{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DSRB4L7GOZS7OE5QXGXT36D57I","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":"6baf9ef444ac3a77dd887dd39955b40332e0f497b1527a3c23f959750fecaeb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-23T21:19:30Z","title_canon_sha256":"008560d7a7cca96c3d06aa5ea9c467648a68f5a7e86e694548604246c75a84a4"},"schema_version":"1.0","source":{"id":"1208.4863","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4863","created_at":"2026-05-18T03:14:06Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4863v4","created_at":"2026-05-18T03:14:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4863","created_at":"2026-05-18T03:14:06Z"},{"alias_kind":"pith_short_12","alias_value":"DSRB4L7GOZS7","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DSRB4L7GOZS7OE5Q","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DSRB4L7G","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:1adfd6abdfb1814ae81431f455950a371a7cd1435ff4d48389d606603ebd0eff","target":"graph","created_at":"2026-05-18T03:14:06Z","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":"Let p(k) denote the partition function of k. For each k >= 2, we describe a list of p(k)-1 quasirandom properties that a k-uniform hypergraph can have. Our work connects previous notions on linear hypergraph quasirandomness of Kohayakawa-R\\\"odl-Skokan and Conlon-H\\`{a}n-Person-Schacht and the spectral approach of Friedman-Wigderson. For each of the quasirandom properties that are described, we define a largest and second largest eigenvalue. We show that a hypergraph satisfies these quasirandom properties if and only if it has a large spectral gap. This answers a question of Conlon-H\\`{a}n-Pers","authors_text":"Dhruv Mubayi, John Lenz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-23T21:19:30Z","title":"Eigenvalues and Linear Quasirandom Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4863","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":"sha256:0eeb7ca1e99df69e74a5c9c809d05f4742ff56a2a7aa89f38379317ae31b1a5b","target":"record","created_at":"2026-05-18T03:14:06Z","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":"6baf9ef444ac3a77dd887dd39955b40332e0f497b1527a3c23f959750fecaeb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-23T21:19:30Z","title_canon_sha256":"008560d7a7cca96c3d06aa5ea9c467648a68f5a7e86e694548604246c75a84a4"},"schema_version":"1.0","source":{"id":"1208.4863","kind":"arxiv","version":4}},"canonical_sha256":"1ca21e2fe67665f713b0b9af3df87dfa200c71e202e2b2e80d4bc9a6e28e9055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ca21e2fe67665f713b0b9af3df87dfa200c71e202e2b2e80d4bc9a6e28e9055","first_computed_at":"2026-05-18T03:14:06.985275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:06.985275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+qDm2sdCEVA3dgwx/imam+qO61WhUNgpe0LdLUNeS8c4x2sWPKQkwglhlTEBGK9R6vZEHRM5a41QaVOU0iwmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:06.985941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4863","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eeb7ca1e99df69e74a5c9c809d05f4742ff56a2a7aa89f38379317ae31b1a5b","sha256:1adfd6abdfb1814ae81431f455950a371a7cd1435ff4d48389d606603ebd0eff"],"state_sha256":"7ac905567e0eb40d5a1275255021bf78faa968d7b44c93c4134e99e07bc32109"}