{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ME5B56257AAYDGI7Z2VH7ATP2L","short_pith_number":"pith:ME5B5625","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"},"canonical_sha256":"613a1efb5df80181991fceaa7f826fd2dffb2af7326231bf90d6a7960fe69bdf","source":{"kind":"arxiv","id":"1310.6477","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6477","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6477v1","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6477","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"ME5B56257AAY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"ME5B56257AAYDGI7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"ME5B5625","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ME5B56257AAYDGI7Z2VH7ATP2L","target":"record","payload":{"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"},"canonical_sha256":"613a1efb5df80181991fceaa7f826fd2dffb2af7326231bf90d6a7960fe69bdf","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"},"source_kind":"arxiv","source_id":"1310.6477","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"efAJPtNsF9EsQZNOwXQ6TICls1jYGGPzvbqapWbCDXefu3O2wcuEfNHzqXRLFCi5ya8CYyoXk9s+ZrbXncoUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:40:41.799805Z"},"content_sha256":"f19815b9769100ac91c24ccacd99c2c24f740705f1c26c207054df9e752465f9","schema_version":"1.0","event_id":"sha256:f19815b9769100ac91c24ccacd99c2c24f740705f1c26c207054df9e752465f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ME5B56257AAYDGI7Z2VH7ATP2L","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+AFuX4FU7l606MGVL1JGwDrJSutxyG9V50QO16t56AQ9QDsPkBvEYvoJ8Sp3O4RxGXJyOO1KKp1mXeS3haxCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:40:41.800152Z"},"content_sha256":"c7052bff85e33273906ac0cc81a4b9f9d8cd1a8068fd9869734bedd9be61416a","schema_version":"1.0","event_id":"sha256:c7052bff85e33273906ac0cc81a4b9f9d8cd1a8068fd9869734bedd9be61416a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/bundle.json","state_url":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ME5B56257AAYDGI7Z2VH7ATP2L/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":"2026-06-12T01:40:41Z","links":{"resolver":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L","bundle":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/bundle.json","state":"https://pith.science/pith/ME5B56257AAYDGI7Z2VH7ATP2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ME5B56257AAYDGI7Z2VH7ATP2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ME5B56257AAYDGI7Z2VH7ATP2L","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":"53e8977e1505941d73b7d0530101eac31b1b51a105df812e79a69ea12085c8f1","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-24T04:06:22Z","title_canon_sha256":"b0cdcb822457100e51e80b0d5fe471f5cfd3f5723e8cee6bbcbc611ef8a34f12"},"schema_version":"1.0","source":{"id":"1310.6477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6477","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6477v1","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6477","created_at":"2026-05-18T00:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"ME5B56257AAY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"ME5B56257AAYDGI7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"ME5B5625","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:c7052bff85e33273906ac0cc81a4b9f9d8cd1a8068fd9869734bedd9be61416a","target":"graph","created_at":"2026-05-18T00:18:56Z","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":"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","authors_text":"Ori Parzanchevski","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-24T04:06:22Z","title":"Mixing in high-dimensional expanders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6477","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:f19815b9769100ac91c24ccacd99c2c24f740705f1c26c207054df9e752465f9","target":"record","created_at":"2026-05-18T00:18:56Z","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":"53e8977e1505941d73b7d0530101eac31b1b51a105df812e79a69ea12085c8f1","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-24T04:06:22Z","title_canon_sha256":"b0cdcb822457100e51e80b0d5fe471f5cfd3f5723e8cee6bbcbc611ef8a34f12"},"schema_version":"1.0","source":{"id":"1310.6477","kind":"arxiv","version":1}},"canonical_sha256":"613a1efb5df80181991fceaa7f826fd2dffb2af7326231bf90d6a7960fe69bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"613a1efb5df80181991fceaa7f826fd2dffb2af7326231bf90d6a7960fe69bdf","first_computed_at":"2026-05-18T00:18:56.261921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:56.261921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2z3w9/FURSthGw0l9bZ/nj0FaMqUxwDgtAJf912OZBkqNwr7PFTMaY8ZQ1b41ItMQyj4VkNvt0rPniQNxYgYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:56.262365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f19815b9769100ac91c24ccacd99c2c24f740705f1c26c207054df9e752465f9","sha256:c7052bff85e33273906ac0cc81a4b9f9d8cd1a8068fd9869734bedd9be61416a"],"state_sha256":"8823821dd4ebbab443cd7d8c7c5652e825c878ef0b40814ba00123324b5923b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97fKQkxNb2coqLaRYSoMA0EcUXtHoAF0/NRj3rP3yul36JwxupgdUWjxvse9/MLNp32fOgGHfgSlhcE+Uky8DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:40:41.802066Z","bundle_sha256":"fc38f1496360c8fbf70024e504e4aefd26726a4a9f84fe7acda40a796e8cb7d5"}}