{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TCBJ2Q3FTEFMMFWCF4WWFTRTDC","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":"dd2d68f50368bf16236de039d98f07abda09258369fc6cb75757b218e3eabdd8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-25T15:46:18Z","title_canon_sha256":"25337e987f46496bdffdf76afd4fe4d7e6e8110e8c03071e1743864befb4c95b"},"schema_version":"1.0","source":{"id":"1406.6617","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6617","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6617v2","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6617","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"pith_short_12","alias_value":"TCBJ2Q3FTEFM","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TCBJ2Q3FTEFMMFWC","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TCBJ2Q3F","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:2c181214fbc6e3b6e8da7f18964b6d7099f953dc93704ba4697f54f60ef5ea1b","target":"graph","created_at":"2026-05-17T23:49:44Z","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 derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality $CD(0,\\infty)$. This estimate is independent of the size of the graph and provides a general method to obtain higher order spectral estimates. The operation of taking Cartesian products is shown to be an efficient way for constructing new weighted graphs satisfying $CD(0,\\infty)$. We also discuss a higher order Cheeger constant ratio estimate and related topics about expanders.","authors_text":"Norbert Peyerimhoff, Shiping Liu","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-25T15:46:18Z","title":"Eigenvalue ratios of nonnegatively curved graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6617","kind":"arxiv","version":2},"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":"sha256:2bc495df01bb81af718418b932737fa59888e69dfa071beb06f3166f41e9ed1b","target":"record","created_at":"2026-05-17T23:49:44Z","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":"dd2d68f50368bf16236de039d98f07abda09258369fc6cb75757b218e3eabdd8","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-25T15:46:18Z","title_canon_sha256":"25337e987f46496bdffdf76afd4fe4d7e6e8110e8c03071e1743864befb4c95b"},"schema_version":"1.0","source":{"id":"1406.6617","kind":"arxiv","version":2}},"canonical_sha256":"98829d4365990ac616c22f2d62ce33189bb457e83ce678be92cb6b3ee3dd50cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98829d4365990ac616c22f2d62ce33189bb457e83ce678be92cb6b3ee3dd50cf","first_computed_at":"2026-05-17T23:49:44.609767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:44.609767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i6VbsMvmm071aBIvsHLatuPdlWDNtXJFt96UGdcl3E907L7GdrqEedRRn4tViB2xjFX91lT329OvE5gCiSyVCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:44.610302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6617","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bc495df01bb81af718418b932737fa59888e69dfa071beb06f3166f41e9ed1b","sha256:2c181214fbc6e3b6e8da7f18964b6d7099f953dc93704ba4697f54f60ef5ea1b"],"state_sha256":"b086be9f70dfd3619dbf6267920676bc257a4b58d59b59b9309701be9e2beaea"}