{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LF452LHGWY3KPB2KJNRVDEHHBY","short_pith_number":"pith:LF452LHG","canonical_record":{"source":{"id":"1603.06898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-22T18:28:09Z","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"title_canon_sha256":"3be2f6a50cface3b9d8e1bbe48ff3965d67cc13c150de2e6d1be3c9498353e00","abstract_canon_sha256":"1d01e445d8a0835eb5f6dc350513ae7237cf0605fe0853136858f8d582923d51"},"schema_version":"1.0"},"canonical_sha256":"5979dd2ce6b636a7874a4b635190e70e13f0ed280e733e2ab4db6b267b5ade70","source":{"kind":"arxiv","id":"1603.06898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06898","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06898v1","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06898","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"LF452LHGWY3K","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LF452LHGWY3KPB2K","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LF452LHG","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LF452LHGWY3KPB2KJNRVDEHHBY","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-22T18:28:09Z","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"title_canon_sha256":"3be2f6a50cface3b9d8e1bbe48ff3965d67cc13c150de2e6d1be3c9498353e00","abstract_canon_sha256":"1d01e445d8a0835eb5f6dc350513ae7237cf0605fe0853136858f8d582923d51"},"schema_version":"1.0"},"canonical_sha256":"5979dd2ce6b636a7874a4b635190e70e13f0ed280e733e2ab4db6b267b5ade70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:34.475773Z","signature_b64":"oSccNj5BkhMev2b1fBgAIqWTwLCNt7iloEkQ5hHSHcB4fLLKl/KttXysr2AI8Fn5qPLeGehCPndOVM6YnIJfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5979dd2ce6b636a7874a4b635190e70e13f0ed280e733e2ab4db6b267b5ade70","last_reissued_at":"2026-05-18T01:18:34.475228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:34.475228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06898","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":"2026-05-18T01:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rws/QbCUyzvbEHn6LiUzhrljaZTKye+MaeXUBKYHpN687QlfGdFweWjwufK2FmLsk0py8ibYAyHRvJpM55q1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:25:16.422025Z"},"content_sha256":"928f9d8e9280a09605b25a71d45e5b2edaf3d39f88acc2b470b97d6743b0f807","schema_version":"1.0","event_id":"sha256:928f9d8e9280a09605b25a71d45e5b2edaf3d39f88acc2b470b97d6743b0f807"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LF452LHGWY3KPB2KJNRVDEHHBY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edge-exchangeable graphs and sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Diana Cai, Tamara Broderick","submitted_at":"2016-03-22T18:28:09Z","abstract_excerpt":"A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability for random graphs in contrast to the established notion of infinite exchangeability for random graphs --- which has traditionally relied on exchangeability of nodes (rather than edges) in a graph. We show that, unlike node exchangeability, edge exchangeability encompasses models "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06898","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":"2026-05-18T01:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z406uy7AoYLhtXxCiXxNRsshsssJHRY4vKx9jM2wFJNsAu2yV4ZSaCRiIofrG0QRwi1loubWenznYg1Agg/6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:25:16.422382Z"},"content_sha256":"32ef817777862852c2c34c3ac707caa47c682ef91ca13505621c1cb4516eb830","schema_version":"1.0","event_id":"sha256:32ef817777862852c2c34c3ac707caa47c682ef91ca13505621c1cb4516eb830"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LF452LHGWY3KPB2KJNRVDEHHBY/bundle.json","state_url":"https://pith.science/pith/LF452LHGWY3KPB2KJNRVDEHHBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LF452LHGWY3KPB2KJNRVDEHHBY/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":"2026-06-23T02:25:16Z","links":{"resolver":"https://pith.science/pith/LF452LHGWY3KPB2KJNRVDEHHBY","bundle":"https://pith.science/pith/LF452LHGWY3KPB2KJNRVDEHHBY/bundle.json","state":"https://pith.science/pith/LF452LHGWY3KPB2KJNRVDEHHBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LF452LHGWY3KPB2KJNRVDEHHBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LF452LHGWY3KPB2KJNRVDEHHBY","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":"1d01e445d8a0835eb5f6dc350513ae7237cf0605fe0853136858f8d582923d51","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-22T18:28:09Z","title_canon_sha256":"3be2f6a50cface3b9d8e1bbe48ff3965d67cc13c150de2e6d1be3c9498353e00"},"schema_version":"1.0","source":{"id":"1603.06898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06898","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06898v1","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06898","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"LF452LHGWY3K","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LF452LHGWY3KPB2K","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LF452LHG","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:32ef817777862852c2c34c3ac707caa47c682ef91ca13505621c1cb4516eb830","target":"graph","created_at":"2026-05-18T01:18:34Z","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":"A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability for random graphs in contrast to the established notion of infinite exchangeability for random graphs --- which has traditionally relied on exchangeability of nodes (rather than edges) in a graph. We show that, unlike node exchangeability, edge exchangeability encompasses models ","authors_text":"Diana Cai, Tamara Broderick","cross_cats":["stat.ME","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-22T18:28:09Z","title":"Edge-exchangeable graphs and sparsity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06898","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":"sha256:928f9d8e9280a09605b25a71d45e5b2edaf3d39f88acc2b470b97d6743b0f807","target":"record","created_at":"2026-05-18T01:18:34Z","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":"1d01e445d8a0835eb5f6dc350513ae7237cf0605fe0853136858f8d582923d51","cross_cats_sorted":["stat.ME","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-22T18:28:09Z","title_canon_sha256":"3be2f6a50cface3b9d8e1bbe48ff3965d67cc13c150de2e6d1be3c9498353e00"},"schema_version":"1.0","source":{"id":"1603.06898","kind":"arxiv","version":1}},"canonical_sha256":"5979dd2ce6b636a7874a4b635190e70e13f0ed280e733e2ab4db6b267b5ade70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5979dd2ce6b636a7874a4b635190e70e13f0ed280e733e2ab4db6b267b5ade70","first_computed_at":"2026-05-18T01:18:34.475228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:34.475228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oSccNj5BkhMev2b1fBgAIqWTwLCNt7iloEkQ5hHSHcB4fLLKl/KttXysr2AI8Fn5qPLeGehCPndOVM6YnIJfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:34.475773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:928f9d8e9280a09605b25a71d45e5b2edaf3d39f88acc2b470b97d6743b0f807","sha256:32ef817777862852c2c34c3ac707caa47c682ef91ca13505621c1cb4516eb830"],"state_sha256":"8f6c85048d1c70d85b276c547b62f1e89254ac3256d563c11a467fd894f5541f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+V1v5IqwAT0P+5CG3o2L2RX4n0C3qhWTp/cglmV5q2w9UhrN2/pKfVbab+HQ/22v5asq/W7RSXXSBxzNXVt+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:25:16.424337Z","bundle_sha256":"188a3c4ebfdb0bc91774949122bff499a291423e0f6c855dc93615fa070efdbd"}}