{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OH3SLESHDESZZWSXPNMKCARDUP","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":"32c8fe0dc930c5d2055d2a99d0331cfb25c49489fd168791f00a9d923de1ae1e","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2022-03-17T00:39:47Z","title_canon_sha256":"904ba8b17be84c51a04d2ef32c0306d2906e46bc31b449d8706e7fd5329568c9"},"schema_version":"1.0","source":{"id":"2203.09000","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.09000","created_at":"2026-07-05T08:08:14Z"},{"alias_kind":"arxiv_version","alias_value":"2203.09000v4","created_at":"2026-07-05T08:08:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.09000","created_at":"2026-07-05T08:08:14Z"},{"alias_kind":"pith_short_12","alias_value":"OH3SLESHDESZ","created_at":"2026-07-05T08:08:14Z"},{"alias_kind":"pith_short_16","alias_value":"OH3SLESHDESZZWSX","created_at":"2026-07-05T08:08:14Z"},{"alias_kind":"pith_short_8","alias_value":"OH3SLESH","created_at":"2026-07-05T08:08:14Z"}],"graph_snapshots":[{"event_id":"sha256:c6bd059c25994cf8de088f2505384869b3bf5946c069b010abce1d35c5a3e2b6","target":"graph","created_at":"2026-07-05T08:08:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.09000/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a multivariate extension of the Lorenz curve based on multivariate rearrangements of optimal transport theory. We define a vector Lorenz map as the integral of the vector quantile map associated with a multivariate resource allocation. Each component of the Lorenz map is the cumulative share of each resource, as in the traditional univariate case. The pointwise ordering of such Lorenz maps defines a new multivariate majorization order, which is equivalent to preference by any social planner with inequality averse multivariate rank dependent social evaluation functional. We define a ","authors_text":"Brendan Pass, Jorge A. Rivero, Marc Henry, Yanqin Fan","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2022-03-17T00:39:47Z","title":"Lorenz map, inequality ordering and curves based on multidimensional rearrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.09000","kind":"arxiv","version":4},"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":"sha256:4106db5bd4738724205e867e115f09a72e54c7d8a53707a50894a251ada8f732","target":"record","created_at":"2026-07-05T08:08:14Z","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":"32c8fe0dc930c5d2055d2a99d0331cfb25c49489fd168791f00a9d923de1ae1e","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.EM","submitted_at":"2022-03-17T00:39:47Z","title_canon_sha256":"904ba8b17be84c51a04d2ef32c0306d2906e46bc31b449d8706e7fd5329568c9"},"schema_version":"1.0","source":{"id":"2203.09000","kind":"arxiv","version":4}},"canonical_sha256":"71f725924719259cda577b58a10223a3cd234a33e79aed0581135facd025b42f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f725924719259cda577b58a10223a3cd234a33e79aed0581135facd025b42f","first_computed_at":"2026-07-05T08:08:14.717472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:08:14.717472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4FZPFQfWdAs0bxWt31VPhWzWbdYV3jWG9Y6UCsZIqqnf4hHZC5yO76yztojuBzrTw3Deutup3xSvIoImaN4LAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:08:14.717834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.09000","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4106db5bd4738724205e867e115f09a72e54c7d8a53707a50894a251ada8f732","sha256:c6bd059c25994cf8de088f2505384869b3bf5946c069b010abce1d35c5a3e2b6"],"state_sha256":"2c9d9c0ef059bf5211b04ea2acbe771f9471a14cc773840f3b6064b5ffbeb55e"}