{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6JR36ERHTRP4AQMS6IETGDDGLI","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":"b7ec9c6eaab2632d94c9198486a06dc49dc89cdff75ab030f77fb098a2ac73a9","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-29T13:41:29Z","title_canon_sha256":"b50422991f007efb641e40c182f76b6bd5ffaddcfe76743e288158f85b275843"},"schema_version":"1.0","source":{"id":"1811.12138","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12138","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12138v2","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12138","created_at":"2026-05-17T23:42:08Z"},{"alias_kind":"pith_short_12","alias_value":"6JR36ERHTRP4","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6JR36ERHTRP4AQMS","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6JR36ERH","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:31ddda59680f366e18084fc0a811de098acf211b9a7260ec084c99bdd774576d","target":"graph","created_at":"2026-05-17T23:42:08Z","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 graph on $n$ vertices and $\\lambda_1\\geq \\lambda_2\\geq \\ldots \\geq \\lambda_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\\sum_{i=1}^n e^{\\lambda_i}.$ In this work, we using an increasing sequence converging to the $\\lambda_1$ to obtain an increasing sequence of lower bounds for $EE(G)$. In addition, we generalize this succession for the Estrada index of an arbitrary nonnegative Hermitian matrix.","authors_text":"Jonnathan Rodr\\'iguez, Juan R. Carmona","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-29T13:41:29Z","title":"An increasing sequence of lower bounds for the Estrada index of graphs and matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12138","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":"sha256:8d01058105a6655c0c744251b2de6e8430dc34ded9d28cc21e070fc981eaa5fc","target":"record","created_at":"2026-05-17T23:42:08Z","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":"b7ec9c6eaab2632d94c9198486a06dc49dc89cdff75ab030f77fb098a2ac73a9","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-29T13:41:29Z","title_canon_sha256":"b50422991f007efb641e40c182f76b6bd5ffaddcfe76743e288158f85b275843"},"schema_version":"1.0","source":{"id":"1811.12138","kind":"arxiv","version":2}},"canonical_sha256":"f263bf12279c5fc04192f209330c665a0306b2304e42c186bf0a52958a870cad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f263bf12279c5fc04192f209330c665a0306b2304e42c186bf0a52958a870cad","first_computed_at":"2026-05-17T23:42:08.531507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:08.531507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"REBHY7tTnnlCTG2MgR9tWEw5MuAdWVeZmGpd4dvWBMDGp1hEllYt53aXW0dP9s0uHOBy1nWR5g/cAmRG4eZICA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:08.532100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12138","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d01058105a6655c0c744251b2de6e8430dc34ded9d28cc21e070fc981eaa5fc","sha256:31ddda59680f366e18084fc0a811de098acf211b9a7260ec084c99bdd774576d"],"state_sha256":"48e498ade8aeeb970cdae8b228225a736a50f3dc5a233493a70eac382719bea1"}