{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VE3OO2R7JIFCH7MYBKCTSQ5IQD","short_pith_number":"pith:VE3OO2R7","canonical_record":{"source":{"id":"1509.02711","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-09T10:34:46Z","cross_cats_sorted":["q-fin.GN"],"title_canon_sha256":"fed8a0929bc7330bae440dde93f661d2d7ea964cd717f670613d800ffcc07f32","abstract_canon_sha256":"2d06ffad97b36b4cec7e6005bda59f49852a563eb41a77f7e35563f6206556b6"},"schema_version":"1.0"},"canonical_sha256":"a936e76a3f4a0a23fd980a853943a880d326379767916bcd8e08672d917ed6d2","source":{"kind":"arxiv","id":"1509.02711","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02711","created_at":"2026-05-18T01:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02711v3","created_at":"2026-05-18T01:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02711","created_at":"2026-05-18T01:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"VE3OO2R7JIFC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VE3OO2R7JIFCH7MY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VE3OO2R7","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VE3OO2R7JIFCH7MYBKCTSQ5IQD","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02711","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-09T10:34:46Z","cross_cats_sorted":["q-fin.GN"],"title_canon_sha256":"fed8a0929bc7330bae440dde93f661d2d7ea964cd717f670613d800ffcc07f32","abstract_canon_sha256":"2d06ffad97b36b4cec7e6005bda59f49852a563eb41a77f7e35563f6206556b6"},"schema_version":"1.0"},"canonical_sha256":"a936e76a3f4a0a23fd980a853943a880d326379767916bcd8e08672d917ed6d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:54.258228Z","signature_b64":"+m3TwEjkdWhguBcR8Zn5tNLN8F60DsGfMVMk0hCth2vJxquYh2CRsdhKIVEs23ZeqM+dH/gNVvKpmcU42fm/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a936e76a3f4a0a23fd980a853943a880d326379767916bcd8e08672d917ed6d2","last_reissued_at":"2026-05-18T01:18:54.257775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:54.257775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02711","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3pBx7/DSPKuhkhWCvAAb/ZbRIH7S3ycPKtFzsjXT/vQjLzgRtV2ZioXlPN4R2jYB12e4BzF/NTx/td33T18ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:14:22.429008Z"},"content_sha256":"04eedeced2eaaf9a70a2f50e9357e1faf2e145a5da1022f4c0cdec5a058c242c","schema_version":"1.0","event_id":"sha256:04eedeced2eaaf9a70a2f50e9357e1faf2e145a5da1022f4c0cdec5a058c242c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VE3OO2R7JIFCH7MYBKCTSQ5IQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inequality measures in kinetic exchange models of wealth distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.GN"],"primary_cat":"physics.soc-ph","authors_text":"Arnab Chatterjee, Asim Ghosh, Bikas K. Chakrabarti, Jun-ichi Inoue","submitted_at":"2015-09-09T10:34:46Z","abstract_excerpt":"In this paper, we study the inequality indices for some models of wealth exchange. We calculated Gini index and newly introduced k-index and compare the results with reported empirical data available for different countries. We have found lower and upper bounds for the indices and discuss the efficiencies of the models. Some exact analytical calculations are given for a few cases. We also exactly compute the quantities for Gamma and double Gamma distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02711","kind":"arxiv","version":3},"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":"2026-05-18T01:18:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s//35+m1lhPDWiH+1M9S+8QjdPjeL5IYxY2rt0STWhY9N2pTmxhlYR+jhf7tHET0qRv1jqI3XyDVu2zw3hw+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:14:22.429367Z"},"content_sha256":"a4840b08c8810b16b29576ca3aafb541ee89345b61a87322bf690375eee92b83","schema_version":"1.0","event_id":"sha256:a4840b08c8810b16b29576ca3aafb541ee89345b61a87322bf690375eee92b83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VE3OO2R7JIFCH7MYBKCTSQ5IQD/bundle.json","state_url":"https://pith.science/pith/VE3OO2R7JIFCH7MYBKCTSQ5IQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VE3OO2R7JIFCH7MYBKCTSQ5IQD/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":"2026-05-28T01:14:22Z","links":{"resolver":"https://pith.science/pith/VE3OO2R7JIFCH7MYBKCTSQ5IQD","bundle":"https://pith.science/pith/VE3OO2R7JIFCH7MYBKCTSQ5IQD/bundle.json","state":"https://pith.science/pith/VE3OO2R7JIFCH7MYBKCTSQ5IQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VE3OO2R7JIFCH7MYBKCTSQ5IQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VE3OO2R7JIFCH7MYBKCTSQ5IQD","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":"2d06ffad97b36b4cec7e6005bda59f49852a563eb41a77f7e35563f6206556b6","cross_cats_sorted":["q-fin.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-09T10:34:46Z","title_canon_sha256":"fed8a0929bc7330bae440dde93f661d2d7ea964cd717f670613d800ffcc07f32"},"schema_version":"1.0","source":{"id":"1509.02711","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02711","created_at":"2026-05-18T01:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02711v3","created_at":"2026-05-18T01:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02711","created_at":"2026-05-18T01:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"VE3OO2R7JIFC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VE3OO2R7JIFCH7MY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VE3OO2R7","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:a4840b08c8810b16b29576ca3aafb541ee89345b61a87322bf690375eee92b83","target":"graph","created_at":"2026-05-18T01:18:54Z","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 this paper, we study the inequality indices for some models of wealth exchange. We calculated Gini index and newly introduced k-index and compare the results with reported empirical data available for different countries. We have found lower and upper bounds for the indices and discuss the efficiencies of the models. Some exact analytical calculations are given for a few cases. We also exactly compute the quantities for Gamma and double Gamma distributions.","authors_text":"Arnab Chatterjee, Asim Ghosh, Bikas K. Chakrabarti, Jun-ichi Inoue","cross_cats":["q-fin.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-09T10:34:46Z","title":"Inequality measures in kinetic exchange models of wealth distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02711","kind":"arxiv","version":3},"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":"sha256:04eedeced2eaaf9a70a2f50e9357e1faf2e145a5da1022f4c0cdec5a058c242c","target":"record","created_at":"2026-05-18T01:18:54Z","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":"2d06ffad97b36b4cec7e6005bda59f49852a563eb41a77f7e35563f6206556b6","cross_cats_sorted":["q-fin.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-09-09T10:34:46Z","title_canon_sha256":"fed8a0929bc7330bae440dde93f661d2d7ea964cd717f670613d800ffcc07f32"},"schema_version":"1.0","source":{"id":"1509.02711","kind":"arxiv","version":3}},"canonical_sha256":"a936e76a3f4a0a23fd980a853943a880d326379767916bcd8e08672d917ed6d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a936e76a3f4a0a23fd980a853943a880d326379767916bcd8e08672d917ed6d2","first_computed_at":"2026-05-18T01:18:54.257775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:54.257775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+m3TwEjkdWhguBcR8Zn5tNLN8F60DsGfMVMk0hCth2vJxquYh2CRsdhKIVEs23ZeqM+dH/gNVvKpmcU42fm/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:54.258228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02711","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04eedeced2eaaf9a70a2f50e9357e1faf2e145a5da1022f4c0cdec5a058c242c","sha256:a4840b08c8810b16b29576ca3aafb541ee89345b61a87322bf690375eee92b83"],"state_sha256":"0fd452acb85981ea160b4adac05fd4877f1bb073f7a90bfb6c4d7f036bbb2a0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QT7TfXUmgDrSSVCQdeEU73Hl8KPJSFnqhIvOCpiG7LwY4O5wAWO6aVFR/w7/DgmELrtRSFau1xbs4CbPPV+/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:14:22.431459Z","bundle_sha256":"d11a2924063033d841455b7b761b294001b27578e69abd9a71557d714d8882d6"}}