{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6MSS5EZIJ2JZBWBQI3VLHPH2FO","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":"3e6e7bf35947c1be600435958eae962e20ba126f7dd6e8950f5f829649e5b15b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-06T12:12:42Z","title_canon_sha256":"96f495a5c968b9e962d46d0c0658d6bd7be249be3eb52750e773db13e96fc221"},"schema_version":"1.0","source":{"id":"1102.1144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1144","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1144v1","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1144","created_at":"2026-05-18T04:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"6MSS5EZIJ2JZ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6MSS5EZIJ2JZBWBQ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6MSS5EZI","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:b65aec71340d0dbf437e32c3ed403591f6661fee0b0d675e47f31e188302afcc","target":"graph","created_at":"2026-05-18T04:29:54Z","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":"Let $G$ be a simple graph and $\\alpha$ a real number. The quantity $s_{\\alpha}(G)$ defined as the sum of the $\\alpha$-th power of the non-zero Laplacian eigenvalues of $G$ generalizes several concepts in the literature. The Laplacian Estrada index is a newly introduced graph invariant based on Laplacian eigenvalues. We establish bounds for $s_{\\alpha}$ and Laplacian Estrada index related to the degree sequences.","authors_text":"Bo Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-06T12:12:42Z","title":"On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1144","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":"sha256:53b34bd9648e505bb3a6fa55ac7f8e1a497702c3da0fd7c24d22c08d62e66f82","target":"record","created_at":"2026-05-18T04:29:54Z","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":"3e6e7bf35947c1be600435958eae962e20ba126f7dd6e8950f5f829649e5b15b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-02-06T12:12:42Z","title_canon_sha256":"96f495a5c968b9e962d46d0c0658d6bd7be249be3eb52750e773db13e96fc221"},"schema_version":"1.0","source":{"id":"1102.1144","kind":"arxiv","version":1}},"canonical_sha256":"f3252e93284e9390d83046eab3bcfa2ba08a69727f37cf90f5de8af2e403df06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3252e93284e9390d83046eab3bcfa2ba08a69727f37cf90f5de8af2e403df06","first_computed_at":"2026-05-18T04:29:54.933370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:54.933370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w0FqpeWziHepI0EqjBgMVqmrmbDyQj3i7ReqbYaQll7FSHVg7A1UhQEVADJ+IKviQkuGjE/BsWlc1Tycs8VqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:54.934025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53b34bd9648e505bb3a6fa55ac7f8e1a497702c3da0fd7c24d22c08d62e66f82","sha256:b65aec71340d0dbf437e32c3ed403591f6661fee0b0d675e47f31e188302afcc"],"state_sha256":"e8155316103098c3fc8702ac3b2bec584723a7fef9522dd7e812777c5dd0f675"}