{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TIBH3TIWDAJBSTUVLPLQ3YSW2F","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":"bdeb29759fbcb4480c098fea83050ce74902d75f9d4bd29402b21b6757aea8aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T17:30:09Z","title_canon_sha256":"e31fb2558f70a66dc6840503d2321c0f9c1af1ed5174272fa2a83728b3d36910"},"schema_version":"1.0","source":{"id":"1110.2444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2444","created_at":"2026-05-18T04:11:09Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2444v1","created_at":"2026-05-18T04:11:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2444","created_at":"2026-05-18T04:11:09Z"},{"alias_kind":"pith_short_12","alias_value":"TIBH3TIWDAJB","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TIBH3TIWDAJBSTUV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TIBH3TIW","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:cf869e7c573b23ff4e60c78c525796c4be37dc152795c5175dedd986e90d14af","target":"graph","created_at":"2026-05-18T04:11:09Z","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":"The spectral radius $\\rho(G)$ of a graph $G$ is the largest eigenvalue of its adjacency matrix $A(G)$. For a fixed integer $e\\ge 1$, let $G^{min}_{n,n-e}$ be a graph with minimal spectral radius among all connected graphs on $n$ vertices with diameter $n-e$. Let $P_{n_1,n_2,...,n_t,p}^{m_1,m_2,...,m_t}$ be a tree obtained from a path of $p$ vertices ($0 \\sim 1 \\sim 2 \\sim ... \\sim (p-1)$) by linking one pendant path $P_{n_i}$ at $m_i$ for each $i\\in\\{1,2,...,t\\}$. For $e=1,2,3,4,5$, $G^{min}_{n,n-e}$ were determined in the literature. Cioab\\v{a}-van Dam-Koolen-Lee \\cite{CDK} conjectured for fi","authors_text":"Jingfen Lan, Lingsheng Shi, Linyuan Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T17:30:09Z","title":"Graphs with Diameter $n-e$ Minimizing the Spectral Radius"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2444","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:eb95030c3322004492713d40fdb44b52ad4e1da2c502a36e8cf9ca809704e96f","target":"record","created_at":"2026-05-18T04:11:09Z","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":"bdeb29759fbcb4480c098fea83050ce74902d75f9d4bd29402b21b6757aea8aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-11T17:30:09Z","title_canon_sha256":"e31fb2558f70a66dc6840503d2321c0f9c1af1ed5174272fa2a83728b3d36910"},"schema_version":"1.0","source":{"id":"1110.2444","kind":"arxiv","version":1}},"canonical_sha256":"9a027dcd161812194e955bd70de256d14e29f198e0c113e29e8feef02f74eb0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a027dcd161812194e955bd70de256d14e29f198e0c113e29e8feef02f74eb0c","first_computed_at":"2026-05-18T04:11:09.027370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:09.027370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0HGCk8xUExu9A+DymyEKy8hbF1rysBwavYNOGEaRgMaf4NAAZ4FBkv3vq+nX80bDR80pa03I9E4rNNVA138RDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:09.027986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb95030c3322004492713d40fdb44b52ad4e1da2c502a36e8cf9ca809704e96f","sha256:cf869e7c573b23ff4e60c78c525796c4be37dc152795c5175dedd986e90d14af"],"state_sha256":"c9d96c6556db863a8e8b970044756ee196318efd7ce0d689ba3ef103e4c4f972"}