{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6PDSXE5JAAQ2IFMARKD35ORGMB","short_pith_number":"pith:6PDSXE5J","schema_version":"1.0","canonical_sha256":"f3c72b93a90021a415808a87beba266075e9b17cbc8a77386c377b43d4b3deea","source":{"kind":"arxiv","id":"1702.05894","version":1},"attestation_state":"computed","paper":{"title":"Schoenberg Representations and Gramian Matrices of Mat\\'ern Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dohie Kim, Hera Yun, Kyungwon Park, Yong-Kum Cho","submitted_at":"2017-02-20T08:32:09Z","abstract_excerpt":"We represent Mat\\'ern functions in terms of Schoenberg's integrals which ensure the positive definiteness and prove the systems of translates of Mat\\'ern functions form Riesz sequences in $L^2(\\R^n)$ or Sobolev spaces. Our approach is based on a new class of integral transforms that generalize Fourier transforms for radial functions. We also consider inverse multi-quadrics and obtain similar results."},"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":"1702.05894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-20T08:32:09Z","cross_cats_sorted":[],"title_canon_sha256":"4d06defd191b967b1a35a05438628727a82ef76e286648269c35fdf44dbcf086","abstract_canon_sha256":"9a46bda132c8a2cba4f19ff795d1c3e7c0defc8f316d1ceb322b8eae1cb323ba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:24.971427Z","signature_b64":"Q9yfHhRzHl9EKRDpe3yr7xSTLAA+IFR8Xf7M5g+8AvXysM0TsTX68jNxrvOVWujWlrgGs1I7ejWe+uR5X9VuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3c72b93a90021a415808a87beba266075e9b17cbc8a77386c377b43d4b3deea","last_reissued_at":"2026-05-18T00:50:24.970656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:24.970656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schoenberg Representations and Gramian Matrices of Mat\\'ern Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dohie Kim, Hera Yun, Kyungwon Park, Yong-Kum Cho","submitted_at":"2017-02-20T08:32:09Z","abstract_excerpt":"We represent Mat\\'ern functions in terms of Schoenberg's integrals which ensure the positive definiteness and prove the systems of translates of Mat\\'ern functions form Riesz sequences in $L^2(\\R^n)$ or Sobolev spaces. Our approach is based on a new class of integral transforms that generalize Fourier transforms for radial functions. We also consider inverse multi-quadrics and obtain similar results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05894","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":"1702.05894","created_at":"2026-05-18T00:50:24.970820+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.05894v1","created_at":"2026-05-18T00:50:24.970820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05894","created_at":"2026-05-18T00:50:24.970820+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PDSXE5JAAQ2","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PDSXE5JAAQ2IFMA","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PDSXE5J","created_at":"2026-05-18T12:31:03.183658+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/6PDSXE5JAAQ2IFMARKD35ORGMB","json":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB.json","graph_json":"https://pith.science/api/pith-number/6PDSXE5JAAQ2IFMARKD35ORGMB/graph.json","events_json":"https://pith.science/api/pith-number/6PDSXE5JAAQ2IFMARKD35ORGMB/events.json","paper":"https://pith.science/paper/6PDSXE5J"},"agent_actions":{"view_html":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB","download_json":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB.json","view_paper":"https://pith.science/paper/6PDSXE5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.05894&json=true","fetch_graph":"https://pith.science/api/pith-number/6PDSXE5JAAQ2IFMARKD35ORGMB/graph.json","fetch_events":"https://pith.science/api/pith-number/6PDSXE5JAAQ2IFMARKD35ORGMB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB/action/storage_attestation","attest_author":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB/action/author_attestation","sign_citation":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB/action/citation_signature","submit_replication":"https://pith.science/pith/6PDSXE5JAAQ2IFMARKD35ORGMB/action/replication_record"}},"created_at":"2026-05-18T00:50:24.970820+00:00","updated_at":"2026-05-18T00:50:24.970820+00:00"}