{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CQC4JBPBLFNSTZZ63KMAMOHZ75","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":"0be2b5825e6b9976893ecfdb0a440c2314e8dd84141c66460912ddcfcba33bbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T02:00:47Z","title_canon_sha256":"f44c7300a88eac461518cbff179aa085d72a7b0341a6b697cd3fce0f13ef925b"},"schema_version":"1.0","source":{"id":"2506.11401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11401","created_at":"2026-07-05T11:21:03Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11401v1","created_at":"2026-07-05T11:21:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11401","created_at":"2026-07-05T11:21:03Z"},{"alias_kind":"pith_short_12","alias_value":"CQC4JBPBLFNS","created_at":"2026-07-05T11:21:03Z"},{"alias_kind":"pith_short_16","alias_value":"CQC4JBPBLFNSTZZ6","created_at":"2026-07-05T11:21:03Z"},{"alias_kind":"pith_short_8","alias_value":"CQC4JBPB","created_at":"2026-07-05T11:21:03Z"}],"graph_snapshots":[{"event_id":"sha256:fe53fb80376114e679df8a98b4ccc6b2cbc19e1b9f86b2ca756916a238b470c1","target":"graph","created_at":"2026-07-05T11:21:03Z","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/2506.11401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the extremal graph $G$ of order $n$ that maximizes the sum of the spectral radii of $G$ and its complement. This resolves a conjecture posed by Stevanovi\\'{c} in 2007.","authors_text":"Chih-wen Weng, Yen-Jen Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T02:00:47Z","title":"Nordhaus-Gaddum inequality for the spectral radius of a graph of order $n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11401","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:dda7e4ac3b45c0474d0bc04cdc5466781d8cfce9b21e6e5c62d7f51433127d7b","target":"record","created_at":"2026-07-05T11:21:03Z","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":"0be2b5825e6b9976893ecfdb0a440c2314e8dd84141c66460912ddcfcba33bbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-06-13T02:00:47Z","title_canon_sha256":"f44c7300a88eac461518cbff179aa085d72a7b0341a6b697cd3fce0f13ef925b"},"schema_version":"1.0","source":{"id":"2506.11401","kind":"arxiv","version":1}},"canonical_sha256":"1405c485e1595b29e73eda980638f9ff689a437ef1a49b40aa3c7a38cbdb969a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1405c485e1595b29e73eda980638f9ff689a437ef1a49b40aa3c7a38cbdb969a","first_computed_at":"2026-07-05T11:21:03.744536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:03.744536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AdD3GnYvW8d1+E4cwQWO7AlbU6REIUVLBAix1xmEtC7TT3lh6k1wsBBYdKpM5I+34Laa0qK5hG0qMYvXePDrCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:03.744993Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dda7e4ac3b45c0474d0bc04cdc5466781d8cfce9b21e6e5c62d7f51433127d7b","sha256:fe53fb80376114e679df8a98b4ccc6b2cbc19e1b9f86b2ca756916a238b470c1"],"state_sha256":"e0e95b95bb5daccdb81469eca1846f3660751adeedd3cfac864ba16d25eceeb2"}