{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3JV4LXIVJNG22XQQHHZ63OTDX6","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":"58ddc625af1309669bf46e79bc4e68c0a90d2c9647237a0a5ec1eda43cd70262","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2016-05-16T06:36:44Z","title_canon_sha256":"a0cef0a5653be5fae696a0be514d56d81facc9794a80b07da22836a18c3aedfb"},"schema_version":"1.0","source":{"id":"1605.04662","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04662","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04662v2","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04662","created_at":"2026-05-18T00:50:01Z"},{"alias_kind":"pith_short_12","alias_value":"3JV4LXIVJNG2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3JV4LXIVJNG22XQQ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3JV4LXIV","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:14bb9f049426b4c6af8175858458f4f679569515ae12a6d1d52e9e23131f801f","target":"graph","created_at":"2026-05-18T00:50:01Z","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 goal in network science is the geometrical characterization of complex networks. In this direction, we (arXiv:1603.00386; J. Stat. Mech. (2016) P063206) have recently introduced the Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of Forman curvature in diverse model and real-world undirected networks revealed that this measure captures several aspects of the organization of complex undirected networks. However, many important real-world networks are inherently directed in nature, and the Forman curvature for undirected networks is unsuitable for ","authors_text":"Areejit Samal, Emil Saucan, J\\\"urgen Jost, R.P. Sreejith","cross_cats":["cond-mat.dis-nn","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2016-05-16T06:36:44Z","title":"Forman curvature for directed networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04662","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":"sha256:2370876d81177b2b948abc78b1af8f2ff59ded95ac3d9f1661de28d5b3a27238","target":"record","created_at":"2026-05-18T00:50:01Z","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":"58ddc625af1309669bf46e79bc4e68c0a90d2c9647237a0a5ec1eda43cd70262","cross_cats_sorted":["cond-mat.dis-nn","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.MN","submitted_at":"2016-05-16T06:36:44Z","title_canon_sha256":"a0cef0a5653be5fae696a0be514d56d81facc9794a80b07da22836a18c3aedfb"},"schema_version":"1.0","source":{"id":"1605.04662","kind":"arxiv","version":2}},"canonical_sha256":"da6bc5dd154b4dad5e1039f3edba63bf8838c8d9eaafa294c788b23e852602c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da6bc5dd154b4dad5e1039f3edba63bf8838c8d9eaafa294c788b23e852602c7","first_computed_at":"2026-05-18T00:50:01.294436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:01.294436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iec/GaFBwVa0OyCytXCipJK+mn9xB7tVbrq7dv5Nxlu2t0LVYxh4NXAUy1KbCt3h/6vTaJPhQgKKRnsG8d4QCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:01.295100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04662","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2370876d81177b2b948abc78b1af8f2ff59ded95ac3d9f1661de28d5b3a27238","sha256:14bb9f049426b4c6af8175858458f4f679569515ae12a6d1d52e9e23131f801f"],"state_sha256":"e372ce4361ddd37ba7457215d5e021ec96b2d73fc658f59e37a3ee8c71f461ac"}