{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:HXPDIULNZSQI3ANCWEFHPT5X2B","short_pith_number":"pith:HXPDIULN","canonical_record":{"source":{"id":"2008.10751","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2020-08-24T23:57:12Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"fff255d1d6005902b25bfa6a68035020cd06caca705cccb489f1ad9b68dfca23","abstract_canon_sha256":"fd9f4125dc5511fd935e05ae06a37da28d1f75bf3126f5760d5aebfd6fc725ad"},"schema_version":"1.0"},"canonical_sha256":"3dde34516dcca08d81a2b10a77cfb7d05de38b02079e08e68dfdb8616dca84eb","source":{"kind":"arxiv","id":"2008.10751","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.10751","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"arxiv_version","alias_value":"2008.10751v2","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.10751","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_12","alias_value":"HXPDIULNZSQI","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_16","alias_value":"HXPDIULNZSQI3ANC","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_8","alias_value":"HXPDIULN","created_at":"2026-07-05T01:57:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:HXPDIULNZSQI3ANCWEFHPT5X2B","target":"record","payload":{"canonical_record":{"source":{"id":"2008.10751","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2020-08-24T23:57:12Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"fff255d1d6005902b25bfa6a68035020cd06caca705cccb489f1ad9b68dfca23","abstract_canon_sha256":"fd9f4125dc5511fd935e05ae06a37da28d1f75bf3126f5760d5aebfd6fc725ad"},"schema_version":"1.0"},"canonical_sha256":"3dde34516dcca08d81a2b10a77cfb7d05de38b02079e08e68dfdb8616dca84eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:57:19.603671Z","signature_b64":"8xNioGUP64IqPh7WVz5dmsoFy/0BZy22kN9Qiv7Tz1ziqGNAdo508+gdoPrtAkOMJ8bZwPrhN4Uj+Psxea1MDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dde34516dcca08d81a2b10a77cfb7d05de38b02079e08e68dfdb8616dca84eb","last_reissued_at":"2026-07-05T01:57:19.603235Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:57:19.603235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.10751","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":"2026-07-05T01:57:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+2/v2fn8EFn3iX5mZbiIvE2y4go2IKAPMVuFcZ8DB/OgyRS4KnYCwOgmSQsb45LZjpYHl0kJf/PjJOx+8p9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T03:51:47.273516Z"},"content_sha256":"ec3883ba991f08777ae14a7cecf5b499c78db291f8a1cff3f4b399daaaa42284","schema_version":"1.0","event_id":"sha256:ec3883ba991f08777ae14a7cecf5b499c78db291f8a1cff3f4b399daaaa42284"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:HXPDIULNZSQI3ANCWEFHPT5X2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degree difference: A simple measure to characterize structural heterogeneity in complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cs.SI","authors_text":"Amirhossein Farzam, Areejit Samal, J\\\"urgen Jost","submitted_at":"2020-08-24T23:57:12Z","abstract_excerpt":"Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, `degree difference' (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.10751","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.10751/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:57:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V1C1T4zkdrIK065Dogv0xqXCWIhFCtuL4M+pYC5MLnxDmYBPvGi+qiHmIx0RcKry5l0ARMTqap2NKFHt1S0lBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T03:51:47.274366Z"},"content_sha256":"c480d9af366f8ea003cf894faa2fc8c7999c6c2cdbb88dac4037815da3e9f82e","schema_version":"1.0","event_id":"sha256:c480d9af366f8ea003cf894faa2fc8c7999c6c2cdbb88dac4037815da3e9f82e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXPDIULNZSQI3ANCWEFHPT5X2B/bundle.json","state_url":"https://pith.science/pith/HXPDIULNZSQI3ANCWEFHPT5X2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXPDIULNZSQI3ANCWEFHPT5X2B/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":"2026-08-07T03:51:47Z","links":{"resolver":"https://pith.science/pith/HXPDIULNZSQI3ANCWEFHPT5X2B","bundle":"https://pith.science/pith/HXPDIULNZSQI3ANCWEFHPT5X2B/bundle.json","state":"https://pith.science/pith/HXPDIULNZSQI3ANCWEFHPT5X2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXPDIULNZSQI3ANCWEFHPT5X2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HXPDIULNZSQI3ANCWEFHPT5X2B","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":"fd9f4125dc5511fd935e05ae06a37da28d1f75bf3126f5760d5aebfd6fc725ad","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2020-08-24T23:57:12Z","title_canon_sha256":"fff255d1d6005902b25bfa6a68035020cd06caca705cccb489f1ad9b68dfca23"},"schema_version":"1.0","source":{"id":"2008.10751","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.10751","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"arxiv_version","alias_value":"2008.10751v2","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.10751","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_12","alias_value":"HXPDIULNZSQI","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_16","alias_value":"HXPDIULNZSQI3ANC","created_at":"2026-07-05T01:57:19Z"},{"alias_kind":"pith_short_8","alias_value":"HXPDIULN","created_at":"2026-07-05T01:57:19Z"}],"graph_snapshots":[{"event_id":"sha256:c480d9af366f8ea003cf894faa2fc8c7999c6c2cdbb88dac4037815da3e9f82e","target":"graph","created_at":"2026-07-05T01:57:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.10751/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we analyze a simple, elegant yet underexplored measure, `degree difference' (DD) between vertices of an edge, to understand the local network geometry. We describe the connection between DD and global assortativity of the network from both formal and conceptual perspective, and show that DD can reveal structural properties that are not obtained from other such measur","authors_text":"Amirhossein Farzam, Areejit Samal, J\\\"urgen Jost","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2020-08-24T23:57:12Z","title":"Degree difference: A simple measure to characterize structural heterogeneity in complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.10751","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:ec3883ba991f08777ae14a7cecf5b499c78db291f8a1cff3f4b399daaaa42284","target":"record","created_at":"2026-07-05T01:57:19Z","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":"fd9f4125dc5511fd935e05ae06a37da28d1f75bf3126f5760d5aebfd6fc725ad","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2020-08-24T23:57:12Z","title_canon_sha256":"fff255d1d6005902b25bfa6a68035020cd06caca705cccb489f1ad9b68dfca23"},"schema_version":"1.0","source":{"id":"2008.10751","kind":"arxiv","version":2}},"canonical_sha256":"3dde34516dcca08d81a2b10a77cfb7d05de38b02079e08e68dfdb8616dca84eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dde34516dcca08d81a2b10a77cfb7d05de38b02079e08e68dfdb8616dca84eb","first_computed_at":"2026-07-05T01:57:19.603235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:57:19.603235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8xNioGUP64IqPh7WVz5dmsoFy/0BZy22kN9Qiv7Tz1ziqGNAdo508+gdoPrtAkOMJ8bZwPrhN4Uj+Psxea1MDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:57:19.603671Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.10751","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec3883ba991f08777ae14a7cecf5b499c78db291f8a1cff3f4b399daaaa42284","sha256:c480d9af366f8ea003cf894faa2fc8c7999c6c2cdbb88dac4037815da3e9f82e"],"state_sha256":"2663e67353fbfbe0db7ee2394f648c988452f97d1bd707442ea0d172c3c8a7d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PqaS1HoGlR+B/dq8eo2Th9225gdGuUPna9t9YVyLRMekAue97GkFh2QTwH2phMS3GSXnA+LULBg5Y5nA53AAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T03:51:47.281377Z","bundle_sha256":"4b559039ac6ba82abf499f92d482abe48265da81d4ade6dcfa60825321690156"}}