{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EAYELX6Y2NBZ4U2JPRHH6LYGAW","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":"3e84298e1ad90181197d65695d51d15c6a9d6584a1217750ecb7b2b808cbe603","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-11T08:15:21Z","title_canon_sha256":"6390f72cfae3ba7f094091b381a070442cb8c1abdccf9f5d3ed20bf2fa8d3d92"},"schema_version":"1.0","source":{"id":"1711.04095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04095","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04095v1","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04095","created_at":"2026-05-18T00:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"EAYELX6Y2NBZ","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EAYELX6Y2NBZ4U2J","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EAYELX6Y","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:4bd480b99fdb4d5cf70d95cdd6e6adad53fbb007606a3b844b3538c28fbc33bf","target":"graph","created_at":"2026-05-18T00:30:50Z","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 energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Akbari et al. \\cite{S. Akbari} proved that for a complete multipartite graph $K_{t_1 ,\\ldots,t_k}$, if $t_i\\geq 2 \\ (i=1,\\ldots,k)$, then deleting any edge will increase the energy. A natural question is how the energy changes when $\\min\\{t_1 ,\\ldots,t_k\\}=1$. In this paper, we will answer this question and completely determine how the energy of a complete multipartite graph changes when one edge is removed.","authors_text":"Chang-Xiang He, Hai-Ying Shan, Zhen-Sheng Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-11T08:15:21Z","title":"The energy change of the complete multipartite graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04095","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:afaa70db1e55f7f5354fa9e19d9620234a18858cfc3b547e131b9f9ee21115bb","target":"record","created_at":"2026-05-18T00:30:50Z","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":"3e84298e1ad90181197d65695d51d15c6a9d6584a1217750ecb7b2b808cbe603","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-11T08:15:21Z","title_canon_sha256":"6390f72cfae3ba7f094091b381a070442cb8c1abdccf9f5d3ed20bf2fa8d3d92"},"schema_version":"1.0","source":{"id":"1711.04095","kind":"arxiv","version":1}},"canonical_sha256":"203045dfd8d3439e53497c4e7f2f0605ae9036c84c75bea47488f6aa666c865d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"203045dfd8d3439e53497c4e7f2f0605ae9036c84c75bea47488f6aa666c865d","first_computed_at":"2026-05-18T00:30:50.089173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:50.089173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dFDIg5kBZ+mbbN+qUXRseJy4GWD1mEBjEpZu0ARFatzw4pyULyREamqaNUzBA+D5V/ghhUSrCzgt8xhtSJqhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:50.089847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afaa70db1e55f7f5354fa9e19d9620234a18858cfc3b547e131b9f9ee21115bb","sha256:4bd480b99fdb4d5cf70d95cdd6e6adad53fbb007606a3b844b3538c28fbc33bf"],"state_sha256":"9871c19aacfd72f6f45403702c878895a87199b01a7c4b2b295d8100c041d370"}