{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B3ECGSLU6Z5EFYZEUF22Q22IVR","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":"a1b4bb56b4b1f6b862fd93cd11d93d1315262ea1fd17eadde32c8c4c60c0e436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-19T21:07:18Z","title_canon_sha256":"0d757f4cf749cedec9fe442989c15a633758aaeef5482efc187c71411e925e4e"},"schema_version":"1.0","source":{"id":"1511.06378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.06378","created_at":"2026-05-18T01:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1511.06378v1","created_at":"2026-05-18T01:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06378","created_at":"2026-05-18T01:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"B3ECGSLU6Z5E","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B3ECGSLU6Z5EFYZE","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B3ECGSLU","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:f3ae6b778358b7fa81e2e92d214b7d037cdb92902fa531170fb1f77df5a78d76","target":"graph","created_at":"2026-05-18T01:26:24Z","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":"The principal ratio of a connected graph, denoted $\\gamma(G)$, is the ratio of the maximum and minimum entries of its first eigenvector. Cioab\\u{a} and Gregory conjectured that the graph on $n$ vertices maximizing $\\gamma(G)$ is a kite graph: a complete graph with a pendant path. In this paper we prove their conjecture.","authors_text":"Josh Tobin, Michael Tait","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-19T21:07:18Z","title":"Characterizing graphs of maximum principal ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06378","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":"sha256:068a23714e1bbd19f348668e47f5feb4c35dd7d536087360e38c655084ac5510","target":"record","created_at":"2026-05-18T01:26:24Z","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":"a1b4bb56b4b1f6b862fd93cd11d93d1315262ea1fd17eadde32c8c4c60c0e436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-19T21:07:18Z","title_canon_sha256":"0d757f4cf749cedec9fe442989c15a633758aaeef5482efc187c71411e925e4e"},"schema_version":"1.0","source":{"id":"1511.06378","kind":"arxiv","version":1}},"canonical_sha256":"0ec8234974f67a42e324a175a86b48ac67f0ebb4a7f47e6573cf2807bbfed830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ec8234974f67a42e324a175a86b48ac67f0ebb4a7f47e6573cf2807bbfed830","first_computed_at":"2026-05-18T01:26:24.563278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:24.563278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qA0FcLD9P9REQEXmmgwAAXS/J/6F+o2QMROGifhYbWCKdBAWqF4DveHyrlqGpTfmooZrMqdlJntOKH8gNUxbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:24.563707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.06378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:068a23714e1bbd19f348668e47f5feb4c35dd7d536087360e38c655084ac5510","sha256:f3ae6b778358b7fa81e2e92d214b7d037cdb92902fa531170fb1f77df5a78d76"],"state_sha256":"4b8026527413ad187fad499a86d41d863c331a43a1852483f0fd204493d0c2f3"}