{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ME5B56257AAYDGI7Z2VH7ATP2L","short_pith_number":"pith:ME5B5625","schema_version":"1.0","canonical_sha256":"613a1efb5df80181991fceaa7f826fd2dffb2af7326231bf90d6a7960fe69bdf","source":{"kind":"arxiv","id":"1310.6477","version":1},"attestation_state":"computed","paper":{"title":"Mixing in high-dimensional expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CO","authors_text":"Ori Parzanchevski","submitted_at":"2013-10-24T04:06:22Z","abstract_excerpt":"We prove a generalization of the Expander Mixing Lemma for arbitrary (finite) simplicial complexes. The original lemma states that concentration of the Laplace spectrum of a graph implies combinatorial expansion (which is also referred to as mixing, or quasi-randomness). Recently, an analogue of this Lemma was proved for simplicial complexes of arbitrary dimension, provided that the skeleton of the complex is complete. More precisely, it was shown that a concentrated spectrum of the simplicial Hodge Laplacian implies a similar type of expansion as in graphs. In this paper we remove the assumpt"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.6477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-24T04:06:22Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"b0cdcb822457100e51e80b0d5fe471f5cfd3f5723e8cee6bbcbc611ef8a34f12","abstract_canon_sha256":"53e8977e1505941d73b7d0530101eac31b1b51a105df812e79a69ea12085c8f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:56.262365Z","signature_b64":"2z3w9/FURSthGw0l9bZ/nj0FaMqUxwDgtAJf912OZBkqNwr7PFTMaY8ZQ1b41ItMQyj4VkNvt0rPniQNxYgYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"613a1efb5df80181991fceaa7f826fd2dffb2af7326231bf90d6a7960fe69bdf","last_reissued_at":"2026-05-18T00:18:56.261921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:56.261921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixing in high-dimensional expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CO","authors_text":"Ori Parzanchevski","submitted_at":"2013-10-24T04:06:22Z","abstract_excerpt":"We prove a generalization of the Expander Mixing Lemma for arbitrary (finite) simplicial complexes. The original lemma states that concentration of the Laplace spectrum of a graph implies combinatorial expansion (which is also referred to as mixing, or quasi-randomness). Recently, an analogue of this Lemma was proved for simplicial complexes of arbitrary dimension, provided that the skeleton of the complex is complete. More precisely, it was shown that a concentrated spectrum of the simplicial Hodge Laplacian implies a similar type of expansion as in graphs. In this paper we remove the assumpt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6477","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.6477","created_at":"2026-05-18T00:18:56.261984+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.6477v1","created_at":"2026-05-18T00:18:56.261984+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6477","created_at":"2026-05-18T00:18:56.261984+00:00"},{"alias_kind":"pith_short_12","alias_value":"ME5B56257AAY","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"ME5B56257AAYDGI7","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"ME5B5625","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L","json":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L.json","graph_json":"https://pith.science/api/pith-number/ME5B56257AAYDGI7Z2VH7ATP2L/graph.json","events_json":"https://pith.science/api/pith-number/ME5B56257AAYDGI7Z2VH7ATP2L/events.json","paper":"https://pith.science/paper/ME5B5625"},"agent_actions":{"view_html":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L","download_json":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L.json","view_paper":"https://pith.science/paper/ME5B5625","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.6477&json=true","fetch_graph":"https://pith.science/api/pith-number/ME5B56257AAYDGI7Z2VH7ATP2L/graph.json","fetch_events":"https://pith.science/api/pith-number/ME5B56257AAYDGI7Z2VH7ATP2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/action/storage_attestation","attest_author":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/action/author_attestation","sign_citation":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/action/citation_signature","submit_replication":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/action/replication_record"}},"created_at":"2026-05-18T00:18:56.261984+00:00","updated_at":"2026-05-18T00:18:56.261984+00:00"}