{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2MXNIC6LS7QX7BPG75YVQOLKBN","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":"71b61f9b9851b89e7979ecbf043cdb897534b64a1fcf208b1f7b99537e8f7bca","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-25T01:45:50Z","title_canon_sha256":"79d36c936160204bafb47fbbc96e19e5375677bda295dfb2c9f40dbe99f47160"},"schema_version":"1.0","source":{"id":"2110.12576","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.12576","created_at":"2026-07-05T05:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"2110.12576v4","created_at":"2026-07-05T05:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.12576","created_at":"2026-07-05T05:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"2MXNIC6LS7QX","created_at":"2026-07-05T05:51:24Z"},{"alias_kind":"pith_short_16","alias_value":"2MXNIC6LS7QX7BPG","created_at":"2026-07-05T05:51:24Z"},{"alias_kind":"pith_short_8","alias_value":"2MXNIC6L","created_at":"2026-07-05T05:51:24Z"}],"graph_snapshots":[{"event_id":"sha256:247e61948c1f08c210a756de05628c6a626a714a1da84798c33f12d3faa19ce0","target":"graph","created_at":"2026-07-05T05:51:24Z","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/2110.12576/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a connected graph $\\mathcal{G}=(V,E)$ with $n$ nodes, $m$ edges, and Laplacian matrix $\\boldsymbol{{\\mathit{L}}}$, a grounded Laplacian matrix $\\boldsymbol{{\\mathit{L}}}(S)$ of $\\mathcal{G}$ is a $(n-k) \\times (n-k)$ principal submatrix of $\\boldsymbol{{\\mathit{L}}}$, obtained from $\\boldsymbol{{\\mathit{L}}}$ by deleting $k$ rows and columns corresponding to $k$ selected nodes forming a set $S\\subseteq V$. The smallest eigenvalue $\\lambda(S)$ of $\\boldsymbol{{\\mathit{L}}}(S)$ plays a pivotal role in various dynamics defined on $\\mathcal{G}$. For example, $\\lambda(S)$ characterizes the conv","authors_text":"Run Wang, Wei Li, Xiaotian Zhou, Zhongzhi Zhang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-25T01:45:50Z","title":"Maximizing the Smallest Eigenvalue of Grounded Laplacian Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12576","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":"sha256:34dcec4cc4cdaa14b23f1d7a7ca623f1c24fa77f19464df77f9cb34637d20e45","target":"record","created_at":"2026-07-05T05:51:24Z","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":"71b61f9b9851b89e7979ecbf043cdb897534b64a1fcf208b1f7b99537e8f7bca","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-25T01:45:50Z","title_canon_sha256":"79d36c936160204bafb47fbbc96e19e5375677bda295dfb2c9f40dbe99f47160"},"schema_version":"1.0","source":{"id":"2110.12576","kind":"arxiv","version":4}},"canonical_sha256":"d32ed40bcb97e17f85e6ff7158396a0b68123a579f9bb136b928ffb5e980511b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d32ed40bcb97e17f85e6ff7158396a0b68123a579f9bb136b928ffb5e980511b","first_computed_at":"2026-07-05T05:51:24.553503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:51:24.553503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v7f5GSmLFx9v4AC330OpZJQPzi6to3kq5bMrYnskyBPgBWYzRs7tCFCjjqZR1kRWoCmgbOjQS/sNhrTwZbJHCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:51:24.553851Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.12576","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34dcec4cc4cdaa14b23f1d7a7ca623f1c24fa77f19464df77f9cb34637d20e45","sha256:247e61948c1f08c210a756de05628c6a626a714a1da84798c33f12d3faa19ce0"],"state_sha256":"3d0125f091f6e57e443f38449130a22b91e6e68b0d06f928a3417c4367addb51"}