{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X6P4S7SLKBTWMYFRYXWYMDRYJR","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":"d00bfb0ed4adcda025d38dca2e79a443ff2da33cb280389d42ea24f1da942ff2","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2014-12-23T01:02:26Z","title_canon_sha256":"19817b60536bc8fda964976932398a8bf7ce5765e9b2df43eb0e70b856582693"},"schema_version":"1.0","source":{"id":"1412.7227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7227","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7227v1","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7227","created_at":"2026-05-18T01:22:41Z"},{"alias_kind":"pith_short_12","alias_value":"X6P4S7SLKBTW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X6P4S7SLKBTWMYFR","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X6P4S7SL","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:c5d6b3209dcccea21cdb57fbb121f5ba70742c7c2388d8ff46e39b2d8ab80422","target":"graph","created_at":"2026-05-18T01:22:41Z","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":"In recent work, Boltzmann and Fokker-Planck equations were derived for the \"Yard-Sale Model\" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy -- complete concentration of wealth by a single individual. In this work, we prove that conjecture by demonstrating that the Gini coefficient, a measure of inequality commonly used by economists, is an $H$ function of both the Boltzmann and Fokker-Planck equations for the model.","authors_text":"Bruce M. Boghosian, Jeremy Marcq, Merek Johnson","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2014-12-23T01:02:26Z","title":"An $H$ theorem for Boltzmann's equation for the Yard-Sale Model of asset exchange"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7227","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":"sha256:5d66be58db601445d37cef16c1367db3cf08159ae679eb2537f8802444781e3b","target":"record","created_at":"2026-05-18T01:22:41Z","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":"d00bfb0ed4adcda025d38dca2e79a443ff2da33cb280389d42ea24f1da942ff2","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-fin.GN","submitted_at":"2014-12-23T01:02:26Z","title_canon_sha256":"19817b60536bc8fda964976932398a8bf7ce5765e9b2df43eb0e70b856582693"},"schema_version":"1.0","source":{"id":"1412.7227","kind":"arxiv","version":1}},"canonical_sha256":"bf9fc97e4b50676660b1c5ed860e384c4dcdfa256c1fcc7896576025b26c2fec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf9fc97e4b50676660b1c5ed860e384c4dcdfa256c1fcc7896576025b26c2fec","first_computed_at":"2026-05-18T01:22:41.510388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:41.510388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/1iwMv9m4BxGUvJt9uGaHaqW3wG4oKHlvzrLQ/dZy6WIaPdYYyP/pjuhc97GJu/QnEXyTWt87l2zbX//2p3eDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:41.510950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d66be58db601445d37cef16c1367db3cf08159ae679eb2537f8802444781e3b","sha256:c5d6b3209dcccea21cdb57fbb121f5ba70742c7c2388d8ff46e39b2d8ab80422"],"state_sha256":"c165baf6a575ab9896f6d2238c6e94cf46caa188dc158825586836faf5df8d0a"}