{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:67KODJQ7HTYL2W7QXJTFW725QP","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":"106d212ace3b5adbcc46ea577ec822b0a166e6782976437c4b07f9db2c18ccbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-17T02:14:04Z","title_canon_sha256":"992344686ee3071afa9432ccb6944f8616fc29b1be7406b1eab1d6a382762157"},"schema_version":"1.0","source":{"id":"1908.06224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06224","created_at":"2026-07-04T23:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06224v1","created_at":"2026-07-04T23:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06224","created_at":"2026-07-04T23:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"67KODJQ7HTYL","created_at":"2026-07-04T23:58:13Z"},{"alias_kind":"pith_short_16","alias_value":"67KODJQ7HTYL2W7Q","created_at":"2026-07-04T23:58:13Z"},{"alias_kind":"pith_short_8","alias_value":"67KODJQ7","created_at":"2026-07-04T23:58:13Z"}],"graph_snapshots":[{"event_id":"sha256:f6382baa10a609d372c7266a6ed0cf389c6d1d707f75f21ad8a11bca9cb9975e","target":"graph","created_at":"2026-07-04T23:58:13Z","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/1908.06224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The general spectral radius of a graph $G$, denoted by $\\Theta(G,\\alpha)$, is the maximal eigenvalue of $M_{\\alpha}(G)=A(G)+\\alpha D(G)$ $(\\alpha\\geq 0)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the diagonal matrix of vertex degrees of $G$, respectively. A graph $G$ is called $\\Theta_\\alpha$-maximal in a class of connected simple graphs $\\mathcal {G}$ if $\\Theta(G,\\alpha)$ is maximal among all graphs of $\\mathcal {G}$. A $t$-cone $c$-cyclic graph is the join of a complete graph $K_t$ and a $c$-cyclic connected simple graph. Let $\\pi=\\big(d_1,d_2,\\ldots,d_n\\big)$ and $\\pi'=\\big(d'_","authors_text":"Muhuo Liu, Yufei Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-17T02:14:04Z","title":"The general spectral radius and majorization theorem of $t$-cone graphs with given degree sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06224","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":"sha256:726084702c2985e5d3c223bd4043d2eccdddd250a3148721c3aafa7a8a94489d","target":"record","created_at":"2026-07-04T23:58:13Z","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":"106d212ace3b5adbcc46ea577ec822b0a166e6782976437c4b07f9db2c18ccbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-17T02:14:04Z","title_canon_sha256":"992344686ee3071afa9432ccb6944f8616fc29b1be7406b1eab1d6a382762157"},"schema_version":"1.0","source":{"id":"1908.06224","kind":"arxiv","version":1}},"canonical_sha256":"f7d4e1a61f3cf0bd5bf0ba665b7f5d83ec8770928abcdb4b8827d0c4b2b09b9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7d4e1a61f3cf0bd5bf0ba665b7f5d83ec8770928abcdb4b8827d0c4b2b09b9b","first_computed_at":"2026-07-04T23:58:13.559389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:13.559389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zUXRhwWsOfPhUPDeoOHaG4hw83S82Uko5L1MQTpgjayvs52fdtmc98NFai7M8MewOZUnsq4CaKN9X61/q7yNCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:13.559884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:726084702c2985e5d3c223bd4043d2eccdddd250a3148721c3aafa7a8a94489d","sha256:f6382baa10a609d372c7266a6ed0cf389c6d1d707f75f21ad8a11bca9cb9975e"],"state_sha256":"6585f58e6aab7de9a09f9b72508e1c9dec62ecd1ffec5a252de1440a048f8a87"}