{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:YAZ4GSDTMVJEYYFOG2U4Q4W7BR","short_pith_number":"pith:YAZ4GSDT","schema_version":"1.0","canonical_sha256":"c033c3487365524c60ae36a9c872df0c634cdf9f4c5297467f6ef7cd6c7ff4f7","source":{"kind":"arxiv","id":"2310.09149","version":3},"attestation_state":"computed","paper":{"title":"Structured Approximations of Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"stat.ML","authors_text":"Keaton Hamm, Varun Khurana","submitted_at":"2023-10-13T14:43:11Z","abstract_excerpt":"We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints. We obtain three sets of results. First, for measures with densities bounded away from zero on a bounded Lipschitz domain $\\Omega$, we prove that any approximation scheme for functions in $\\mathrm{L}_p(\\Omega)$ transfers, with linear rate, to a corresponding approximation scheme for measures in $\\mathrm{W}_p(\\Omega)$. The argument applies a theorem of Bogovskii on regu"},"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":"2310.09149","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-10-13T14:43:11Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"924b411b9e72e3b2498627d124434ad7cc744680bd324181e0daa2cecdf46549","abstract_canon_sha256":"c74b03886e57cfcce71410e260e77d01c6f26fc0e4706cdfdc0301c2882dfad8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:33.425827Z","signature_b64":"n+NbGV+kNEinKrVbrh6xkW6QMTyyiKH/qg52PQ3mHr9g4j1osPp8s9IxwK8V5bzWBhDqDo8MfelYk237YLrTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c033c3487365524c60ae36a9c872df0c634cdf9f4c5297467f6ef7cd6c7ff4f7","last_reissued_at":"2026-06-25T01:18:33.425412Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:33.425412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structured Approximations of Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"stat.ML","authors_text":"Keaton Hamm, Varun Khurana","submitted_at":"2023-10-13T14:43:11Z","abstract_excerpt":"We study the approximation of probability measures in the Wasserstein-$p$ distance by structured classes of approximators, motivated by applications in imaging, machine learning, and physical measurement under sensor constraints. We obtain three sets of results. First, for measures with densities bounded away from zero on a bounded Lipschitz domain $\\Omega$, we prove that any approximation scheme for functions in $\\mathrm{L}_p(\\Omega)$ transfers, with linear rate, to a corresponding approximation scheme for measures in $\\mathrm{W}_p(\\Omega)$. The argument applies a theorem of Bogovskii on regu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.09149","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.09149/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":"2310.09149","created_at":"2026-06-25T01:18:33.425476+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.09149v3","created_at":"2026-06-25T01:18:33.425476+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.09149","created_at":"2026-06-25T01:18:33.425476+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAZ4GSDTMVJE","created_at":"2026-06-25T01:18:33.425476+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAZ4GSDTMVJEYYFO","created_at":"2026-06-25T01:18:33.425476+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAZ4GSDT","created_at":"2026-06-25T01:18:33.425476+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/YAZ4GSDTMVJEYYFOG2U4Q4W7BR","json":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR.json","graph_json":"https://pith.science/api/pith-number/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/graph.json","events_json":"https://pith.science/api/pith-number/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/events.json","paper":"https://pith.science/paper/YAZ4GSDT"},"agent_actions":{"view_html":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR","download_json":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR.json","view_paper":"https://pith.science/paper/YAZ4GSDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.09149&json=true","fetch_graph":"https://pith.science/api/pith-number/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/graph.json","fetch_events":"https://pith.science/api/pith-number/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/action/storage_attestation","attest_author":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/action/author_attestation","sign_citation":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/action/citation_signature","submit_replication":"https://pith.science/pith/YAZ4GSDTMVJEYYFOG2U4Q4W7BR/action/replication_record"}},"created_at":"2026-06-25T01:18:33.425476+00:00","updated_at":"2026-06-25T01:18:33.425476+00:00"}