{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GMXQPPWFUT5RQ2YJOCY5ZM2ETC","short_pith_number":"pith:GMXQPPWF","canonical_record":{"source":{"id":"1101.2696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-14T00:01:06Z","cross_cats_sorted":[],"title_canon_sha256":"f22f52a50f719f21134a1b95b0636bb88c1d888d9ff7938d3ffdc0176aa02619","abstract_canon_sha256":"2acaab338c0c70afe93f8924c2b416e4747f95a210198d55ccca357256396818"},"schema_version":"1.0"},"canonical_sha256":"332f07bec5a4fb186b0970b1dcb344988a4deec74018ddbe35d3046dbeab62de","source":{"kind":"arxiv","id":"1101.2696","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2696","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2696v1","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2696","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"GMXQPPWFUT5R","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GMXQPPWFUT5RQ2YJ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GMXQPPWF","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GMXQPPWFUT5RQ2YJOCY5ZM2ETC","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2696","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-14T00:01:06Z","cross_cats_sorted":[],"title_canon_sha256":"f22f52a50f719f21134a1b95b0636bb88c1d888d9ff7938d3ffdc0176aa02619","abstract_canon_sha256":"2acaab338c0c70afe93f8924c2b416e4747f95a210198d55ccca357256396818"},"schema_version":"1.0"},"canonical_sha256":"332f07bec5a4fb186b0970b1dcb344988a4deec74018ddbe35d3046dbeab62de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:31.887791Z","signature_b64":"nECSNmPCJxU2wM3Y3/PwlLcVNn+q8N7apfCcyO8DJvj/k0d0Pe4ISC+luOH9tbGXBl8R3+x8EOBVGci5F0AAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"332f07bec5a4fb186b0970b1dcb344988a4deec74018ddbe35d3046dbeab62de","last_reissued_at":"2026-05-18T04:31:31.887244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:31.887244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2696","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MdZhuELtLlSIoXbb9Xe3CQbRX8o3fZFkzFyBdKsD8Jkr3pJ56hJaTBRNsX9fyivperjMUaRU0wSYGsh/QkTPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:35:47.613565Z"},"content_sha256":"50ab5b027dbee7870548ad57d6be4dd5cb2bc126a0bc4575369950a9549fbbf6","schema_version":"1.0","event_id":"sha256:50ab5b027dbee7870548ad57d6be4dd5cb2bc126a0bc4575369950a9549fbbf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GMXQPPWFUT5RQ2YJOCY5ZM2ETC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the $L_p$-error of approximation of bivariate functions by harmonic splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Tatyana Leskevich, Yuliya Babenko","submitted_at":"2011-01-14T00:01:06Z","abstract_excerpt":"Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline \"interpolation\" (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the $L_p$-error for adaptive approximation by harmonic splines."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2696","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rcOoFo6WhNu9RzO+d3EvLLO9CNet3dKU08SeV3mYNVdFjilMjTKdgY3U+0KFRPALKSD0dWSQC2g4ozMD0yIlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:35:47.613907Z"},"content_sha256":"8c580c2fa7500186be86b9736900580395ad59884acaa68fc8821535acddd9d8","schema_version":"1.0","event_id":"sha256:8c580c2fa7500186be86b9736900580395ad59884acaa68fc8821535acddd9d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMXQPPWFUT5RQ2YJOCY5ZM2ETC/bundle.json","state_url":"https://pith.science/pith/GMXQPPWFUT5RQ2YJOCY5ZM2ETC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMXQPPWFUT5RQ2YJOCY5ZM2ETC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T16:35:47Z","links":{"resolver":"https://pith.science/pith/GMXQPPWFUT5RQ2YJOCY5ZM2ETC","bundle":"https://pith.science/pith/GMXQPPWFUT5RQ2YJOCY5ZM2ETC/bundle.json","state":"https://pith.science/pith/GMXQPPWFUT5RQ2YJOCY5ZM2ETC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMXQPPWFUT5RQ2YJOCY5ZM2ETC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GMXQPPWFUT5RQ2YJOCY5ZM2ETC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2acaab338c0c70afe93f8924c2b416e4747f95a210198d55ccca357256396818","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-14T00:01:06Z","title_canon_sha256":"f22f52a50f719f21134a1b95b0636bb88c1d888d9ff7938d3ffdc0176aa02619"},"schema_version":"1.0","source":{"id":"1101.2696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2696","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2696v1","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2696","created_at":"2026-05-18T04:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"GMXQPPWFUT5R","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GMXQPPWFUT5RQ2YJ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GMXQPPWF","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:8c580c2fa7500186be86b9736900580395ad59884acaa68fc8821535acddd9d8","target":"graph","created_at":"2026-05-18T04:31:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline \"interpolation\" (on the lines of a grid) as an alternative to polynomial spline interpolation (at vertices of a grid). We will discuss some advantages and drawbacks of this approach and present the asymptotics of the $L_p$-error for adaptive approximation by harmonic splines.","authors_text":"Tatyana Leskevich, Yuliya Babenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-14T00:01:06Z","title":"On the $L_p$-error of approximation of bivariate functions by harmonic splines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2696","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:50ab5b027dbee7870548ad57d6be4dd5cb2bc126a0bc4575369950a9549fbbf6","target":"record","created_at":"2026-05-18T04:31:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2acaab338c0c70afe93f8924c2b416e4747f95a210198d55ccca357256396818","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-14T00:01:06Z","title_canon_sha256":"f22f52a50f719f21134a1b95b0636bb88c1d888d9ff7938d3ffdc0176aa02619"},"schema_version":"1.0","source":{"id":"1101.2696","kind":"arxiv","version":1}},"canonical_sha256":"332f07bec5a4fb186b0970b1dcb344988a4deec74018ddbe35d3046dbeab62de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"332f07bec5a4fb186b0970b1dcb344988a4deec74018ddbe35d3046dbeab62de","first_computed_at":"2026-05-18T04:31:31.887244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:31.887244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nECSNmPCJxU2wM3Y3/PwlLcVNn+q8N7apfCcyO8DJvj/k0d0Pe4ISC+luOH9tbGXBl8R3+x8EOBVGci5F0AAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:31.887791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50ab5b027dbee7870548ad57d6be4dd5cb2bc126a0bc4575369950a9549fbbf6","sha256:8c580c2fa7500186be86b9736900580395ad59884acaa68fc8821535acddd9d8"],"state_sha256":"263e4e522276f774ce807e51f4b4ef09411246578b1da3d5c2de5f4d147594ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmOfxb2npXO5EKF1MDjcRFAFDfL/zdydnswMpwNCmqh4/0BDyVUywtLxgLaDb9s+0IwF/PaGPEvJyy3dTYUeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:35:47.615900Z","bundle_sha256":"79cf108c4e50af70dd40a18580b3e0b8e9aa4ea7a11bde5465d35e7a71e9e7f4"}}