{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WSIRR2DDM5M7LKQJLOV2JBW7BA","short_pith_number":"pith:WSIRR2DD","schema_version":"1.0","canonical_sha256":"b49118e8636759f5aa095baba486df080aff00d6ca48c8c3bc88b9c3a4cd74a0","source":{"kind":"arxiv","id":"1403.0619","version":1},"attestation_state":"computed","paper":{"title":"von Neumann indices and classes of positive definite functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Feng Tian, Palle Jorgensen","submitted_at":"2014-03-03T22:24:30Z","abstract_excerpt":"With view to applications, we establish a correspondence between two problems: (i) the problem of finding continuous positive definite extensions of functions $F$ which are defined on open bounded domains $\\Omega$ in $\\mathbb{R}$, on the one hand; and (ii) spectral theory for elliptic differential operators acting on $\\Omega$, (constant coefficients.) A novelty in our approach is the use of a reproducing kernel Hilbert space $\\mathscr{H}_{F}$ computed directly from $\\left(\\Omega,F\\right)$, as well as algorithms for computing relevant orthonormal bases in $\\mathscr{H}_{F}$."},"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":"1403.0619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-03-03T22:24:30Z","cross_cats_sorted":[],"title_canon_sha256":"d272266ce31478924a07373bafb11bc4c9140cbaf6deb2dc19d139d5b5c4d8e2","abstract_canon_sha256":"0e7c768d566ac4a5b5865f98570099a81fd317c9262347d78f65a743054f913d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:20.561067Z","signature_b64":"MEDWeQ7yt8S98uFUk6re70BOtBORrXmHiPlZueYquUg802fkvGIwj6767r5rdoARRYCJz/SFPV9PmMP5jM7vDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b49118e8636759f5aa095baba486df080aff00d6ca48c8c3bc88b9c3a4cd74a0","last_reissued_at":"2026-05-18T01:44:20.560258Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:20.560258Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"von Neumann indices and classes of positive definite functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Feng Tian, Palle Jorgensen","submitted_at":"2014-03-03T22:24:30Z","abstract_excerpt":"With view to applications, we establish a correspondence between two problems: (i) the problem of finding continuous positive definite extensions of functions $F$ which are defined on open bounded domains $\\Omega$ in $\\mathbb{R}$, on the one hand; and (ii) spectral theory for elliptic differential operators acting on $\\Omega$, (constant coefficients.) A novelty in our approach is the use of a reproducing kernel Hilbert space $\\mathscr{H}_{F}$ computed directly from $\\left(\\Omega,F\\right)$, as well as algorithms for computing relevant orthonormal bases in $\\mathscr{H}_{F}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0619","kind":"arxiv","version":1},"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":"1403.0619","created_at":"2026-05-18T01:44:20.560371+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.0619v1","created_at":"2026-05-18T01:44:20.560371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0619","created_at":"2026-05-18T01:44:20.560371+00:00"},{"alias_kind":"pith_short_12","alias_value":"WSIRR2DDM5M7","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WSIRR2DDM5M7LKQJ","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WSIRR2DD","created_at":"2026-05-18T12:28:54.890064+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/WSIRR2DDM5M7LKQJLOV2JBW7BA","json":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA.json","graph_json":"https://pith.science/api/pith-number/WSIRR2DDM5M7LKQJLOV2JBW7BA/graph.json","events_json":"https://pith.science/api/pith-number/WSIRR2DDM5M7LKQJLOV2JBW7BA/events.json","paper":"https://pith.science/paper/WSIRR2DD"},"agent_actions":{"view_html":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA","download_json":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA.json","view_paper":"https://pith.science/paper/WSIRR2DD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.0619&json=true","fetch_graph":"https://pith.science/api/pith-number/WSIRR2DDM5M7LKQJLOV2JBW7BA/graph.json","fetch_events":"https://pith.science/api/pith-number/WSIRR2DDM5M7LKQJLOV2JBW7BA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA/action/storage_attestation","attest_author":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA/action/author_attestation","sign_citation":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA/action/citation_signature","submit_replication":"https://pith.science/pith/WSIRR2DDM5M7LKQJLOV2JBW7BA/action/replication_record"}},"created_at":"2026-05-18T01:44:20.560371+00:00","updated_at":"2026-05-18T01:44:20.560371+00:00"}