{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MIK3S5UOWAWHPDVSIXTYUKUOHL","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":"bb215f2c5ea4000ef19bd07e19e11284980005fdd26862ab5ef537049776adc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-12T09:39:01Z","title_canon_sha256":"5f4e05ae366b98fa35c76fba989cfd85972296512606d118d0c440b22c635645"},"schema_version":"1.0","source":{"id":"1705.04484","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04484","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04484v1","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04484","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"MIK3S5UOWAWH","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MIK3S5UOWAWHPDVS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MIK3S5UO","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:9ad5465db36e475b94c8c780d86c729684a073bb9003113f52cea0709a70a811","target":"graph","created_at":"2026-05-18T00:44:37Z","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":"Following Escobar [Esc97] and Jammes [Jam15], we introduce two types of isoperimetric constants and give lower bound estimates for the first nontrivial eigenvalues of Dirichlet-to-Neumann operators on finite graphs with boundary respectively.","authors_text":"Bobo Hua, Yan Huang, Zuoqin Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-12T09:39:01Z","title":"First eigenvalue estimates of Dirichlet-to-Neumann operators on graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04484","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:e2560d099d6b25874b7f4d059c7318b0ea6e4fa259a47407436217eac6202aab","target":"record","created_at":"2026-05-18T00:44:37Z","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":"bb215f2c5ea4000ef19bd07e19e11284980005fdd26862ab5ef537049776adc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-05-12T09:39:01Z","title_canon_sha256":"5f4e05ae366b98fa35c76fba989cfd85972296512606d118d0c440b22c635645"},"schema_version":"1.0","source":{"id":"1705.04484","kind":"arxiv","version":1}},"canonical_sha256":"6215b9768eb02c778eb245e78a2a8e3ae82896c2b365a4f00aebabe015e1a74f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6215b9768eb02c778eb245e78a2a8e3ae82896c2b365a4f00aebabe015e1a74f","first_computed_at":"2026-05-18T00:44:37.972038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:37.972038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+4ln0JKqP2DK9eRsLVc++e7aExk298o9qCnVg2kyF0FwTmv/2QGsvBqiri89K1GjPNcLPc2KDtK8gt+us4GABw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:37.972412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04484","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2560d099d6b25874b7f4d059c7318b0ea6e4fa259a47407436217eac6202aab","sha256:9ad5465db36e475b94c8c780d86c729684a073bb9003113f52cea0709a70a811"],"state_sha256":"a3212de1c292335c079bed690a80ac4537825d1fe55b745e7d8212bf5d213c94"}