{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CJMEYNTZBB7UZW55ZC24JHUT5E","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":"e92d98383c4ed194bea25f7f51956b876afed876497b0e503ea89d75e1aedf8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-12T21:23:27Z","title_canon_sha256":"53f5c71d6ccc95600881f4be115044a385121ab85e182d082be94483bad1bb2c"},"schema_version":"1.0","source":{"id":"1307.3582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3582","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3582v1","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3582","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"CJMEYNTZBB7U","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CJMEYNTZBB7UZW55","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CJMEYNTZ","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:08638075912db29a6cb619a57547c2c74c6e3dba46002f9baf6619e73d5204f6","target":"graph","created_at":"2026-05-18T03:18:28Z","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 X be a 2-dimensional simplicial complex. The degree of an edge e is the number of 2-faces of X containing e. The complex X is an \\epsilon-expander if the coboundary d_1(\\phi) of every Z_2-valued 1-cochain \\phi \\in C^1(X;Z_2) satisfies |support(d_1(\\phi))| \\geq \\epsilon |\\supp(\\phi+d_0(\\psi))| for some 0-cochain \\psi. Using a new model of random 2-complexes we show the existence of an infinite family of 2-dimensional \\epsilon-expanders with maximum edge degree d, for some fixed \\epsilon>0 and d.","authors_text":"Alexander Lubotzky, Roy Meshulam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-12T21:23:27Z","title":"Random Latin squares and 2-dimensional expanders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3582","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":"sha256:575b5e69098fcc33e45ad6df8021e45f522a1a0eb684feea1f4b035e80aaf1f1","target":"record","created_at":"2026-05-18T03:18:28Z","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":"e92d98383c4ed194bea25f7f51956b876afed876497b0e503ea89d75e1aedf8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-12T21:23:27Z","title_canon_sha256":"53f5c71d6ccc95600881f4be115044a385121ab85e182d082be94483bad1bb2c"},"schema_version":"1.0","source":{"id":"1307.3582","kind":"arxiv","version":1}},"canonical_sha256":"12584c3679087f4cdbbdc8b5c49e93e929774d8ea6fe621d99823d1eb8cb3d2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12584c3679087f4cdbbdc8b5c49e93e929774d8ea6fe621d99823d1eb8cb3d2e","first_computed_at":"2026-05-18T03:18:28.496765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:28.496765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JcE3NtBoPpKB0dQflr/ZE0MVbIRs0+HR9kPcXooECL1ntQ0ioe+c6Ic6C5oQtQc1F3jc8Ighwk5agIgdx3ZzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:28.497186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:575b5e69098fcc33e45ad6df8021e45f522a1a0eb684feea1f4b035e80aaf1f1","sha256:08638075912db29a6cb619a57547c2c74c6e3dba46002f9baf6619e73d5204f6"],"state_sha256":"49eac93a656c6114f5937f87ee55e85c1dd16782757c694d3b5f9f211a1869b9"}