{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:U43AEV4A7GECDIUYZ7H4TQGSD5","short_pith_number":"pith:U43AEV4A","canonical_record":{"source":{"id":"1101.4757","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-25T09:46:49Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"title_canon_sha256":"759bf0b2878da0a8d335b4f42f9e7e9085985d2080ea7d89c6e6ba0719cf1445","abstract_canon_sha256":"1c509f4a30ab575f705f7ec8acab09c796f80df406435b1d35ceb96d1376e763"},"schema_version":"1.0"},"canonical_sha256":"a736025780f98821a298cfcfc9c0d21f7bc000d4f1318839c4733a168edc0244","source":{"kind":"arxiv","id":"1101.4757","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4757","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4757v2","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4757","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"U43AEV4A7GEC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U43AEV4A7GECDIUY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U43AEV4A","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:U43AEV4A7GECDIUYZ7H4TQGSD5","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4757","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-25T09:46:49Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"title_canon_sha256":"759bf0b2878da0a8d335b4f42f9e7e9085985d2080ea7d89c6e6ba0719cf1445","abstract_canon_sha256":"1c509f4a30ab575f705f7ec8acab09c796f80df406435b1d35ceb96d1376e763"},"schema_version":"1.0"},"canonical_sha256":"a736025780f98821a298cfcfc9c0d21f7bc000d4f1318839c4733a168edc0244","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:49.894839Z","signature_b64":"foaSoMjCuhAq4RDs9eFruEXwZGBueXjD0bK4luGMhsR6Sz6VtsdNXkHjnMiKyRH1+gXG9L/V/30UN1LPeOAABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a736025780f98821a298cfcfc9c0d21f7bc000d4f1318839c4733a168edc0244","last_reissued_at":"2026-05-18T02:22:49.892697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:49.892697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4757","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":"2026-05-18T02:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wo9CIRDiQZaxE+Sf3yzzi/Cjln+tM7X+1FxPUZhLWPMjbxuBkrdtJ2/qeBlzO0DBgPNEyorZzjm/grM5zEH6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:54:18.495221Z"},"content_sha256":"d9c32c874fb26f72f2c3ab4ca4abc1e7fe7785c4160517b92d4c65315aaca2b2","schema_version":"1.0","event_id":"sha256:d9c32c874fb26f72f2c3ab4ca4abc1e7fe7785c4160517b92d4c65315aaca2b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:U43AEV4A7GECDIUYZ7H4TQGSD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"primary_cat":"physics.data-an","authors_text":"Jobst Heitzig, Jonathan F. Donges, J\\\"urgen Kurths, Norbert Marwan, Yong Zou","submitted_at":"2011-01-25T09:46:49Z","abstract_excerpt":"When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4757","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":""},"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":"2026-05-18T02:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+AgzQScBQSAOYoxVxxN+Q3PonMNvf60UFP3PTk9uQ+8JMUq6oC/PMaRN1KyuJzsAc5KZqy5xjb8S/obkOPUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:54:18.495806Z"},"content_sha256":"03cd49d8d061ead71ba41d284cba807c2c101c5a60418d30801040c7a533ea40","schema_version":"1.0","event_id":"sha256:03cd49d8d061ead71ba41d284cba807c2c101c5a60418d30801040c7a533ea40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U43AEV4A7GECDIUYZ7H4TQGSD5/bundle.json","state_url":"https://pith.science/pith/U43AEV4A7GECDIUYZ7H4TQGSD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U43AEV4A7GECDIUYZ7H4TQGSD5/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":"2026-05-30T07:54:18Z","links":{"resolver":"https://pith.science/pith/U43AEV4A7GECDIUYZ7H4TQGSD5","bundle":"https://pith.science/pith/U43AEV4A7GECDIUYZ7H4TQGSD5/bundle.json","state":"https://pith.science/pith/U43AEV4A7GECDIUYZ7H4TQGSD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U43AEV4A7GECDIUYZ7H4TQGSD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U43AEV4A7GECDIUYZ7H4TQGSD5","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":"1c509f4a30ab575f705f7ec8acab09c796f80df406435b1d35ceb96d1376e763","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-25T09:46:49Z","title_canon_sha256":"759bf0b2878da0a8d335b4f42f9e7e9085985d2080ea7d89c6e6ba0719cf1445"},"schema_version":"1.0","source":{"id":"1101.4757","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4757","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4757v2","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4757","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"U43AEV4A7GEC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U43AEV4A7GECDIUY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U43AEV4A","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:03cd49d8d061ead71ba41d284cba807c2c101c5a60418d30801040c7a533ea40","target":"graph","created_at":"2026-05-18T02:22:49Z","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":"When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network stat","authors_text":"Jobst Heitzig, Jonathan F. Donges, J\\\"urgen Kurths, Norbert Marwan, Yong Zou","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-25T09:46:49Z","title":"Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4757","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:d9c32c874fb26f72f2c3ab4ca4abc1e7fe7785c4160517b92d4c65315aaca2b2","target":"record","created_at":"2026-05-18T02:22:49Z","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":"1c509f4a30ab575f705f7ec8acab09c796f80df406435b1d35ceb96d1376e763","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-01-25T09:46:49Z","title_canon_sha256":"759bf0b2878da0a8d335b4f42f9e7e9085985d2080ea7d89c6e6ba0719cf1445"},"schema_version":"1.0","source":{"id":"1101.4757","kind":"arxiv","version":2}},"canonical_sha256":"a736025780f98821a298cfcfc9c0d21f7bc000d4f1318839c4733a168edc0244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a736025780f98821a298cfcfc9c0d21f7bc000d4f1318839c4733a168edc0244","first_computed_at":"2026-05-18T02:22:49.892697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:49.892697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"foaSoMjCuhAq4RDs9eFruEXwZGBueXjD0bK4luGMhsR6Sz6VtsdNXkHjnMiKyRH1+gXG9L/V/30UN1LPeOAABw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:49.894839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4757","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9c32c874fb26f72f2c3ab4ca4abc1e7fe7785c4160517b92d4c65315aaca2b2","sha256:03cd49d8d061ead71ba41d284cba807c2c101c5a60418d30801040c7a533ea40"],"state_sha256":"fb51c6e4897e385657329cb58b3bd4f716f6dac95ed9e45005ff0d8fd16d7321"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ubxB+Vrgv6cyez46l5+SbHn+JThX/tvaseIcsE+6fjNLhqD5nHQLnNXtYxj0YanFO4TjfAsyjdEIKlXuBq17BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:54:18.498360Z","bundle_sha256":"9ebb9b17f939be5ba17b5bb4bedf3f3f15c5f620e5622624b83439de815c5326"}}