{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SIHRXOLSAFYUOURFOJAWXCPSU5","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":"eb98dd56ccabadde808ff9b8ca04c64b2c7e6c0448119fa83ef6f8d8d00484e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-05-05T03:32:27Z","title_canon_sha256":"5a42e7d5857502ecd640943cce6c80bf4e661e9bd57ecaef15c4fc89a3b60169"},"schema_version":"1.0","source":{"id":"1605.01483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01483","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01483v1","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01483","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"SIHRXOLSAFYU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SIHRXOLSAFYUOURF","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SIHRXOLS","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:8ac185b3865f52de1e7d8e98966ce82a2e5855d404b07ea719227075cea9f509","target":"graph","created_at":"2026-05-18T01:15:33Z","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 celebrated Cheeger's Inequality establishes a bound on the edge expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency matrix (and other related matrices) of graphs. It has remained open to define a suitable spectral model for hypergraphs whose spectra can be used to estimate various combinatorial properties of the hypergraph.\n  In this paper we introduce a new hypergraph Laplacian operator generalizing the Laplacian matrix of graphs. In particular, the operator is induced by","authors_text":"Anand Louis, Chenzi Zhang, T-H. Hubert Chan, Zhihao Gavin Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-05-05T03:32:27Z","title":"Spectral Properties of Hypergraph Laplacian and Approximation Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01483","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:ee10cee642ab6121d75cb43fcf92bea7f772ab4f3f2067ece60ac664612e27c3","target":"record","created_at":"2026-05-18T01:15:33Z","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":"eb98dd56ccabadde808ff9b8ca04c64b2c7e6c0448119fa83ef6f8d8d00484e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-05-05T03:32:27Z","title_canon_sha256":"5a42e7d5857502ecd640943cce6c80bf4e661e9bd57ecaef15c4fc89a3b60169"},"schema_version":"1.0","source":{"id":"1605.01483","kind":"arxiv","version":1}},"canonical_sha256":"920f1bb972017147522572416b89f2a76125065890e6858339d68dd9c3e7976c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"920f1bb972017147522572416b89f2a76125065890e6858339d68dd9c3e7976c","first_computed_at":"2026-05-18T01:15:33.560381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:33.560381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kox/iYAZcPlNHf2HmNy+1YcPD0s1L3gEXTblX5QTTBU0MlEPtvYP3hvsgiISrBipLz65cmz0G6ZFBtfh6JtzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:33.561018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee10cee642ab6121d75cb43fcf92bea7f772ab4f3f2067ece60ac664612e27c3","sha256:8ac185b3865f52de1e7d8e98966ce82a2e5855d404b07ea719227075cea9f509"],"state_sha256":"31e8b1da67d600d7a5d759349e08da467f8fec064bfa2e87adca739885c6bc5b"}