{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OG3ABVOG4WQPRXOVDRQG6EZL2B","short_pith_number":"pith:OG3ABVOG","schema_version":"1.0","canonical_sha256":"71b600d5c6e5a0f8ddd51c606f132bd059a9984ab4bb1a41b45da6ec34bd6526","source":{"kind":"arxiv","id":"2406.07972","version":2},"attestation_state":"computed","paper":{"title":"Expected value and a Cayley-Menger type formula for the generalized earth mover's distance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"William Q. Erickson","submitted_at":"2024-06-12T07:54:14Z","abstract_excerpt":"The earth mover's distance (EMD), also known as the 1-Wasserstein metric, measures the minimum amount of work required to transform one probability distribution into another. The EMD can be naturally generalized to measure the \"distance\" between any number (say $d$) of distributions. In previous work (2021), we found a recursive formula for the expected value of the generalized EMD, assuming the uniform distribution on the standard $n$-simplex. This recursion, however, was computationally expensive, requiring $\\binom{d+n}{d}$ many iterations. The main result of the present paper is a nonrecurs"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2406.07972","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-06-12T07:54:14Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6dbeccd031cc9baa86b45fea766573408c62a4602256cb38991b82991cd743f5","abstract_canon_sha256":"58d23ff30bef8720ab6d39ae9feb60a08e97a3175910bed2d7fb0c00cf67d546"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:47:21.831866Z","signature_b64":"t8+xgH7uio9xknxcaigssnC4BNqsszlfa79YxksnMnpFEFN+wWvMmIoWqFLXSS+00GTBVG+lb6ds1O1/U7QXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71b600d5c6e5a0f8ddd51c606f132bd059a9984ab4bb1a41b45da6ec34bd6526","last_reissued_at":"2026-07-05T09:47:21.831339Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:47:21.831339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expected value and a Cayley-Menger type formula for the generalized earth mover's distance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"William Q. Erickson","submitted_at":"2024-06-12T07:54:14Z","abstract_excerpt":"The earth mover's distance (EMD), also known as the 1-Wasserstein metric, measures the minimum amount of work required to transform one probability distribution into another. The EMD can be naturally generalized to measure the \"distance\" between any number (say $d$) of distributions. In previous work (2021), we found a recursive formula for the expected value of the generalized EMD, assuming the uniform distribution on the standard $n$-simplex. This recursion, however, was computationally expensive, requiring $\\binom{d+n}{d}$ many iterations. The main result of the present paper is a nonrecurs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07972","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.07972/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2406.07972","created_at":"2026-07-05T09:47:21.831406+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.07972v2","created_at":"2026-07-05T09:47:21.831406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07972","created_at":"2026-07-05T09:47:21.831406+00:00"},{"alias_kind":"pith_short_12","alias_value":"OG3ABVOG4WQP","created_at":"2026-07-05T09:47:21.831406+00:00"},{"alias_kind":"pith_short_16","alias_value":"OG3ABVOG4WQPRXOV","created_at":"2026-07-05T09:47:21.831406+00:00"},{"alias_kind":"pith_short_8","alias_value":"OG3ABVOG","created_at":"2026-07-05T09:47:21.831406+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.04412","citing_title":"Approximation Models for Shared Mobility Rebalancing Under Structured Spatial Imbalance","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B","json":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B.json","graph_json":"https://pith.science/api/pith-number/OG3ABVOG4WQPRXOVDRQG6EZL2B/graph.json","events_json":"https://pith.science/api/pith-number/OG3ABVOG4WQPRXOVDRQG6EZL2B/events.json","paper":"https://pith.science/paper/OG3ABVOG"},"agent_actions":{"view_html":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B","download_json":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B.json","view_paper":"https://pith.science/paper/OG3ABVOG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.07972&json=true","fetch_graph":"https://pith.science/api/pith-number/OG3ABVOG4WQPRXOVDRQG6EZL2B/graph.json","fetch_events":"https://pith.science/api/pith-number/OG3ABVOG4WQPRXOVDRQG6EZL2B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B/action/storage_attestation","attest_author":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B/action/author_attestation","sign_citation":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B/action/citation_signature","submit_replication":"https://pith.science/pith/OG3ABVOG4WQPRXOVDRQG6EZL2B/action/replication_record"}},"created_at":"2026-07-05T09:47:21.831406+00:00","updated_at":"2026-07-05T09:47:21.831406+00:00"}