{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:P7MGZ3TCZ7H3ABUWN5PFOVD74V","short_pith_number":"pith:P7MGZ3TC","schema_version":"1.0","canonical_sha256":"7fd86cee62cfcfb006966f5e57547fe54586d8e41ad1071267d4540a044b8b03","source":{"kind":"arxiv","id":"1501.01899","version":3},"attestation_state":"computed","paper":{"title":"Cardinal Interpolation With General Multiquadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeff Ledford, Keaton Hamm","submitted_at":"2015-01-08T16:42:56Z","abstract_excerpt":"This paper studies the cardinal interpolation operators associated with the general multiquadrics, $\\phi_{\\alpha,c}(x) = (\\|x\\|^2+c^2)^\\alpha$, $x\\in\\mathbb{R}^d$. These operators take the form $$\\mathscr{I}_{\\alpha,c}\\mathbf{y}(x) = \\sum_{j\\in\\mathbb{Z}^d}y_jL_{\\alpha,c}(x-j),\\quad\\mathbf{y}=(y_j)_{j\\in\\mathbb{Z}^d},\\quad x\\in\\mathbb{R}^d,$$ where $L_{\\alpha,c}$ is a fundamental function formed by integer translates of $\\phi_{\\alpha,c}$ which satisfies the interpolatory condition $L_{\\alpha,c}(k) = \\delta_{0,k},\\; k\\in\\mathbb{Z}^d$.\n  We consider recovery results for interpolation of bandlimi"},"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":"1501.01899","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-01-08T16:42:56Z","cross_cats_sorted":[],"title_canon_sha256":"3834f61914f651421a22e9050f76402e41ca4aab0d0b2519247eea95457867d2","abstract_canon_sha256":"f5ae9eb0084deeaa3cfc60885794fd9d2a946704a81ea8db5cbdd8677b7259db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:39.129673Z","signature_b64":"zDEahTOpY4BjhPPDjWCB818Ql0RlOYKbKG4O9odUgsNk1Fzrw1hq7DjrDJ5czInhdDUUd3tl2/CZsyjGaXSqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fd86cee62cfcfb006966f5e57547fe54586d8e41ad1071267d4540a044b8b03","last_reissued_at":"2026-05-18T00:44:39.129200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:39.129200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cardinal Interpolation With General Multiquadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jeff Ledford, Keaton Hamm","submitted_at":"2015-01-08T16:42:56Z","abstract_excerpt":"This paper studies the cardinal interpolation operators associated with the general multiquadrics, $\\phi_{\\alpha,c}(x) = (\\|x\\|^2+c^2)^\\alpha$, $x\\in\\mathbb{R}^d$. These operators take the form $$\\mathscr{I}_{\\alpha,c}\\mathbf{y}(x) = \\sum_{j\\in\\mathbb{Z}^d}y_jL_{\\alpha,c}(x-j),\\quad\\mathbf{y}=(y_j)_{j\\in\\mathbb{Z}^d},\\quad x\\in\\mathbb{R}^d,$$ where $L_{\\alpha,c}$ is a fundamental function formed by integer translates of $\\phi_{\\alpha,c}$ which satisfies the interpolatory condition $L_{\\alpha,c}(k) = \\delta_{0,k},\\; k\\in\\mathbb{Z}^d$.\n  We consider recovery results for interpolation of bandlimi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01899","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":""},"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":"1501.01899","created_at":"2026-05-18T00:44:39.129260+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.01899v3","created_at":"2026-05-18T00:44:39.129260+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01899","created_at":"2026-05-18T00:44:39.129260+00:00"},{"alias_kind":"pith_short_12","alias_value":"P7MGZ3TCZ7H3","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"P7MGZ3TCZ7H3ABUW","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"P7MGZ3TC","created_at":"2026-05-18T12:29:34.919912+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/P7MGZ3TCZ7H3ABUWN5PFOVD74V","json":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V.json","graph_json":"https://pith.science/api/pith-number/P7MGZ3TCZ7H3ABUWN5PFOVD74V/graph.json","events_json":"https://pith.science/api/pith-number/P7MGZ3TCZ7H3ABUWN5PFOVD74V/events.json","paper":"https://pith.science/paper/P7MGZ3TC"},"agent_actions":{"view_html":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V","download_json":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V.json","view_paper":"https://pith.science/paper/P7MGZ3TC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.01899&json=true","fetch_graph":"https://pith.science/api/pith-number/P7MGZ3TCZ7H3ABUWN5PFOVD74V/graph.json","fetch_events":"https://pith.science/api/pith-number/P7MGZ3TCZ7H3ABUWN5PFOVD74V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V/action/storage_attestation","attest_author":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V/action/author_attestation","sign_citation":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V/action/citation_signature","submit_replication":"https://pith.science/pith/P7MGZ3TCZ7H3ABUWN5PFOVD74V/action/replication_record"}},"created_at":"2026-05-18T00:44:39.129260+00:00","updated_at":"2026-05-18T00:44:39.129260+00:00"}