{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:X5HYOCVAYLIGI7HBBOG7BJ56U7","short_pith_number":"pith:X5HYOCVA","canonical_record":{"source":{"id":"1604.04585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T17:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"7e00a68515ca537786b6ca57b4dbc07029eb9cca89d85b245e35e1a542842f5a","abstract_canon_sha256":"b94cc2fa1c0213e6d743c4f522e86650eee5e8658f373adfa5ba0a8aabd38d1d"},"schema_version":"1.0"},"canonical_sha256":"bf4f870aa0c2d0647ce10b8df0a7bea7fb1274196cc5ce8e86fa8e2b2ee98379","source":{"kind":"arxiv","id":"1604.04585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04585","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04585v1","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04585","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"X5HYOCVAYLIG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X5HYOCVAYLIGI7HB","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X5HYOCVA","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:X5HYOCVAYLIGI7HBBOG7BJ56U7","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T17:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"7e00a68515ca537786b6ca57b4dbc07029eb9cca89d85b245e35e1a542842f5a","abstract_canon_sha256":"b94cc2fa1c0213e6d743c4f522e86650eee5e8658f373adfa5ba0a8aabd38d1d"},"schema_version":"1.0"},"canonical_sha256":"bf4f870aa0c2d0647ce10b8df0a7bea7fb1274196cc5ce8e86fa8e2b2ee98379","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:01.751155Z","signature_b64":"bxz4t+wQ1ghHtVWwXyghyKxEioaY3uxqX8ClYbXzBSEfCrxmlEr/CpOi2ShXGItB3YDdC19sPD1686g3bPsyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf4f870aa0c2d0647ce10b8df0a7bea7fb1274196cc5ce8e86fa8e2b2ee98379","last_reissued_at":"2026-05-18T01:17:01.750312Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:01.750312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04585","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":"2026-05-18T01:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LthFkZ6kxtxmCZi7zcC8VEUUbbdNs84/b87Q0iR1rK5pVddHsZT7+1cAMT3umeBy5A6Tx7/W0qSjnhe+J9bfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:47:31.220608Z"},"content_sha256":"2f3f81123ce4a4475b5868850b1806dadcaf5ec2ab49a0ec007cacc122236a09","schema_version":"1.0","event_id":"sha256:2f3f81123ce4a4475b5868850b1806dadcaf5ec2ab49a0ec007cacc122236a09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:X5HYOCVAYLIGI7HBBOG7BJ56U7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient computation of partition of unity interpolants through a block-based searching technique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"A. de Rossi, E. Perracchione, R. Cavoretto","submitted_at":"2016-04-15T17:54:20Z","abstract_excerpt":"In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weight functions. In particular we present a new space-partitioning data structure based on a partition of the underlying generic domain in blocks. This approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points, leading to an optimized searching routine. Complexity analysis and numerica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04585","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":"2026-05-18T01:17:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5G+gi93J6ensBIG8y088PHnDqK42Nu8s0kkuWUY+QkulNyjPF0wHAiWOXymUNSjWt8GMjbj45SYgKKt2CR6kDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:47:31.220949Z"},"content_sha256":"e5b02c2330d2014b98bc7cbd9dae64194cfa9013059f33f23daae665b6b92035","schema_version":"1.0","event_id":"sha256:e5b02c2330d2014b98bc7cbd9dae64194cfa9013059f33f23daae665b6b92035"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5HYOCVAYLIGI7HBBOG7BJ56U7/bundle.json","state_url":"https://pith.science/pith/X5HYOCVAYLIGI7HBBOG7BJ56U7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5HYOCVAYLIGI7HBBOG7BJ56U7/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":"2026-06-03T04:47:31Z","links":{"resolver":"https://pith.science/pith/X5HYOCVAYLIGI7HBBOG7BJ56U7","bundle":"https://pith.science/pith/X5HYOCVAYLIGI7HBBOG7BJ56U7/bundle.json","state":"https://pith.science/pith/X5HYOCVAYLIGI7HBBOG7BJ56U7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5HYOCVAYLIGI7HBBOG7BJ56U7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X5HYOCVAYLIGI7HBBOG7BJ56U7","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":"b94cc2fa1c0213e6d743c4f522e86650eee5e8658f373adfa5ba0a8aabd38d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T17:54:20Z","title_canon_sha256":"7e00a68515ca537786b6ca57b4dbc07029eb9cca89d85b245e35e1a542842f5a"},"schema_version":"1.0","source":{"id":"1604.04585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04585","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04585v1","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04585","created_at":"2026-05-18T01:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"X5HYOCVAYLIG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X5HYOCVAYLIGI7HB","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X5HYOCVA","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:e5b02c2330d2014b98bc7cbd9dae64194cfa9013059f33f23daae665b6b92035","target":"graph","created_at":"2026-05-18T01:17:01Z","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":"In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weight functions. In particular we present a new space-partitioning data structure based on a partition of the underlying generic domain in blocks. This approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points, leading to an optimized searching routine. Complexity analysis and numerica","authors_text":"A. de Rossi, E. Perracchione, R. Cavoretto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T17:54:20Z","title":"Efficient computation of partition of unity interpolants through a block-based searching technique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04585","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":"sha256:2f3f81123ce4a4475b5868850b1806dadcaf5ec2ab49a0ec007cacc122236a09","target":"record","created_at":"2026-05-18T01:17:01Z","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":"b94cc2fa1c0213e6d743c4f522e86650eee5e8658f373adfa5ba0a8aabd38d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-15T17:54:20Z","title_canon_sha256":"7e00a68515ca537786b6ca57b4dbc07029eb9cca89d85b245e35e1a542842f5a"},"schema_version":"1.0","source":{"id":"1604.04585","kind":"arxiv","version":1}},"canonical_sha256":"bf4f870aa0c2d0647ce10b8df0a7bea7fb1274196cc5ce8e86fa8e2b2ee98379","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf4f870aa0c2d0647ce10b8df0a7bea7fb1274196cc5ce8e86fa8e2b2ee98379","first_computed_at":"2026-05-18T01:17:01.750312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:01.750312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bxz4t+wQ1ghHtVWwXyghyKxEioaY3uxqX8ClYbXzBSEfCrxmlEr/CpOi2ShXGItB3YDdC19sPD1686g3bPsyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:01.751155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f3f81123ce4a4475b5868850b1806dadcaf5ec2ab49a0ec007cacc122236a09","sha256:e5b02c2330d2014b98bc7cbd9dae64194cfa9013059f33f23daae665b6b92035"],"state_sha256":"f8d020b3fb23d627569a2c0d77a56360f280627a2700d6ebdecaa8ffc109f735"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ZaUAz3R3bMoZ1VDzLvCdacefdMSsdgplZ5B7D39cKaK6Y9EBr9dpCUi6E860s960nPXkJxnjpvmUt6uBkAxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:47:31.222821Z","bundle_sha256":"c49284a415b7b5fe44ba5cdc6f7e30185565d22aef21c30eee2cc01902eb30bd"}}