{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EPYELA4UWWA7KPL2JW5GPJ2K5G","short_pith_number":"pith:EPYELA4U","canonical_record":{"source":{"id":"1602.04650","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-02-15T12:28:20Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"2a2fe38f44b0062780f16d6202d6fe991bbeb39a06caa779bd72ff191b5c2bd9","abstract_canon_sha256":"c59697c9b50c045c4610fb956ec12a55a40527a5b29f09235413dec63aa0e919"},"schema_version":"1.0"},"canonical_sha256":"23f0458394b581f53d7a4dba67a74ae9a313d6038d5e5edb2240eb23b6ea5a0f","source":{"kind":"arxiv","id":"1602.04650","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04650","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04650v2","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04650","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"EPYELA4UWWA7","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EPYELA4UWWA7KPL2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EPYELA4U","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EPYELA4UWWA7KPL2JW5GPJ2K5G","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04650","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-02-15T12:28:20Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"2a2fe38f44b0062780f16d6202d6fe991bbeb39a06caa779bd72ff191b5c2bd9","abstract_canon_sha256":"c59697c9b50c045c4610fb956ec12a55a40527a5b29f09235413dec63aa0e919"},"schema_version":"1.0"},"canonical_sha256":"23f0458394b581f53d7a4dba67a74ae9a313d6038d5e5edb2240eb23b6ea5a0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:19.726173Z","signature_b64":"WvJm4PAV1bg2nCICiYScLpQEauORNpn0uKseId0395Z4f96+BmlzJ716eZB4X3GeSkLpofhfYkJnezy2Ry9MAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23f0458394b581f53d7a4dba67a74ae9a313d6038d5e5edb2240eb23b6ea5a0f","last_reissued_at":"2026-05-18T01:03:19.725652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:19.725652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04650","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NY0BnricLcMJINGc+1fQybBaIdd1aPQbpuVs2UoIyjMEnqsPWi2REDcaQgdbMqI/yzunatsRF9g7u8I+EZ+CDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:47:42.481071Z"},"content_sha256":"c3615b3ed56e96df4b8b27a0c84a9ebedc7c49f60a803270d5e958e296c7375f","schema_version":"1.0","event_id":"sha256:c3615b3ed56e96df4b8b27a0c84a9ebedc7c49f60a803270d5e958e296c7375f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EPYELA4UWWA7KPL2JW5GPJ2K5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolae Are No Hyperbole: Modelling Communities That Are Not Cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Pauli Miettinen, Saskia Metzler, Stephan G\\\"unnemann","submitted_at":"2016-02-15T12:28:20Z","abstract_excerpt":"Cliques are frequently used to model communities: a community is a set of nodes where each pair is equally likely to be connected. But studying real-world communities reveals that they have more structure than that. In particular, the nodes can be ordered in such a way that (almost) all edges in the community lie below a hyperbola. In this paper we present three new models for communities that capture this phenomenon. Our models explain the structure of the communities differently, but we also prove that they are identical in their expressive power. Our models fit to real-world data much bette"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04650","kind":"arxiv","version":2},"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":"2026-05-18T01:03:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1DX8tWJku9B0dNgwko1XL5V88PN4zqrS5JzJ+EjGSCH/H4Q9/1KhVw1OLKRQ1Mo/FPev8grlqaa1yYeTLG3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:47:42.481873Z"},"content_sha256":"dec0833aab1ab410bdda10759aa7c34615194bfa4f0ab9c828b5eabf14ba2598","schema_version":"1.0","event_id":"sha256:dec0833aab1ab410bdda10759aa7c34615194bfa4f0ab9c828b5eabf14ba2598"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPYELA4UWWA7KPL2JW5GPJ2K5G/bundle.json","state_url":"https://pith.science/pith/EPYELA4UWWA7KPL2JW5GPJ2K5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPYELA4UWWA7KPL2JW5GPJ2K5G/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":"2026-06-07T18:47:42Z","links":{"resolver":"https://pith.science/pith/EPYELA4UWWA7KPL2JW5GPJ2K5G","bundle":"https://pith.science/pith/EPYELA4UWWA7KPL2JW5GPJ2K5G/bundle.json","state":"https://pith.science/pith/EPYELA4UWWA7KPL2JW5GPJ2K5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPYELA4UWWA7KPL2JW5GPJ2K5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EPYELA4UWWA7KPL2JW5GPJ2K5G","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":"c59697c9b50c045c4610fb956ec12a55a40527a5b29f09235413dec63aa0e919","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-02-15T12:28:20Z","title_canon_sha256":"2a2fe38f44b0062780f16d6202d6fe991bbeb39a06caa779bd72ff191b5c2bd9"},"schema_version":"1.0","source":{"id":"1602.04650","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04650","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04650v2","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04650","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"EPYELA4UWWA7","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EPYELA4UWWA7KPL2","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EPYELA4U","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:dec0833aab1ab410bdda10759aa7c34615194bfa4f0ab9c828b5eabf14ba2598","target":"graph","created_at":"2026-05-18T01:03:19Z","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":"Cliques are frequently used to model communities: a community is a set of nodes where each pair is equally likely to be connected. But studying real-world communities reveals that they have more structure than that. In particular, the nodes can be ordered in such a way that (almost) all edges in the community lie below a hyperbola. In this paper we present three new models for communities that capture this phenomenon. Our models explain the structure of the communities differently, but we also prove that they are identical in their expressive power. Our models fit to real-world data much bette","authors_text":"Pauli Miettinen, Saskia Metzler, Stephan G\\\"unnemann","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-02-15T12:28:20Z","title":"Hyperbolae Are No Hyperbole: Modelling Communities That Are Not Cliques"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04650","kind":"arxiv","version":2},"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:c3615b3ed56e96df4b8b27a0c84a9ebedc7c49f60a803270d5e958e296c7375f","target":"record","created_at":"2026-05-18T01:03:19Z","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":"c59697c9b50c045c4610fb956ec12a55a40527a5b29f09235413dec63aa0e919","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-02-15T12:28:20Z","title_canon_sha256":"2a2fe38f44b0062780f16d6202d6fe991bbeb39a06caa779bd72ff191b5c2bd9"},"schema_version":"1.0","source":{"id":"1602.04650","kind":"arxiv","version":2}},"canonical_sha256":"23f0458394b581f53d7a4dba67a74ae9a313d6038d5e5edb2240eb23b6ea5a0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23f0458394b581f53d7a4dba67a74ae9a313d6038d5e5edb2240eb23b6ea5a0f","first_computed_at":"2026-05-18T01:03:19.725652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:19.725652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WvJm4PAV1bg2nCICiYScLpQEauORNpn0uKseId0395Z4f96+BmlzJ716eZB4X3GeSkLpofhfYkJnezy2Ry9MAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:19.726173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04650","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3615b3ed56e96df4b8b27a0c84a9ebedc7c49f60a803270d5e958e296c7375f","sha256:dec0833aab1ab410bdda10759aa7c34615194bfa4f0ab9c828b5eabf14ba2598"],"state_sha256":"d95b74c712a350a4ba2811dad4c36ae141b35ab5606bdea3bce9e161ffbce779"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qgc+FNoaZ8MXvAHIIa/dpUW2HC7ndkjfEhL4DzaWPKtWPIQiaQTet/9iPsTJl3egR5NGfENMFhPairqQ1QGLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:47:42.485875Z","bundle_sha256":"54fe864ab14df4f879dbea8f4627dcec25866d232a2e48d8a92b12033f8bb976"}}