{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G2TZDVO3IOGVS24ZVUVQOOQTSX","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":"ba37ed2706e1e34eb6de16e3de2ab8f7cbe69054e02beb8e1b665cb7b8bde176","cross_cats_sorted":["physics.data-an","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-07-17T16:10:24Z","title_canon_sha256":"c5c605cb03461d8e431c189047dc5b16fe09a2d1ccbaefabfacbed82e56d8fcd"},"schema_version":"1.0","source":{"id":"1407.4718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4718","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4718v1","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4718","created_at":"2026-05-18T02:47:23Z"},{"alias_kind":"pith_short_12","alias_value":"G2TZDVO3IOGV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G2TZDVO3IOGVS24Z","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G2TZDVO3","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:5e656c7d528f32bb2b8a5c533165349722b8efe5c1c37cd8b87b9dac8e21b2d7","target":"graph","created_at":"2026-05-18T02:47:23Z","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":"We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogene","authors_text":"Alessandro Belmonte, Riccardo Di Clemente, Sergey V. Buldyrev","cross_cats":["physics.data-an","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-07-17T16:10:24Z","title":"The Italian primary school-size distribution and the city-size: a complex nexus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4718","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":"sha256:79f1967668e8ce6fa7968805c70b5283a66d20613f7cc3aa49b63dfd092ca64e","target":"record","created_at":"2026-05-18T02:47:23Z","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":"ba37ed2706e1e34eb6de16e3de2ab8f7cbe69054e02beb8e1b665cb7b8bde176","cross_cats_sorted":["physics.data-an","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-07-17T16:10:24Z","title_canon_sha256":"c5c605cb03461d8e431c189047dc5b16fe09a2d1ccbaefabfacbed82e56d8fcd"},"schema_version":"1.0","source":{"id":"1407.4718","kind":"arxiv","version":1}},"canonical_sha256":"36a791d5db438d596b99ad2b073a1395df1f9192c1644dbd2a1e3cdf6871e0a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36a791d5db438d596b99ad2b073a1395df1f9192c1644dbd2a1e3cdf6871e0a5","first_computed_at":"2026-05-18T02:47:23.490639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:23.490639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s8UR0nJy3CYG35U3qzlt2oKF8HXfDgsqWKrAHJHu+O/3pk2uZhqjooNZDtMTRPwxGVEKU8vUdo/mqa/QsIZGDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:23.491030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79f1967668e8ce6fa7968805c70b5283a66d20613f7cc3aa49b63dfd092ca64e","sha256:5e656c7d528f32bb2b8a5c533165349722b8efe5c1c37cd8b87b9dac8e21b2d7"],"state_sha256":"f655485f3cd1670b4693a395e866db959675c33419f46e14d0a133c8ce224b50"}