","created_at":"2026-05-17T23:53:06Z","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":"c62bf636c74da9e4b0581afab181f4af76453b56759760d19d9cca58131e79fc","cross_cats_sorted":["math.CO","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-10T00:37:06Z","title_canon_sha256":"5d203144d08bef543cfbd719f788aa2e9ead3aa0f4454ac0aef2e25e33f4cafc"},"schema_version":"1.0","source":{"id":"1803.03728","kind":"arxiv","version":3}},"canonical_sha256":"d4abd5e19d3c1e3c0081ceb48ca0fc4aa369d8c25ca7ca814ba4dfcd796746e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4abd5e19d3c1e3c0081ceb48ca0fc4aa369d8c25ca7ca814ba4dfcd796746e4","first_computed_at":"2026-05-17T23:53:06.660157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:06.660157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OGVfM7Ecv1j/oC5bbCsDqdlid8sc45muYMUeBdlJ4Y07pIUkUVgBLHlWILbFL9l0UX+4AmLUuvRgKKMrx75mCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:06.660676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03728","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1da763226e46de55137f475ce91017e3fd4ef4f3c35762a8dd964abfb471d293","sha256:bc75532d1c2d3351c90d3004619ae8f8e24f64501c4c7199046eda0c564cccbf"],"state_sha256":"3a0c927907ae2cdeb43bde124708bc3e58420493cd04cedbde2c04c9b6ec6482"}