{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XNJIBVYQM3VTQ4Y2ULISCK47UW","short_pith_number":"pith:XNJIBVYQ","canonical_record":{"source":{"id":"1107.4649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-07-23T01:43:48Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"2e85c5ccbb4f7c89710663d86e14d7940defc2b1d016cc66a6991358b48468e1","abstract_canon_sha256":"87cf08cbc6a27872e762382486b286a33b0425e8087e159d314b2ec8f33526a4"},"schema_version":"1.0"},"canonical_sha256":"bb5280d71066eb38731aa2d1212b9fa591be7cb3150aa58d8fb1b905defc26f0","source":{"kind":"arxiv","id":"1107.4649","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4649","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4649v2","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4649","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"XNJIBVYQM3VT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XNJIBVYQM3VTQ4Y2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XNJIBVYQ","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XNJIBVYQM3VTQ4Y2ULISCK47UW","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-07-23T01:43:48Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"2e85c5ccbb4f7c89710663d86e14d7940defc2b1d016cc66a6991358b48468e1","abstract_canon_sha256":"87cf08cbc6a27872e762382486b286a33b0425e8087e159d314b2ec8f33526a4"},"schema_version":"1.0"},"canonical_sha256":"bb5280d71066eb38731aa2d1212b9fa591be7cb3150aa58d8fb1b905defc26f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:25.142627Z","signature_b64":"9QNlUF+77E0+/KIjvYCxYV6r0mx12oljUKBefEuGCJuIQzfuiXxO9pRyQqx2rzpocbKZ3sYFf6DR+vmoOTcXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb5280d71066eb38731aa2d1212b9fa591be7cb3150aa58d8fb1b905defc26f0","last_reissued_at":"2026-05-18T04:02:25.142138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:25.142138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4649","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTCIo/hcXuWzfW3ou+25PRHD7mMLxpTeqPcAh7TgKznOTJ+EnjjbTgvqwFVNyNfVnnafk153Umt9CzY50d8LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:55:00.181404Z"},"content_sha256":"ff5eb833a968151ff9463b4816d25b56ba247405acd084ea916b8acff50a7225","schema_version":"1.0","event_id":"sha256:ff5eb833a968151ff9463b4816d25b56ba247405acd084ea916b8acff50a7225"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XNJIBVYQM3VTQ4Y2ULISCK47UW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mandelbrot Law of Evolving Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"physics.data-an","authors_text":"Bing-Hong Wang, Tao Zhou, Xue-Zao Ren, Zimo Yang","submitted_at":"2011-07-23T01:43:48Z","abstract_excerpt":"Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although the shifting coefficient highly affects the shape of distribution, it receives less attention in the literature and in fact, mainstream analytical method based on backward or forward difference will lead to considerable deviations to its value. In this Letter, we show that the degree distribution of a growing network with linear preferential attachment approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4649","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":"2026-05-18T04:02:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+V8D9q/YLzFWDjKbeRgMGbJm+Fm1iKWoazJNq1yosZoNpe1JhUi01bgdAr7Jpo0ATjatw8WaN+9p9hRzFh+3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:55:00.182145Z"},"content_sha256":"4438865a0fbeb900ad59f13710c06b3ffa8b0d3edf0ddad166b6a47368c051a3","schema_version":"1.0","event_id":"sha256:4438865a0fbeb900ad59f13710c06b3ffa8b0d3edf0ddad166b6a47368c051a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNJIBVYQM3VTQ4Y2ULISCK47UW/bundle.json","state_url":"https://pith.science/pith/XNJIBVYQM3VTQ4Y2ULISCK47UW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNJIBVYQM3VTQ4Y2ULISCK47UW/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":"2026-05-26T09:55:00Z","links":{"resolver":"https://pith.science/pith/XNJIBVYQM3VTQ4Y2ULISCK47UW","bundle":"https://pith.science/pith/XNJIBVYQM3VTQ4Y2ULISCK47UW/bundle.json","state":"https://pith.science/pith/XNJIBVYQM3VTQ4Y2ULISCK47UW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNJIBVYQM3VTQ4Y2ULISCK47UW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XNJIBVYQM3VTQ4Y2ULISCK47UW","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":"87cf08cbc6a27872e762382486b286a33b0425e8087e159d314b2ec8f33526a4","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-07-23T01:43:48Z","title_canon_sha256":"2e85c5ccbb4f7c89710663d86e14d7940defc2b1d016cc66a6991358b48468e1"},"schema_version":"1.0","source":{"id":"1107.4649","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4649","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4649v2","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4649","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"XNJIBVYQM3VT","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XNJIBVYQM3VTQ4Y2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XNJIBVYQ","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:4438865a0fbeb900ad59f13710c06b3ffa8b0d3edf0ddad166b6a47368c051a3","target":"graph","created_at":"2026-05-18T04:02:25Z","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":"Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although the shifting coefficient highly affects the shape of distribution, it receives less attention in the literature and in fact, mainstream analytical method based on backward or forward difference will lead to considerable deviations to its value. In this Letter, we show that the degree distribution of a growing network with linear preferential attachment approxi","authors_text":"Bing-Hong Wang, Tao Zhou, Xue-Zao Ren, Zimo Yang","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-07-23T01:43:48Z","title":"Mandelbrot Law of Evolving Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4649","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:ff5eb833a968151ff9463b4816d25b56ba247405acd084ea916b8acff50a7225","target":"record","created_at":"2026-05-18T04:02:25Z","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":"87cf08cbc6a27872e762382486b286a33b0425e8087e159d314b2ec8f33526a4","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2011-07-23T01:43:48Z","title_canon_sha256":"2e85c5ccbb4f7c89710663d86e14d7940defc2b1d016cc66a6991358b48468e1"},"schema_version":"1.0","source":{"id":"1107.4649","kind":"arxiv","version":2}},"canonical_sha256":"bb5280d71066eb38731aa2d1212b9fa591be7cb3150aa58d8fb1b905defc26f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb5280d71066eb38731aa2d1212b9fa591be7cb3150aa58d8fb1b905defc26f0","first_computed_at":"2026-05-18T04:02:25.142138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:25.142138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9QNlUF+77E0+/KIjvYCxYV6r0mx12oljUKBefEuGCJuIQzfuiXxO9pRyQqx2rzpocbKZ3sYFf6DR+vmoOTcXCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:25.142627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4649","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff5eb833a968151ff9463b4816d25b56ba247405acd084ea916b8acff50a7225","sha256:4438865a0fbeb900ad59f13710c06b3ffa8b0d3edf0ddad166b6a47368c051a3"],"state_sha256":"453956d9ea88adb402b3122bab3ef0d5bc6f8b6f96387e1142e524e084ec74e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Hoz7jEizbn1eN72ivkylSdXi/MPrwpf/vBrDm95q7mWk3F7HkwudZdgmiLrpIpFILKpfah5Lu3tUJ0JkJIVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:55:00.186035Z","bundle_sha256":"6078e956fbed2e74c7e1d19c556f932c0d4564556d0ac527acc3dec859bb282d"}}