{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WMSH6C6EBDES25H2VN3BJDPL55","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":"23d97dc6a910f106b9b27313d64001f625212cb994462911ba16e6cd99fbd680","cross_cats_sorted":["cond-mat.stat-mech","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-04-11T10:29:46Z","title_canon_sha256":"2cca09f13cebef6ea95e30f6388fded9e05254ab22f3cc2e0aa5064a49d288f3"},"schema_version":"1.0","source":{"id":"1604.02872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02872","created_at":"2026-05-18T01:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02872v1","created_at":"2026-05-18T01:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02872","created_at":"2026-05-18T01:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"WMSH6C6EBDES","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WMSH6C6EBDES25H2","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WMSH6C6E","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:de58f4e4372adf01d2d8ef13c0fe2c81b7f2f5c796450763eba87578f168bf81","target":"graph","created_at":"2026-05-18T01:10:49Z","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":"One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\\sim x^\\beta, \\beta \\neq 1$. More recently, the generality of this finding has been questioned in studies using new databases and different definitions of city boundaries. In this paper we investigate the existence of nonlinear scaling using a probabilistic framework in which fluctuations are accounted explicitly. In particular, we show that this allows not only to (a) estimate $\\beta$ and confi","authors_text":"E. G. Altmann, J. C. Leitao, J.M. Miotto, M. Gerlach","cross_cats":["cond-mat.stat-mech","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-04-11T10:29:46Z","title":"Is this scaling nonlinear?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02872","kind":"arxiv","version":1},"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:cf299d7c12a9f9c49ed620d4d64d187704d0f335758ef2155faac598ada24790","target":"record","created_at":"2026-05-18T01:10:49Z","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":"23d97dc6a910f106b9b27313d64001f625212cb994462911ba16e6cd99fbd680","cross_cats_sorted":["cond-mat.stat-mech","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-04-11T10:29:46Z","title_canon_sha256":"2cca09f13cebef6ea95e30f6388fded9e05254ab22f3cc2e0aa5064a49d288f3"},"schema_version":"1.0","source":{"id":"1604.02872","kind":"arxiv","version":1}},"canonical_sha256":"b3247f0bc408c92d74faab76148debef436daeb084b5bac666779af4e0e556dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3247f0bc408c92d74faab76148debef436daeb084b5bac666779af4e0e556dd","first_computed_at":"2026-05-18T01:10:49.919722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:49.919722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oy5lg4InkhAyIMfeFvMO+lHAFdIy7mhTcMokKvBk07zbW8apxT/lsJVZZj7Vcc8Lf59VWAd9Tn1feh2qHDdeAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:49.920155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf299d7c12a9f9c49ed620d4d64d187704d0f335758ef2155faac598ada24790","sha256:de58f4e4372adf01d2d8ef13c0fe2c81b7f2f5c796450763eba87578f168bf81"],"state_sha256":"7e0ae6e5cb7fd7ea6036b5b17fb284abf4e35c027f7fff38166a482d4e980668"}