{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KZ5IEUBZTT5VNT36X6JRWQD4HU","short_pith_number":"pith:KZ5IEUBZ","schema_version":"1.0","canonical_sha256":"567a8250399cfb56cf7ebf931b407c3d1ef671b287984fd1082cdc33dce56261","source":{"kind":"arxiv","id":"1703.01494","version":2},"attestation_state":"computed","paper":{"title":"The multidimensional truncated Moment Problem: Carath\\'eodory Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Konrad Schm\\\"udgen, Philipp J. di Dio","submitted_at":"2017-03-04T17:17:46Z","abstract_excerpt":"Let $\\mathcal{A}$ be a finite-dimensional subspace of $C(\\mathcal{X};\\mathbb{R})$, where $\\mathcal{X}$ is a locally compact Hausdorff space, and $\\mathsf{A}=\\{f_1,\\dots,f_m\\}$ a basis of $\\mathcal{A}$. A sequence $s=(s_j)_{j=1}^m$ is called a moment sequence if $s_j=\\int f_j(x) \\, d\\mu(x)$, $j=1,\\dots,m$, for some positive Radon measure $\\mu$ on $\\mathcal{X}$. Each moment sequence $s$ has a finitely atomic representing measure $\\mu$. The smallest possible number of atoms is called the Carath\\'eodory number $\\mathcal{C}_{\\mathsf{A}}(s)$. The largest number $\\mathcal{C}_{\\mathsf{A}}(s)$ among al"},"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":"1703.01494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-04T17:17:46Z","cross_cats_sorted":[],"title_canon_sha256":"4a2edcaeb148210069d59e2d2c7b6bd7bc56fda2b179d83045327e2dfa8dcb7e","abstract_canon_sha256":"9cc9961474f99b767575f76d3e1d7c4e5234d348ce9555cd2b140d39ec6bad28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:04.193592Z","signature_b64":"qften6RD49p2QVQ/Ghqu/KEERptOK+NQnGo3HPImDH2FnsG5JQbz2lCrPGWKayTimbhKUKCkWEMoWoZ/9VXiDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"567a8250399cfb56cf7ebf931b407c3d1ef671b287984fd1082cdc33dce56261","last_reissued_at":"2026-05-18T00:18:04.193034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:04.193034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The multidimensional truncated Moment Problem: Carath\\'eodory Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Konrad Schm\\\"udgen, Philipp J. di Dio","submitted_at":"2017-03-04T17:17:46Z","abstract_excerpt":"Let $\\mathcal{A}$ be a finite-dimensional subspace of $C(\\mathcal{X};\\mathbb{R})$, where $\\mathcal{X}$ is a locally compact Hausdorff space, and $\\mathsf{A}=\\{f_1,\\dots,f_m\\}$ a basis of $\\mathcal{A}$. A sequence $s=(s_j)_{j=1}^m$ is called a moment sequence if $s_j=\\int f_j(x) \\, d\\mu(x)$, $j=1,\\dots,m$, for some positive Radon measure $\\mu$ on $\\mathcal{X}$. Each moment sequence $s$ has a finitely atomic representing measure $\\mu$. The smallest possible number of atoms is called the Carath\\'eodory number $\\mathcal{C}_{\\mathsf{A}}(s)$. The largest number $\\mathcal{C}_{\\mathsf{A}}(s)$ among al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01494","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":"1703.01494","created_at":"2026-05-18T00:18:04.193114+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.01494v2","created_at":"2026-05-18T00:18:04.193114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01494","created_at":"2026-05-18T00:18:04.193114+00:00"},{"alias_kind":"pith_short_12","alias_value":"KZ5IEUBZTT5V","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KZ5IEUBZTT5VNT36","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KZ5IEUBZ","created_at":"2026-05-18T12:31:28.150371+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/KZ5IEUBZTT5VNT36X6JRWQD4HU","json":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU.json","graph_json":"https://pith.science/api/pith-number/KZ5IEUBZTT5VNT36X6JRWQD4HU/graph.json","events_json":"https://pith.science/api/pith-number/KZ5IEUBZTT5VNT36X6JRWQD4HU/events.json","paper":"https://pith.science/paper/KZ5IEUBZ"},"agent_actions":{"view_html":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU","download_json":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU.json","view_paper":"https://pith.science/paper/KZ5IEUBZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.01494&json=true","fetch_graph":"https://pith.science/api/pith-number/KZ5IEUBZTT5VNT36X6JRWQD4HU/graph.json","fetch_events":"https://pith.science/api/pith-number/KZ5IEUBZTT5VNT36X6JRWQD4HU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU/action/storage_attestation","attest_author":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU/action/author_attestation","sign_citation":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU/action/citation_signature","submit_replication":"https://pith.science/pith/KZ5IEUBZTT5VNT36X6JRWQD4HU/action/replication_record"}},"created_at":"2026-05-18T00:18:04.193114+00:00","updated_at":"2026-05-18T00:18:04.193114+00:00"}