{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:S7EQQ7ASFZFU2LD6KJWURV6O5X","short_pith_number":"pith:S7EQQ7AS","schema_version":"1.0","canonical_sha256":"97c9087c122e4b4d2c7e526d48d7ceedca5c3571f3979974b5c76c2f44180286","source":{"kind":"arxiv","id":"2507.00798","version":1},"attestation_state":"computed","paper":{"title":"Improved bound of graph energy in terms of vertex cover number","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CO","authors_text":"Aniruddha Samanta","submitted_at":"2025-07-01T14:30:55Z","abstract_excerpt":"Let $ G $ be a simple graph with the vertex cover number $ \\tau $. The energy $ \\mathcal{E}(G) $ of $ G $ is the sum of the absolute values of all the adjacency eigenvalues of $ G $. In this article, we establish $ \\mathcal{E}(G)\\geq 2\\tau $ for several classes of graphs. The result significantly improves the known result $ \\mathcal{E}(G)\\geq 2\\tau-2c$ for many classes of graphs, where $ c $ is the number of odd cycles."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.00798","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-01T14:30:55Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1e71347650a91e0071c6d225f3074027c67fe6a42f369e54613a4919af9df767","abstract_canon_sha256":"cdb6f0352fcfdf86a8a572c6a4d0655cf648041a1fa512c240efe02c428b08ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:30:14.547447Z","signature_b64":"G41y/206nhByAUaaDmPcsfhB3K2sG+RBjQxEjrEde4IDj0T0Z8Kwb8g4fGhMAKwcF+GHIXoyeoBP/44X9tgzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97c9087c122e4b4d2c7e526d48d7ceedca5c3571f3979974b5c76c2f44180286","last_reissued_at":"2026-07-05T11:30:14.546998Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:30:14.546998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved bound of graph energy in terms of vertex cover number","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CO","authors_text":"Aniruddha Samanta","submitted_at":"2025-07-01T14:30:55Z","abstract_excerpt":"Let $ G $ be a simple graph with the vertex cover number $ \\tau $. The energy $ \\mathcal{E}(G) $ of $ G $ is the sum of the absolute values of all the adjacency eigenvalues of $ G $. In this article, we establish $ \\mathcal{E}(G)\\geq 2\\tau $ for several classes of graphs. The result significantly improves the known result $ \\mathcal{E}(G)\\geq 2\\tau-2c$ for many classes of graphs, where $ c $ is the number of odd cycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00798","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.00798/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.00798","created_at":"2026-07-05T11:30:14.547059+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.00798v1","created_at":"2026-07-05T11:30:14.547059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00798","created_at":"2026-07-05T11:30:14.547059+00:00"},{"alias_kind":"pith_short_12","alias_value":"S7EQQ7ASFZFU","created_at":"2026-07-05T11:30:14.547059+00:00"},{"alias_kind":"pith_short_16","alias_value":"S7EQQ7ASFZFU2LD6","created_at":"2026-07-05T11:30:14.547059+00:00"},{"alias_kind":"pith_short_8","alias_value":"S7EQQ7AS","created_at":"2026-07-05T11:30:14.547059+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.04367","citing_title":"Extremal Graphs for the Energy-Independence Number Inequality","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X","json":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X.json","graph_json":"https://pith.science/api/pith-number/S7EQQ7ASFZFU2LD6KJWURV6O5X/graph.json","events_json":"https://pith.science/api/pith-number/S7EQQ7ASFZFU2LD6KJWURV6O5X/events.json","paper":"https://pith.science/paper/S7EQQ7AS"},"agent_actions":{"view_html":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X","download_json":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X.json","view_paper":"https://pith.science/paper/S7EQQ7AS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.00798&json=true","fetch_graph":"https://pith.science/api/pith-number/S7EQQ7ASFZFU2LD6KJWURV6O5X/graph.json","fetch_events":"https://pith.science/api/pith-number/S7EQQ7ASFZFU2LD6KJWURV6O5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X/action/storage_attestation","attest_author":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X/action/author_attestation","sign_citation":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X/action/citation_signature","submit_replication":"https://pith.science/pith/S7EQQ7ASFZFU2LD6KJWURV6O5X/action/replication_record"}},"created_at":"2026-07-05T11:30:14.547059+00:00","updated_at":"2026-07-05T11:30:14.547059+00:00"}