{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:2MXNIC6LS7QX7BPG75YVQOLKBN","short_pith_number":"pith:2MXNIC6L","canonical_record":{"source":{"id":"2110.12576","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-25T01:45:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"79d36c936160204bafb47fbbc96e19e5375677bda295dfb2c9f40dbe99f47160","abstract_canon_sha256":"71b61f9b9851b89e7979ecbf043cdb897534b64a1fcf208b1f7b99537e8f7bca"},"schema_version":"1.0"},"canonical_sha256":"d32ed40bcb97e17f85e6ff7158396a0b68123a579f9bb136b928ffb5e980511b","source":{"kind":"arxiv","id":"2110.12576","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:2MXNIC6LS7QX7BPG75YVQOLKBN","target":"record","payload":{"canonical_record":{"source":{"id":"2110.12576","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-10-25T01:45:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"79d36c936160204bafb47fbbc96e19e5375677bda295dfb2c9f40dbe99f47160","abstract_canon_sha256":"71b61f9b9851b89e7979ecbf043cdb897534b64a1fcf208b1f7b99537e8f7bca"},"schema_version":"1.0"},"canonical_sha256":"d32ed40bcb97e17f85e6ff7158396a0b68123a579f9bb136b928ffb5e980511b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:51:24.553851Z","signature_b64":"v7f5GSmLFx9v4AC330OpZJQPzi6to3kq5bMrYnskyBPgBWYzRs7tCFCjjqZR1kRWoCmgbOjQS/sNhrTwZbJHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d32ed40bcb97e17f85e6ff7158396a0b68123a579f9bb136b928ffb5e980511b","last_reissued_at":"2026-07-05T05:51:24.553503Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:51:24.553503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.12576","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wl/KXr975O+r18Y54ydioqbJtXWB+bUhbNaih2WXI0WY2FqxFH8IWRSeDBhH9ntXukJ4lAUSOmlE7hjmQTe2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T00:15:21.196238Z"},"content_sha256":"34dcec4cc4cdaa14b23f1d7a7ca623f1c24fa77f19464df77f9cb34637d20e45","schema_version":"1.0","event_id":"sha256:34dcec4cc4cdaa14b23f1d7a7ca623f1c24fa77f19464df77f9cb34637d20e45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:2MXNIC6LS7QX7BPG75YVQOLKBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximizing the Smallest Eigenvalue of Grounded Laplacian Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Run Wang, Wei Li, Xiaotian Zhou, Zhongzhi Zhang","submitted_at":"2021-10-25T01:45:50Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12576","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.12576/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e1QHe+oplUcvAC0fd52tRnAaLEqSUaDFG2QnUrVYIjF/gtOFZPBeZIevOBiVt94oB6oRqHya6cHihZROKpEgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T00:15:21.196530Z"},"content_sha256":"247e61948c1f08c210a756de05628c6a626a714a1da84798c33f12d3faa19ce0","schema_version":"1.0","event_id":"sha256:247e61948c1f08c210a756de05628c6a626a714a1da84798c33f12d3faa19ce0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2MXNIC6LS7QX7BPG75YVQOLKBN/bundle.json","state_url":"https://pith.science/pith/2MXNIC6LS7QX7BPG75YVQOLKBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2MXNIC6LS7QX7BPG75YVQOLKBN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-01T00:15:21Z","links":{"resolver":"https://pith.science/pith/2MXNIC6LS7QX7BPG75YVQOLKBN","bundle":"https://pith.science/pith/2MXNIC6LS7QX7BPG75YVQOLKBN/bundle.json","state":"https://pith.science/pith/2MXNIC6LS7QX7BPG75YVQOLKBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2MXNIC6LS7QX7BPG75YVQOLKBN/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PebnBul18RwA1I/d47gBSWSZbPZzKyrSA30iwWvoKtHWm+GBZO8EOFtWBgLu3XHvsJbo9+YufwwzLm/SV7lNCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T00:15:21.200739Z","bundle_sha256":"ea122cd99713bb198bfa3fcec2540721871b61529fee2f8a6f98a3a664e8cc73"}}