{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QLJQKHM32B6K7LIXT72MDOH4LT","short_pith_number":"pith:QLJQKHM3","schema_version":"1.0","canonical_sha256":"82d3051d9bd07cafad179ff4c1b8fc5cc4b49f739bf1f4e39e4ddd11efac6869","source":{"kind":"arxiv","id":"1201.0455","version":1},"attestation_state":"computed","paper":{"title":"Faber-Krahn type inequality for unicyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guang-Jun Zhang, Jie Zhang, Xiao-Dong Zhang","submitted_at":"2012-01-02T11:18:45Z","abstract_excerpt":"The Faber-Krahn inequality states that the ball has minimal first Dirichlet eigenvalue among all bounded domains with the fixed volume in $\\mathbb{R}^n$. In this paper, we investigate the similar inequality for unicyclic graphs. The results show that the Faber-Krahn type inequality also holds for unicyclic graphs with a given graphic unicyclic degree sequence with minor conditions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.0455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-02T11:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"755da3f5f70ab25aead84b9797b5b11ff092ec55a700723e35cac62c41e603b1","abstract_canon_sha256":"e1c38181307e42beb41f362e6b540cef705a257e72a2f666527d6b01345a7a0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:17.474904Z","signature_b64":"u56iyYBLRH78/gb5XWfp7Zh19uQrPtFVQPHRfHdORS6s3/vvrSd/WcPmkzy/P3yADbDex+E7230LgEaKSk+YBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82d3051d9bd07cafad179ff4c1b8fc5cc4b49f739bf1f4e39e4ddd11efac6869","last_reissued_at":"2026-05-18T04:05:17.474308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:17.474308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faber-Krahn type inequality for unicyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guang-Jun Zhang, Jie Zhang, Xiao-Dong Zhang","submitted_at":"2012-01-02T11:18:45Z","abstract_excerpt":"The Faber-Krahn inequality states that the ball has minimal first Dirichlet eigenvalue among all bounded domains with the fixed volume in $\\mathbb{R}^n$. In this paper, we investigate the similar inequality for unicyclic graphs. The results show that the Faber-Krahn type inequality also holds for unicyclic graphs with a given graphic unicyclic degree sequence with minor conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0455","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.0455","created_at":"2026-05-18T04:05:17.474405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.0455v1","created_at":"2026-05-18T04:05:17.474405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0455","created_at":"2026-05-18T04:05:17.474405+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLJQKHM32B6K","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLJQKHM32B6K7LIX","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLJQKHM3","created_at":"2026-05-18T12:27:18.751474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT","json":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT.json","graph_json":"https://pith.science/api/pith-number/QLJQKHM32B6K7LIXT72MDOH4LT/graph.json","events_json":"https://pith.science/api/pith-number/QLJQKHM32B6K7LIXT72MDOH4LT/events.json","paper":"https://pith.science/paper/QLJQKHM3"},"agent_actions":{"view_html":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT","download_json":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT.json","view_paper":"https://pith.science/paper/QLJQKHM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.0455&json=true","fetch_graph":"https://pith.science/api/pith-number/QLJQKHM32B6K7LIXT72MDOH4LT/graph.json","fetch_events":"https://pith.science/api/pith-number/QLJQKHM32B6K7LIXT72MDOH4LT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT/action/storage_attestation","attest_author":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT/action/author_attestation","sign_citation":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT/action/citation_signature","submit_replication":"https://pith.science/pith/QLJQKHM32B6K7LIXT72MDOH4LT/action/replication_record"}},"created_at":"2026-05-18T04:05:17.474405+00:00","updated_at":"2026-05-18T04:05:17.474405+00:00"}