{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:V7ITKDLAWF2LUJN2H2EJ47YGYA","short_pith_number":"pith:V7ITKDLA","schema_version":"1.0","canonical_sha256":"afd1350d60b174ba25ba3e889e7f06c022ab697db87a6de492c1d6803e2dd444","source":{"kind":"arxiv","id":"1603.00386","version":1},"attestation_state":"computed","paper":{"title":"Forman curvature for complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"primary_cat":"q-bio.MN","authors_text":"Areejit Samal, Emil Saucan, J\\\"urgen Jost, Karthikeyan Mohanraj, R.P. Sreejith","submitted_at":"2016-03-01T18:15:41Z","abstract_excerpt":"We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However,"},"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":"1603.00386","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2016-03-01T18:15:41Z","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"title_canon_sha256":"0aca579c26e7a1ee67b68a28ec80c4359786f8fb057e75a4fb9b78e22ca17e61","abstract_canon_sha256":"87aa46f5d23cd40cca67aeb26a6fc925e3ec5abb3b6e7b7c3b3cec40355b0eb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:01.473908Z","signature_b64":"YqR4Lq21oU4TfoapdAeIF3rs7QOk+KVpZ2pEU/RfYDju6XV3LAXLBy6QWbb3ZhGC/mVoFHOwZnJKmA/7dDVZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afd1350d60b174ba25ba3e889e7f06c022ab697db87a6de492c1d6803e2dd444","last_reissued_at":"2026-05-18T01:12:01.473553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:01.473553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forman curvature for complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"primary_cat":"q-bio.MN","authors_text":"Areejit Samal, Emil Saucan, J\\\"urgen Jost, Karthikeyan Mohanraj, R.P. Sreejith","submitted_at":"2016-03-01T18:15:41Z","abstract_excerpt":"We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00386","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":"1603.00386","created_at":"2026-05-18T01:12:01.473616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.00386v1","created_at":"2026-05-18T01:12:01.473616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00386","created_at":"2026-05-18T01:12:01.473616+00:00"},{"alias_kind":"pith_short_12","alias_value":"V7ITKDLAWF2L","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"V7ITKDLAWF2LUJN2","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"V7ITKDLA","created_at":"2026-05-18T12:30:48.956258+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.14178","citing_title":"Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach","ref_index":255,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA","json":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA.json","graph_json":"https://pith.science/api/pith-number/V7ITKDLAWF2LUJN2H2EJ47YGYA/graph.json","events_json":"https://pith.science/api/pith-number/V7ITKDLAWF2LUJN2H2EJ47YGYA/events.json","paper":"https://pith.science/paper/V7ITKDLA"},"agent_actions":{"view_html":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA","download_json":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA.json","view_paper":"https://pith.science/paper/V7ITKDLA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.00386&json=true","fetch_graph":"https://pith.science/api/pith-number/V7ITKDLAWF2LUJN2H2EJ47YGYA/graph.json","fetch_events":"https://pith.science/api/pith-number/V7ITKDLAWF2LUJN2H2EJ47YGYA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA/action/storage_attestation","attest_author":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA/action/author_attestation","sign_citation":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA/action/citation_signature","submit_replication":"https://pith.science/pith/V7ITKDLAWF2LUJN2H2EJ47YGYA/action/replication_record"}},"created_at":"2026-05-18T01:12:01.473616+00:00","updated_at":"2026-05-18T01:12:01.473616+00:00"}