{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6UHR7C4OB2BQV2B54BVIKMROCD","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":"7f734957a737fc9c22ddeada294c782b434d01af20715940f2e028dd64bcbeac","cross_cats_sorted":["math.AP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-29T08:54:29Z","title_canon_sha256":"ebc6bab66ee99c391e3153917ae4d0713b1012d1795608b6e757ab4f9eb65d35"},"schema_version":"1.0","source":{"id":"1810.12003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12003","created_at":"2026-05-18T00:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12003v1","created_at":"2026-05-18T00:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12003","created_at":"2026-05-18T00:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"6UHR7C4OB2BQ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6UHR7C4OB2BQV2B5","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6UHR7C4O","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:778a4d783db640b9345f8ca583f57ba89a9710b1396e32c1b86f1e68e0c7f150","target":"graph","created_at":"2026-05-18T00:02:06Z","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":"In this paper, we establish Buser type inequalities, i.e., upper bounds for eigenvalues in terms of Cheeger constants. We prove the Buser's inequality for an infinite but locally finite connected graph with Ricci curvature lower bounds. Furthermore, we derive that the graph with positive curvature is finite, especially for unbounded Laplacians. By proving Poincar\\'e inequality, we obtain a lower bound on Cheeger constant in terms of positive curvature.","authors_text":"Shuang Liu","cross_cats":["math.AP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-29T08:54:29Z","title":"Buser's inequality on infinite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12003","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:d9f7b211abc02b2f3a4205a37797244646a371a070be8e234c438831a8e1fd4e","target":"record","created_at":"2026-05-18T00:02:06Z","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":"7f734957a737fc9c22ddeada294c782b434d01af20715940f2e028dd64bcbeac","cross_cats_sorted":["math.AP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-29T08:54:29Z","title_canon_sha256":"ebc6bab66ee99c391e3153917ae4d0713b1012d1795608b6e757ab4f9eb65d35"},"schema_version":"1.0","source":{"id":"1810.12003","kind":"arxiv","version":1}},"canonical_sha256":"f50f1f8b8e0e830ae83de06a85322e10ed1cdebf0b20ef402ca4149c0ee315bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f50f1f8b8e0e830ae83de06a85322e10ed1cdebf0b20ef402ca4149c0ee315bc","first_computed_at":"2026-05-18T00:02:06.724159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:06.724159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ahssP8xSz+PZpaFeSBu2caof68aMx9/V7P1jy+wdvcFWebEY3n/ycdQyZW/iLq73XWfstKkvJdlnesp3mVE+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:06.724932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f7b211abc02b2f3a4205a37797244646a371a070be8e234c438831a8e1fd4e","sha256:778a4d783db640b9345f8ca583f57ba89a9710b1396e32c1b86f1e68e0c7f150"],"state_sha256":"d483f796b1920c6e7cd5e95dd524c8fe02c60a676d513da8b7ea2609ffa7e7f6"}