{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:6DL32Y2F3YLYGU6ABJ22DBAIW6","short_pith_number":"pith:6DL32Y2F","schema_version":"1.0","canonical_sha256":"f0d7bd6345de178353c00a75a18408b7ab0ea355f97ec51e0f4f3cfdab25acd5","source":{"kind":"arxiv","id":"2101.10177","version":1},"attestation_state":"computed","paper":{"title":"Relative Canonical Network Ensembles -- (Mis)characterizing Small-World Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"physics.soc-ph","authors_text":"Frank Hellmann, Nora Molkenthin, Oskar Pfeffer","submitted_at":"2021-01-25T15:47:50Z","abstract_excerpt":"What do generic networks that have certain properties look like? We define Relative Canonical Network ensembles as the ensembles that realize a property R while being as indistinguishable as possible from a generic network ensemble. This allows us to study the most generic features of the networks giving rise to the property under investigation. To test the approach we apply it first to the network measure \"small-world-ness\", thought to characterize small-world networks. We find several phase transitions as we go to less and less generic networks in which cliques and hubs emerge. Such features"},"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":"2101.10177","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.soc-ph","submitted_at":"2021-01-25T15:47:50Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"ca4966e39e24fa6cb96235de849f66f96b476c5a02dcd7592ab005bc913c087e","abstract_canon_sha256":"419a0c18a3c8f82610a72fadec7cfc23896a1c1a64090eade02f6dad928e1bc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:09:26.530381Z","signature_b64":"e0Xul8stRo0b868Jp6I3a++pTj0hhP2O/jPV44O4gWON6/8q2INbo/bB7FTXX5H2hCPxAT9fFUXN74x+JfReCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0d7bd6345de178353c00a75a18408b7ab0ea355f97ec51e0f4f3cfdab25acd5","last_reissued_at":"2026-07-05T02:09:26.530028Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:09:26.530028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative Canonical Network Ensembles -- (Mis)characterizing Small-World Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"physics.soc-ph","authors_text":"Frank Hellmann, Nora Molkenthin, Oskar Pfeffer","submitted_at":"2021-01-25T15:47:50Z","abstract_excerpt":"What do generic networks that have certain properties look like? We define Relative Canonical Network ensembles as the ensembles that realize a property R while being as indistinguishable as possible from a generic network ensemble. This allows us to study the most generic features of the networks giving rise to the property under investigation. To test the approach we apply it first to the network measure \"small-world-ness\", thought to characterize small-world networks. We find several phase transitions as we go to less and less generic networks in which cliques and hubs emerge. Such features"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.10177","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.10177/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2101.10177","created_at":"2026-07-05T02:09:26.530080+00:00"},{"alias_kind":"arxiv_version","alias_value":"2101.10177v1","created_at":"2026-07-05T02:09:26.530080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.10177","created_at":"2026-07-05T02:09:26.530080+00:00"},{"alias_kind":"pith_short_12","alias_value":"6DL32Y2F3YLY","created_at":"2026-07-05T02:09:26.530080+00:00"},{"alias_kind":"pith_short_16","alias_value":"6DL32Y2F3YLYGU6A","created_at":"2026-07-05T02:09:26.530080+00:00"},{"alias_kind":"pith_short_8","alias_value":"6DL32Y2F","created_at":"2026-07-05T02:09:26.530080+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/6DL32Y2F3YLYGU6ABJ22DBAIW6","json":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6.json","graph_json":"https://pith.science/api/pith-number/6DL32Y2F3YLYGU6ABJ22DBAIW6/graph.json","events_json":"https://pith.science/api/pith-number/6DL32Y2F3YLYGU6ABJ22DBAIW6/events.json","paper":"https://pith.science/paper/6DL32Y2F"},"agent_actions":{"view_html":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6","download_json":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6.json","view_paper":"https://pith.science/paper/6DL32Y2F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2101.10177&json=true","fetch_graph":"https://pith.science/api/pith-number/6DL32Y2F3YLYGU6ABJ22DBAIW6/graph.json","fetch_events":"https://pith.science/api/pith-number/6DL32Y2F3YLYGU6ABJ22DBAIW6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6/action/storage_attestation","attest_author":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6/action/author_attestation","sign_citation":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6/action/citation_signature","submit_replication":"https://pith.science/pith/6DL32Y2F3YLYGU6ABJ22DBAIW6/action/replication_record"}},"created_at":"2026-07-05T02:09:26.530080+00:00","updated_at":"2026-07-05T02:09:26.530080+00:00"}