{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N4DV24HGVWN27WV2FIUSJ2XZ3P","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":"902011fd7053aab3c141d1d9a4f4f8ed9656756f57cdf381fab53b946644c3f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-07T08:55:28Z","title_canon_sha256":"470ab447d30b1bc940f250757713dc5a9d411e2d2667e5a62f2e78bae0d2e9e8"},"schema_version":"1.0","source":{"id":"1611.01938","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01938","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01938v4","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01938","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"pith_short_12","alias_value":"N4DV24HGVWN2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N4DV24HGVWN27WV2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N4DV24HG","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:869a6bd99e5ea83cb00f1a25724fc798d40f646ef139ddbe76fd51ae1a30d210","target":"graph","created_at":"2026-05-18T00:53:20Z","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":"It is shown how a connected graph and a tree with partially prescribed spectrum can be constructed. These constructions are based on a recent result of Salez that every totally real algebraic integer is an eigenvalue of a tree. Our result implies that for any (not necessarily connected) graph $G$, there is a tree $T$ such that the characteristic polynomial $P(G,x)$ of $G$ can divide the characteristic polynomial $P(T,x)$ of $T$, i.e., $P(G,x)$ is a divisor of $P(T,x)$.","authors_text":"Ivan Gutman, Wasin So, Xueliang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-07T08:55:28Z","title":"Constructions of graphs and trees with partially prescribed spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01938","kind":"arxiv","version":4},"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":"sha256:57bd6f0164a23126fa7cce5ebc6237d88d4ea2634905ddac105ef420e28a092e","target":"record","created_at":"2026-05-18T00:53:20Z","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":"902011fd7053aab3c141d1d9a4f4f8ed9656756f57cdf381fab53b946644c3f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-07T08:55:28Z","title_canon_sha256":"470ab447d30b1bc940f250757713dc5a9d411e2d2667e5a62f2e78bae0d2e9e8"},"schema_version":"1.0","source":{"id":"1611.01938","kind":"arxiv","version":4}},"canonical_sha256":"6f075d70e6ad9bafdaba2a2924eaf9dbd94bbba930ad0fcdb8bc86b0df6d4b6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f075d70e6ad9bafdaba2a2924eaf9dbd94bbba930ad0fcdb8bc86b0df6d4b6f","first_computed_at":"2026-05-18T00:53:20.543123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:20.543123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6gjsLOTvcTWsyahSDzTDc/5z6lviZ9jTdVp40rre6n7hDbny8IgUpekB1dtwQdwj5fME9rPpHghBcSUdrYtgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:20.543621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01938","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57bd6f0164a23126fa7cce5ebc6237d88d4ea2634905ddac105ef420e28a092e","sha256:869a6bd99e5ea83cb00f1a25724fc798d40f646ef139ddbe76fd51ae1a30d210"],"state_sha256":"0ab7ef9eea105b92c1196ccaa9e3055ffd9467b5ae3f147c39792086b3a28002"}