{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KBX5HBT3CBAQYBX5RRL5QUNPJS","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":"f071ed04499ab2985f70cfd5a8ae36d4151c045fca4cf47212e528de13ecd68c","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-12T21:07:58Z","title_canon_sha256":"3e6493bc541fbe3caf170e780b44a9a13539a0d3182310a1bcb4910f4a15d659"},"schema_version":"1.0","source":{"id":"2411.08184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.08184","created_at":"2026-07-05T09:34:42Z"},{"alias_kind":"arxiv_version","alias_value":"2411.08184v1","created_at":"2026-07-05T09:34:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.08184","created_at":"2026-07-05T09:34:42Z"},{"alias_kind":"pith_short_12","alias_value":"KBX5HBT3CBAQ","created_at":"2026-07-05T09:34:42Z"},{"alias_kind":"pith_short_16","alias_value":"KBX5HBT3CBAQYBX5","created_at":"2026-07-05T09:34:42Z"},{"alias_kind":"pith_short_8","alias_value":"KBX5HBT3","created_at":"2026-07-05T09:34:42Z"}],"graph_snapshots":[{"event_id":"sha256:aebad8acc2357edb8fd37e9d2fce9c5ed03532336e909775cbb7fc22d8aa223a","target":"graph","created_at":"2026-07-05T09:34:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.08184/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we prove a conjecture by Wocjan, Elphick and Anekstein (2018) which upper bounds the sum of the squares of the positive (or negative) eigenvalues of the adjacency matrix of a graph by an expression that behaves monotonically in terms of the vector chromatic number. One of our lemmas is a strengthening of the Cauchy-Schwarz inequality for Hermitian matrices when one of the matrices is positive semidefinite.\n  A related conjecture due to Bollob\\'as and Nikiforov (2007) replaces the vector chromatic number by the clique number and sums over the first two eigenvalues only. We prove a","authors_text":"Gabriel Coutinho, Shengtong Zhang, Thom\\'as Jung Spier","cross_cats":["math.OC","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-12T21:07:58Z","title":"Conic programming to understand sums of squares of eigenvalues of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.08184","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":"sha256:20c68d70b435e077f7efdb50dee03f88b35bf5851c559a4c3efbc9185a2cb90a","target":"record","created_at":"2026-07-05T09:34:42Z","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":"f071ed04499ab2985f70cfd5a8ae36d4151c045fca4cf47212e528de13ecd68c","cross_cats_sorted":["math.OC","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-12T21:07:58Z","title_canon_sha256":"3e6493bc541fbe3caf170e780b44a9a13539a0d3182310a1bcb4910f4a15d659"},"schema_version":"1.0","source":{"id":"2411.08184","kind":"arxiv","version":1}},"canonical_sha256":"506fd3867b10410c06fd8c57d851af4cb46baa7d93833c102ba90a43422ed204","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"506fd3867b10410c06fd8c57d851af4cb46baa7d93833c102ba90a43422ed204","first_computed_at":"2026-07-05T09:34:42.896091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:34:42.896091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jd9sdO76H68YEd0GpN5Sa9hglC/ooRSBqXNOMaElAGh8KqMpVnuvhB++L3l4in2U8lFI0Oa5juL9eRWAu8PbAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:34:42.896517Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.08184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20c68d70b435e077f7efdb50dee03f88b35bf5851c559a4c3efbc9185a2cb90a","sha256:aebad8acc2357edb8fd37e9d2fce9c5ed03532336e909775cbb7fc22d8aa223a"],"state_sha256":"ff861411baa9f0f4d680648ef5ad01f652b7c4b3b37977b99b825aeb6a1e4b19"}