{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OQ6DWYU3R3C6MGNBJQ6LCE4FID","short_pith_number":"pith:OQ6DWYU3","schema_version":"1.0","canonical_sha256":"743c3b629b8ec5e619a14c3cb1138540de1f27c4b00ca167fe8146181cd1bf14","source":{"kind":"arxiv","id":"1706.07650","version":2},"attestation_state":"computed","paper":{"title":"Semi-discrete optimal transport - the case p=1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.NA","authors_text":"Dominic Schuhmacher, Valentin Hartmann","submitted_at":"2017-06-23T11:57:37Z","abstract_excerpt":"We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\\mu$ on $\\mathcal{X} \\subset \\mathbb{R}^d$ and a finitely supported measure $\\nu$ on $\\mathbb{R}^d$ when the transport cost is the Euclidean distance. We may think of this problem as closest distance allocation of some ressource continuously distributed over space to a finite number of processing sites with capacity constraints.\n  This article gives a detailed discussion of the problem, including a comparison with the much better studied case of squared Euclidean cost (\"the case $p=2$\"). We p"},"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":"1706.07650","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-06-23T11:57:37Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"b7c1471dca03a28549f863dffd38303715846f73195ae2e6ce31b41ca7c6ed38","abstract_canon_sha256":"46017efc4578f3db82b9132d51b484a693218f6e7f33c117ac08d59b3752a429"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:05.205164Z","signature_b64":"/3ffrvBv9Xr7n2evnu/3zI2RWtK4rce72Df2qcwgBW4mCtJ0KtWwm2gQpMU1tCj45queVPOmjTJaP+98rJlyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"743c3b629b8ec5e619a14c3cb1138540de1f27c4b00ca167fe8146181cd1bf14","last_reissued_at":"2026-05-18T00:04:05.204455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:05.204455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-discrete optimal transport - the case p=1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.NA","authors_text":"Dominic Schuhmacher, Valentin Hartmann","submitted_at":"2017-06-23T11:57:37Z","abstract_excerpt":"We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\\mu$ on $\\mathcal{X} \\subset \\mathbb{R}^d$ and a finitely supported measure $\\nu$ on $\\mathbb{R}^d$ when the transport cost is the Euclidean distance. We may think of this problem as closest distance allocation of some ressource continuously distributed over space to a finite number of processing sites with capacity constraints.\n  This article gives a detailed discussion of the problem, including a comparison with the much better studied case of squared Euclidean cost (\"the case $p=2$\"). We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07650","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.07650","created_at":"2026-05-18T00:04:05.204568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07650v2","created_at":"2026-05-18T00:04:05.204568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07650","created_at":"2026-05-18T00:04:05.204568+00:00"},{"alias_kind":"pith_short_12","alias_value":"OQ6DWYU3R3C6","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OQ6DWYU3R3C6MGNB","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OQ6DWYU3","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID","json":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID.json","graph_json":"https://pith.science/api/pith-number/OQ6DWYU3R3C6MGNBJQ6LCE4FID/graph.json","events_json":"https://pith.science/api/pith-number/OQ6DWYU3R3C6MGNBJQ6LCE4FID/events.json","paper":"https://pith.science/paper/OQ6DWYU3"},"agent_actions":{"view_html":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID","download_json":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID.json","view_paper":"https://pith.science/paper/OQ6DWYU3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07650&json=true","fetch_graph":"https://pith.science/api/pith-number/OQ6DWYU3R3C6MGNBJQ6LCE4FID/graph.json","fetch_events":"https://pith.science/api/pith-number/OQ6DWYU3R3C6MGNBJQ6LCE4FID/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID/action/storage_attestation","attest_author":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID/action/author_attestation","sign_citation":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID/action/citation_signature","submit_replication":"https://pith.science/pith/OQ6DWYU3R3C6MGNBJQ6LCE4FID/action/replication_record"}},"created_at":"2026-05-18T00:04:05.204568+00:00","updated_at":"2026-05-18T00:04:05.204568+00:00"}