{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7YB6VMK2K36XMHSJWZLFTBYJED","short_pith_number":"pith:7YB6VMK2","schema_version":"1.0","canonical_sha256":"fe03eab15a56fd761e49b65659870920eab2054ae0e12a738227e2b818acf0c7","source":{"kind":"arxiv","id":"1712.02943","version":1},"attestation_state":"computed","paper":{"title":"Comparing Three Notions of Discrete Ricci Curvature on Biological Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.MN","authors_text":"Allen Tannenbaum, James Mathews, Maryam Pouryahya","submitted_at":"2017-12-08T05:17:03Z","abstract_excerpt":"In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we employ possible generalizations of the notion of Ricci curvature on Riemannian manifold to discrete spaces in order to infer certain robustness properties of the networks of interest. We compare three possible discrete notions of Ricci curvature (Olivier Ricci curvature, Bakry-\\'Emery Ricci curvature, and Forman Ricci curvature) on some model and biological "},"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":"1712.02943","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2017-12-08T05:17:03Z","cross_cats_sorted":[],"title_canon_sha256":"682fdb632dd24e6ab7d2315339d4a981e3110d34f12d43d656d4f570362a0ffb","abstract_canon_sha256":"e8e5e206866acded2df03e8c3f6c0776e042ccb7422f8957c5ac2116f0c7c89e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:28.820385Z","signature_b64":"rlwZ7OhgExBtRLj7CldRiOWD7CXqTz+/KqwYUxzwRtdBzq7D/AWvghNR0GI9vXZLceqhhQkrhdiv5y0NT02SDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe03eab15a56fd761e49b65659870920eab2054ae0e12a738227e2b818acf0c7","last_reissued_at":"2026-05-18T00:28:28.819862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:28.819862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparing Three Notions of Discrete Ricci Curvature on Biological Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.MN","authors_text":"Allen Tannenbaum, James Mathews, Maryam Pouryahya","submitted_at":"2017-12-08T05:17:03Z","abstract_excerpt":"In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we employ possible generalizations of the notion of Ricci curvature on Riemannian manifold to discrete spaces in order to infer certain robustness properties of the networks of interest. We compare three possible discrete notions of Ricci curvature (Olivier Ricci curvature, Bakry-\\'Emery Ricci curvature, and Forman Ricci curvature) on some model and biological "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02943","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":"1712.02943","created_at":"2026-05-18T00:28:28.819959+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.02943v1","created_at":"2026-05-18T00:28:28.819959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02943","created_at":"2026-05-18T00:28:28.819959+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YB6VMK2K36X","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YB6VMK2K36XMHSJ","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YB6VMK2","created_at":"2026-05-18T12:31:05.417338+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/7YB6VMK2K36XMHSJWZLFTBYJED","json":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED.json","graph_json":"https://pith.science/api/pith-number/7YB6VMK2K36XMHSJWZLFTBYJED/graph.json","events_json":"https://pith.science/api/pith-number/7YB6VMK2K36XMHSJWZLFTBYJED/events.json","paper":"https://pith.science/paper/7YB6VMK2"},"agent_actions":{"view_html":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED","download_json":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED.json","view_paper":"https://pith.science/paper/7YB6VMK2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.02943&json=true","fetch_graph":"https://pith.science/api/pith-number/7YB6VMK2K36XMHSJWZLFTBYJED/graph.json","fetch_events":"https://pith.science/api/pith-number/7YB6VMK2K36XMHSJWZLFTBYJED/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED/action/storage_attestation","attest_author":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED/action/author_attestation","sign_citation":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED/action/citation_signature","submit_replication":"https://pith.science/pith/7YB6VMK2K36XMHSJWZLFTBYJED/action/replication_record"}},"created_at":"2026-05-18T00:28:28.819959+00:00","updated_at":"2026-05-18T00:28:28.819959+00:00"}