{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CYPNWBKLGEG6HUNEEYL6RIQQYB","short_pith_number":"pith:CYPNWBKL","canonical_record":{"source":{"id":"1101.2628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-13T18:09:53Z","cross_cats_sorted":[],"title_canon_sha256":"522599da204b69cc0550b429828084d61d7c0e2f5fe11fb27daafbfb0ea342c1","abstract_canon_sha256":"89658fdf2d3702bed1033b4ed50889a916b33171e8532f19ac379c742b646fe4"},"schema_version":"1.0"},"canonical_sha256":"161edb054b310de3d1a42617e8a210c0617b0ef2274b3ebd18017f93494b0ba8","source":{"kind":"arxiv","id":"1101.2628","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2628","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2628v1","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2628","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"CYPNWBKLGEG6","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CYPNWBKLGEG6HUNE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CYPNWBKL","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CYPNWBKLGEG6HUNEEYL6RIQQYB","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-13T18:09:53Z","cross_cats_sorted":[],"title_canon_sha256":"522599da204b69cc0550b429828084d61d7c0e2f5fe11fb27daafbfb0ea342c1","abstract_canon_sha256":"89658fdf2d3702bed1033b4ed50889a916b33171e8532f19ac379c742b646fe4"},"schema_version":"1.0"},"canonical_sha256":"161edb054b310de3d1a42617e8a210c0617b0ef2274b3ebd18017f93494b0ba8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:41.764607Z","signature_b64":"C4tzPpvqWD8nHJp17idwWXFQ+sNWLxlDcS+5Oedlna+qq0vwapFy/df9dbHXSW+NI3fxQM1BJViBtlrkrsMSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"161edb054b310de3d1a42617e8a210c0617b0ef2274b3ebd18017f93494b0ba8","last_reissued_at":"2026-05-18T04:31:41.764133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:41.764133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2628","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fjPQp0Qp5etxroPaaVd14O3XoqP/0UPQBVqpsOBK8bnYsUPm2UqQCQtlzswJhOlQb9M1uJ5/JaG1RKxSkdyEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:23:13.205254Z"},"content_sha256":"763ba8729b4dbbb64901c0526c276c528273213dc814a46c014e69dd0a06c687","schema_version":"1.0","event_id":"sha256:763ba8729b4dbbb64901c0526c276c528273213dc814a46c014e69dd0a06c687"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CYPNWBKLGEG6HUNEEYL6RIQQYB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact asymptotics of the uniform error of interpolation by multilinear splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yuliya Babenko","submitted_at":"2011-01-13T18:09:53Z","abstract_excerpt":"The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others. In this paper we will investigate the questions regarding adaptive approximation of C2 functions with arbitrary but fixed throughout the domain signature by multilinear splines. In particular, we will s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2628","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qu8/2K2lGn69tn7jKNR5ANqoseHCFK8YKLwaCgKl6BSRKnySUfkdOhUuesTxBB40eRujMMcX0ym1+kbdDX60DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:23:13.205976Z"},"content_sha256":"ba57b3f998d30dd082665ecb4b6172d9135b68ef2d1773c7c3da751f5baa28fc","schema_version":"1.0","event_id":"sha256:ba57b3f998d30dd082665ecb4b6172d9135b68ef2d1773c7c3da751f5baa28fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYPNWBKLGEG6HUNEEYL6RIQQYB/bundle.json","state_url":"https://pith.science/pith/CYPNWBKLGEG6HUNEEYL6RIQQYB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYPNWBKLGEG6HUNEEYL6RIQQYB/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":"2026-05-31T05:23:13Z","links":{"resolver":"https://pith.science/pith/CYPNWBKLGEG6HUNEEYL6RIQQYB","bundle":"https://pith.science/pith/CYPNWBKLGEG6HUNEEYL6RIQQYB/bundle.json","state":"https://pith.science/pith/CYPNWBKLGEG6HUNEEYL6RIQQYB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYPNWBKLGEG6HUNEEYL6RIQQYB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CYPNWBKLGEG6HUNEEYL6RIQQYB","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":"89658fdf2d3702bed1033b4ed50889a916b33171e8532f19ac379c742b646fe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-13T18:09:53Z","title_canon_sha256":"522599da204b69cc0550b429828084d61d7c0e2f5fe11fb27daafbfb0ea342c1"},"schema_version":"1.0","source":{"id":"1101.2628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2628","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2628v1","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2628","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"CYPNWBKLGEG6","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CYPNWBKLGEG6HUNE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CYPNWBKL","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:ba57b3f998d30dd082665ecb4b6172d9135b68ef2d1773c7c3da751f5baa28fc","target":"graph","created_at":"2026-05-18T04:31:41Z","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":"The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design, finite element methods for numerical solutions of partial differential equations, image processing, and mesh generation for computer graphics, among others. In this paper we will investigate the questions regarding adaptive approximation of C2 functions with arbitrary but fixed throughout the domain signature by multilinear splines. In particular, we will s","authors_text":"Yuliya Babenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-13T18:09:53Z","title":"Exact asymptotics of the uniform error of interpolation by multilinear splines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2628","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":"sha256:763ba8729b4dbbb64901c0526c276c528273213dc814a46c014e69dd0a06c687","target":"record","created_at":"2026-05-18T04:31:41Z","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":"89658fdf2d3702bed1033b4ed50889a916b33171e8532f19ac379c742b646fe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-13T18:09:53Z","title_canon_sha256":"522599da204b69cc0550b429828084d61d7c0e2f5fe11fb27daafbfb0ea342c1"},"schema_version":"1.0","source":{"id":"1101.2628","kind":"arxiv","version":1}},"canonical_sha256":"161edb054b310de3d1a42617e8a210c0617b0ef2274b3ebd18017f93494b0ba8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"161edb054b310de3d1a42617e8a210c0617b0ef2274b3ebd18017f93494b0ba8","first_computed_at":"2026-05-18T04:31:41.764133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:41.764133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C4tzPpvqWD8nHJp17idwWXFQ+sNWLxlDcS+5Oedlna+qq0vwapFy/df9dbHXSW+NI3fxQM1BJViBtlrkrsMSAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:41.764607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:763ba8729b4dbbb64901c0526c276c528273213dc814a46c014e69dd0a06c687","sha256:ba57b3f998d30dd082665ecb4b6172d9135b68ef2d1773c7c3da751f5baa28fc"],"state_sha256":"a2653ad55cffd22965ecb2ecacc3406c9a8cadbe2c1f1efc7fa77ecc24ebb3c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkkMrekvaVnu/NLkOh1dckQ2rpfFrTa1QCnrgf2C3y6Bf4uQPSYWBoFznjKK5RIGi2Hl8sB2t4w55nTAfDqjDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:23:13.209793Z","bundle_sha256":"aa5af15c94a63ddc57b956142bbd0420cf681949287917c37fbef0d53d81affe"}}