{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AIPVMTUOH7DBGSVC55J3XIVATW","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":"50855f6123154d27aa850bfce256960688a7a217c1da62a956cf69eb1e8fa2a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-27T12:42:25Z","title_canon_sha256":"8ed8ca06dea3191df64788b183ff9184dda39dcd0558df17d30e786a861a16b5"},"schema_version":"1.0","source":{"id":"1406.7169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7169","created_at":"2026-05-18T02:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7169v1","created_at":"2026-05-18T02:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7169","created_at":"2026-05-18T02:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"AIPVMTUOH7DB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AIPVMTUOH7DBGSVC","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AIPVMTUO","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:62ae06f795237350934c5f676fffd1f540dc63bfe413506d276ea2da332c7cd0","target":"graph","created_at":"2026-05-18T02:48:53Z","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 authors Mili$\\breve{c}$evi$\\acute{c}$ et al. introduced the reformulated Zagreb indices, which is a generalization of classical Zagreb indices of chemical graph theory. In the paper, we characterize the extremal properties of the first reformulated Zagreb index. We first introduce some graph operations which increase or decrease this index. Furthermore, we will determine the extremal tricyclic graphs with minimum and maximum the first Zagreb index by these graph operations.","authors_text":"Shengjin Ji, Xia Li, Yongke Qu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-27T12:42:25Z","title":"On reformulated zagreb indices with respect to tricyclic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7169","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":"sha256:0f46d6ed7b1f2c226d7af1c8f8f95acb8fa53cd1d98130ab5fd538b3d7fce590","target":"record","created_at":"2026-05-18T02:48:53Z","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":"50855f6123154d27aa850bfce256960688a7a217c1da62a956cf69eb1e8fa2a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-27T12:42:25Z","title_canon_sha256":"8ed8ca06dea3191df64788b183ff9184dda39dcd0558df17d30e786a861a16b5"},"schema_version":"1.0","source":{"id":"1406.7169","kind":"arxiv","version":1}},"canonical_sha256":"021f564e8e3fc6134aa2ef53bba2a09dbf51bc49b4a4f528f800bcff9a1085bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021f564e8e3fc6134aa2ef53bba2a09dbf51bc49b4a4f528f800bcff9a1085bc","first_computed_at":"2026-05-18T02:48:53.932020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:53.932020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z9KhTe6c8e1UiJDGmnIzbfpXTwg0xMoYnAgBddi25CeiYt9V1JFDddr886kD7PA6GFUR3gdpAncCfbg+7VYEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:53.932554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f46d6ed7b1f2c226d7af1c8f8f95acb8fa53cd1d98130ab5fd538b3d7fce590","sha256:62ae06f795237350934c5f676fffd1f540dc63bfe413506d276ea2da332c7cd0"],"state_sha256":"42671de71501e42fa9c4a9b862055b6fe5b29b998f1853a732a391f365831c24"}