{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CMQPOJZY2LDUHNWLQ6RBQEU7PP","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":"57296ccff02adeb63fc780e38144a267f68cacc2d491477e3b3087fd71dcf8ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-30T08:44:49Z","title_canon_sha256":"ffaa712a9da8bc9729b7fd28c5dfd23d620ae994ddcaf3b45c8c274dd4be67fc"},"schema_version":"1.0","source":{"id":"1808.10441","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10441","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10441v2","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10441","created_at":"2026-05-18T00:06:00Z"},{"alias_kind":"pith_short_12","alias_value":"CMQPOJZY2LDU","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CMQPOJZY2LDUHNWL","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CMQPOJZY","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:a6811fe60aa5f6a3cd43cda99d5386cc131466e25b14a62ac4ac586ef5dd5a45","target":"graph","created_at":"2026-05-18T00:06:00Z","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":"Applications in chemistry motivated mathematicians to define different topological indices for different types of graphs. The Hyper-Zagreb index (HM) is an important tool as it integrates the first and the second Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.","authors_text":"Hassan Rezapour, Ramin Nasiri, Seyedahmad Mousavi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-30T08:44:49Z","title":"The Hyper-Zagreb Index of Trees and Unicyclic Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10441","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":"sha256:6a7c7859860bc7275f0fdeb367fb2cd9a307252a9451448b321de8068171f279","target":"record","created_at":"2026-05-18T00:06:00Z","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":"57296ccff02adeb63fc780e38144a267f68cacc2d491477e3b3087fd71dcf8ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-30T08:44:49Z","title_canon_sha256":"ffaa712a9da8bc9729b7fd28c5dfd23d620ae994ddcaf3b45c8c274dd4be67fc"},"schema_version":"1.0","source":{"id":"1808.10441","kind":"arxiv","version":2}},"canonical_sha256":"1320f72738d2c743b6cb87a218129f7bc23e64440eaabf71d18b9cf52e442823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1320f72738d2c743b6cb87a218129f7bc23e64440eaabf71d18b9cf52e442823","first_computed_at":"2026-05-18T00:06:00.915273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:00.915273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QsEAKVxIpzAHeMT7Vnjc9HViYzJuOA0iRu9E5hq3G8Jxr8CF+Kdqdfl6CL1fmwSWruPXYt/yTGio7eYD9/XPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:00.915766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10441","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a7c7859860bc7275f0fdeb367fb2cd9a307252a9451448b321de8068171f279","sha256:a6811fe60aa5f6a3cd43cda99d5386cc131466e25b14a62ac4ac586ef5dd5a45"],"state_sha256":"9ad3ce1f1d723cc422e72ed609620f67177cf4c442889ddb2e928dcc3a789067"}