{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MSMN3PHDHKJ4JJJS5BC3IYGXKQ","short_pith_number":"pith:MSMN3PHD","canonical_record":{"source":{"id":"1807.00496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-02T07:25:51Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"db85d32bb915c3bdce52e33d1d8cd690de6912bcb1c4e34b389bd6083fb0fdfd","abstract_canon_sha256":"eff4963a375d7af31cdf86937bec118274f12f7745f706e1400cee3515a1a928"},"schema_version":"1.0"},"canonical_sha256":"6498ddbce33a93c4a532e845b460d75438e1ef332d3527fefc2ae8ef305a857b","source":{"kind":"arxiv","id":"1807.00496","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00496","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00496v2","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00496","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"MSMN3PHDHKJ4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MSMN3PHDHKJ4JJJS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MSMN3PHD","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MSMN3PHDHKJ4JJJS5BC3IYGXKQ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.00496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-02T07:25:51Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"db85d32bb915c3bdce52e33d1d8cd690de6912bcb1c4e34b389bd6083fb0fdfd","abstract_canon_sha256":"eff4963a375d7af31cdf86937bec118274f12f7745f706e1400cee3515a1a928"},"schema_version":"1.0"},"canonical_sha256":"6498ddbce33a93c4a532e845b460d75438e1ef332d3527fefc2ae8ef305a857b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:37.791543Z","signature_b64":"MPx9c/THdADrvCcB2VnF0xLUmjphWozxCoMqtOXZoK861WLRIBYtzyv2ZPquSYOUwBYtgallmhjWQa939zM0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6498ddbce33a93c4a532e845b460d75438e1ef332d3527fefc2ae8ef305a857b","last_reissued_at":"2026-05-17T23:45:37.790768Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:37.790768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.00496","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":"2026-05-17T23:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yn1rBHOx7k6kb0oyFM5DDBDzSU+GOWgF71+r6ToSDaXHhBXUle/y5Uk84OxJzMvu1eDhKbod5ooVNl9pUuQ6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:52:04.721262Z"},"content_sha256":"4cf1b5aac628be32128cc942cbf40e31f76ba1ccf58325fe427b80a660e6ffba","schema_version":"1.0","event_id":"sha256:4cf1b5aac628be32128cc942cbf40e31f76ba1ccf58325fe427b80a660e6ffba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MSMN3PHDHKJ4JJJS5BC3IYGXKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The size distribution of cities: a kinetic explanation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"physics.soc-ph","authors_text":"Giuseppe Toscani, Stefano Gualandi","submitted_at":"2018-07-02T07:25:51Z","abstract_excerpt":"We present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration. In most cases, the Boltzmann-type kinetic description allows to obtain, within an asymptotic procedure, a Fokker--Planck equation with variable coefficients of diffusion and drift, which describes the evolution in time of some probability density of the city size. It is shown that, in dependence of the microscopic rules of migration, the equilibrium density can follow both a power law for large values of the size variable, which contains as particular case a Zipf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00496","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":"2026-05-17T23:45:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMx5EiqZR6CsUWcnUbCaJSCRs1IrY8t5zbugfyoQNXlRozj4c951kCXhIs3kmFiUf7LPmV7TT052ra0CfAFTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:52:04.721652Z"},"content_sha256":"dd37cfa40689451d5963fac30e673be413c9415b3921fe82d4992ed4eaec01ad","schema_version":"1.0","event_id":"sha256:dd37cfa40689451d5963fac30e673be413c9415b3921fe82d4992ed4eaec01ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSMN3PHDHKJ4JJJS5BC3IYGXKQ/bundle.json","state_url":"https://pith.science/pith/MSMN3PHDHKJ4JJJS5BC3IYGXKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSMN3PHDHKJ4JJJS5BC3IYGXKQ/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":"2026-05-29T17:52:04Z","links":{"resolver":"https://pith.science/pith/MSMN3PHDHKJ4JJJS5BC3IYGXKQ","bundle":"https://pith.science/pith/MSMN3PHDHKJ4JJJS5BC3IYGXKQ/bundle.json","state":"https://pith.science/pith/MSMN3PHDHKJ4JJJS5BC3IYGXKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSMN3PHDHKJ4JJJS5BC3IYGXKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MSMN3PHDHKJ4JJJS5BC3IYGXKQ","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":"eff4963a375d7af31cdf86937bec118274f12f7745f706e1400cee3515a1a928","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-02T07:25:51Z","title_canon_sha256":"db85d32bb915c3bdce52e33d1d8cd690de6912bcb1c4e34b389bd6083fb0fdfd"},"schema_version":"1.0","source":{"id":"1807.00496","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00496","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00496v2","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00496","created_at":"2026-05-17T23:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"MSMN3PHDHKJ4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MSMN3PHDHKJ4JJJS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MSMN3PHD","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:dd37cfa40689451d5963fac30e673be413c9415b3921fe82d4992ed4eaec01ad","target":"graph","created_at":"2026-05-17T23:45:37Z","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 present a kinetic approach to the formation of urban agglomerations which is based on simple rules of immigration and emigration. In most cases, the Boltzmann-type kinetic description allows to obtain, within an asymptotic procedure, a Fokker--Planck equation with variable coefficients of diffusion and drift, which describes the evolution in time of some probability density of the city size. It is shown that, in dependence of the microscopic rules of migration, the equilibrium density can follow both a power law for large values of the size variable, which contains as particular case a Zipf","authors_text":"Giuseppe Toscani, Stefano Gualandi","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-02T07:25:51Z","title":"The size distribution of cities: a kinetic explanation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00496","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":"sha256:4cf1b5aac628be32128cc942cbf40e31f76ba1ccf58325fe427b80a660e6ffba","target":"record","created_at":"2026-05-17T23:45:37Z","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":"eff4963a375d7af31cdf86937bec118274f12f7745f706e1400cee3515a1a928","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-07-02T07:25:51Z","title_canon_sha256":"db85d32bb915c3bdce52e33d1d8cd690de6912bcb1c4e34b389bd6083fb0fdfd"},"schema_version":"1.0","source":{"id":"1807.00496","kind":"arxiv","version":2}},"canonical_sha256":"6498ddbce33a93c4a532e845b460d75438e1ef332d3527fefc2ae8ef305a857b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6498ddbce33a93c4a532e845b460d75438e1ef332d3527fefc2ae8ef305a857b","first_computed_at":"2026-05-17T23:45:37.790768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:37.790768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MPx9c/THdADrvCcB2VnF0xLUmjphWozxCoMqtOXZoK861WLRIBYtzyv2ZPquSYOUwBYtgallmhjWQa939zM0BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:37.791543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00496","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cf1b5aac628be32128cc942cbf40e31f76ba1ccf58325fe427b80a660e6ffba","sha256:dd37cfa40689451d5963fac30e673be413c9415b3921fe82d4992ed4eaec01ad"],"state_sha256":"777cbe579d2aa76300357f78b3f56ee63f94b461778ebed5aed168648d273182"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XCSEB39dFtTpY7tt8yVGxLS4YY2OBHGCXGu7bk4GcUokRgmkm9g+4nWCzoBcRos2Ne6XTdizWrskLhoAIC59DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:52:04.723889Z","bundle_sha256":"f69f58611a537812b46750ddc1d7fcb07e4476b4d41d6b56e5955b0170583ec7"}}