{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MV6VIOPYFHARUYYUYD23KQHCY5","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":"1b6f0f8871f420698dba07a43b5e28724252682ad3127dc2f7f020578f3b517b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-07T15:13:37Z","title_canon_sha256":"e36ce2f899201ffa2bacf88d47dca75fda36204744cf6dd2763f8685c0763405"},"schema_version":"1.0","source":{"id":"1207.1802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1802","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1802v2","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1802","created_at":"2026-05-18T02:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"MV6VIOPYFHAR","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MV6VIOPYFHARUYYU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MV6VIOPY","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:1c7704095b31432d01419c10bf76e960d446d08ec1ca5f93b46b8ce9fa28ad12","target":"graph","created_at":"2026-05-18T02:18:04Z","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":"A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. We prove that for a given nullity more than 1, there are only finitely many integral trees. It is also shown that integral trees with nullity 2 and 3 are unique.","authors_text":"A. Mohammadian, B. Tayfeh-Rezaie, E. Ghorbani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-07T15:13:37Z","title":"Integral trees with given nullity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1802","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":"sha256:61911be983c5b2c54225dff101d763f3e72c9a027be1f9a55afc36ef06b6e6d2","target":"record","created_at":"2026-05-18T02:18:04Z","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":"1b6f0f8871f420698dba07a43b5e28724252682ad3127dc2f7f020578f3b517b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-07T15:13:37Z","title_canon_sha256":"e36ce2f899201ffa2bacf88d47dca75fda36204744cf6dd2763f8685c0763405"},"schema_version":"1.0","source":{"id":"1207.1802","kind":"arxiv","version":2}},"canonical_sha256":"657d5439f829c11a6314c0f5b540e2c74b5e775eea996700674f89e0b086f5ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"657d5439f829c11a6314c0f5b540e2c74b5e775eea996700674f89e0b086f5ff","first_computed_at":"2026-05-18T02:18:04.551027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:04.551027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXrMNp74NXHg8JBh+4kzAogUOUpE101SRNF8j4L0P/ZTXVPYUYYDtl+iH8Pqi+WPrRxee7RWxRnL1/laTo1DCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:04.551776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61911be983c5b2c54225dff101d763f3e72c9a027be1f9a55afc36ef06b6e6d2","sha256:1c7704095b31432d01419c10bf76e960d446d08ec1ca5f93b46b8ce9fa28ad12"],"state_sha256":"81a3eb36de6ccf58756d3f994d09f949406bfde2c4047df910e31cbc29ef62f4"}