{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IYZ3OHSNKFPGIKBHXC2K46STZ3","short_pith_number":"pith:IYZ3OHSN","schema_version":"1.0","canonical_sha256":"4633b71e4d515e642827b8b4ae7a53cee2cd2cc9fc2f78ea8c71eda552d8bee2","source":{"kind":"arxiv","id":"1609.00420","version":1},"attestation_state":"computed","paper":{"title":"Note on von Neumann and R\\'enyi entropies of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"David Roberson, Jephian C.-H. Lin, Joshua Lockhart, Leslie Hogben, Michael Dairyko, Michael Young, Simone Severini","submitted_at":"2016-09-01T22:57:52Z","abstract_excerpt":"We conjecture that all connected graphs of order $n$ have von Neumann entropy at least as great as the star $K_{1,n-1}$ and prove this for almost all graphs of order $n$. We show that connected graphs of order $n$ have R\\'enyi 2-entropy at least as great as $K_{1,n-1}$ and for $\\alpha>1$, $K_n$ maximizes R\\'enyi $\\alpha$-entropy over graphs of order $n$. We show that adding an edge to a graph can lower its von Neumann entropy."},"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":"1609.00420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-01T22:57:52Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"023766efa0d10c17aa1017ac0d50b0dc68acb1128dd734bbc9db04b36dcb0e84","abstract_canon_sha256":"9bf625f1b19d007c932737190768537f1f563e5e9c43b3f090a65d19dc5ee7eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:23.916751Z","signature_b64":"MFGyxR31yySfC3RoWzYeQVSeWWHS6EpQeeXKDKDcnZqdrQZJgs9xuHWzBFz9PtlncpDEa9Mmew2MGrZYvyArBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4633b71e4d515e642827b8b4ae7a53cee2cd2cc9fc2f78ea8c71eda552d8bee2","last_reissued_at":"2026-05-18T01:06:23.916041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:23.916041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Note on von Neumann and R\\'enyi entropies of a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CO","authors_text":"David Roberson, Jephian C.-H. Lin, Joshua Lockhart, Leslie Hogben, Michael Dairyko, Michael Young, Simone Severini","submitted_at":"2016-09-01T22:57:52Z","abstract_excerpt":"We conjecture that all connected graphs of order $n$ have von Neumann entropy at least as great as the star $K_{1,n-1}$ and prove this for almost all graphs of order $n$. We show that connected graphs of order $n$ have R\\'enyi 2-entropy at least as great as $K_{1,n-1}$ and for $\\alpha>1$, $K_n$ maximizes R\\'enyi $\\alpha$-entropy over graphs of order $n$. We show that adding an edge to a graph can lower its von Neumann entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00420","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":""},"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":"1609.00420","created_at":"2026-05-18T01:06:23.916151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.00420v1","created_at":"2026-05-18T01:06:23.916151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00420","created_at":"2026-05-18T01:06:23.916151+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYZ3OHSNKFPG","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYZ3OHSNKFPGIKBH","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYZ3OHSN","created_at":"2026-05-18T12:30:22.444734+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3","json":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3.json","graph_json":"https://pith.science/api/pith-number/IYZ3OHSNKFPGIKBHXC2K46STZ3/graph.json","events_json":"https://pith.science/api/pith-number/IYZ3OHSNKFPGIKBHXC2K46STZ3/events.json","paper":"https://pith.science/paper/IYZ3OHSN"},"agent_actions":{"view_html":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3","download_json":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3.json","view_paper":"https://pith.science/paper/IYZ3OHSN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.00420&json=true","fetch_graph":"https://pith.science/api/pith-number/IYZ3OHSNKFPGIKBHXC2K46STZ3/graph.json","fetch_events":"https://pith.science/api/pith-number/IYZ3OHSNKFPGIKBHXC2K46STZ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3/action/storage_attestation","attest_author":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3/action/author_attestation","sign_citation":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3/action/citation_signature","submit_replication":"https://pith.science/pith/IYZ3OHSNKFPGIKBHXC2K46STZ3/action/replication_record"}},"created_at":"2026-05-18T01:06:23.916151+00:00","updated_at":"2026-05-18T01:06:23.916151+00:00"}