{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NIAJAUYSH5EBMMDBNKYPZHZKMH","short_pith_number":"pith:NIAJAUYS","canonical_record":{"source":{"id":"1812.09088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-21T12:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"d5def9ca85993ebcf5fbdc307f0dfe8839d24d6b826d964a25a63e089ced5c01","abstract_canon_sha256":"2e76a4e4c1355aeaf03e19b1b340a541606082cc7ccd9ff45109305b76ab8c15"},"schema_version":"1.0"},"canonical_sha256":"6a009053123f481630616ab0fc9f2a61ebc8830fec371fe7d82bf09886ba234f","source":{"kind":"arxiv","id":"1812.09088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09088","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09088v1","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09088","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"NIAJAUYSH5EB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NIAJAUYSH5EBMMDB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NIAJAUYS","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NIAJAUYSH5EBMMDBNKYPZHZKMH","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-21T12:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"d5def9ca85993ebcf5fbdc307f0dfe8839d24d6b826d964a25a63e089ced5c01","abstract_canon_sha256":"2e76a4e4c1355aeaf03e19b1b340a541606082cc7ccd9ff45109305b76ab8c15"},"schema_version":"1.0"},"canonical_sha256":"6a009053123f481630616ab0fc9f2a61ebc8830fec371fe7d82bf09886ba234f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:45.452026Z","signature_b64":"5h8qv7yWTQM3nCUyqyDUXXw8bivjCa3mPiRyMt6QcNsmymVm28wToYUNiF4urjYuwxfMHTGjeaaUiaZA+2ZDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a009053123f481630616ab0fc9f2a61ebc8830fec371fe7d82bf09886ba234f","last_reissued_at":"2026-05-17T23:57:45.451388Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:45.451388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09088","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":"2026-05-17T23:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+kxXHm3doFaWwTsnvQe8ED9W5khMAtuftB4CXzjNxeiZ9CmkpQW5bqhc8aXlcrXORr/vO8W9w6mHViK1riLOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:02:39.552775Z"},"content_sha256":"101d05859f4f4e3b5909f5067244151fc1aac1542e51125f48c6ecde0e69b055","schema_version":"1.0","event_id":"sha256:101d05859f4f4e3b5909f5067244151fc1aac1542e51125f48c6ecde0e69b055"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NIAJAUYSH5EBMMDBNKYPZHZKMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isogeometric analysis with $C^1$ functions on unstructured quadrilateral meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Giancarlo Sangalli, Mario Kapl, Thomas Takacs","submitted_at":"2018-12-21T12:46:55Z","abstract_excerpt":"In the context of isogeometric analysis, globally $C^1$ isogeometric spaces over unstructured quadrilateral meshes allow the direct solution of fourth order partial differential equations on complex geometries via their Galerkin discretization. The design of such smooth spaces has been intensively studied in the last five years, in particular for the case of planar domains, and is still task of current research. In this paper, we first give a short survey of the developed methods and especially focus on the approach [26]. There, the construction of a specific $C^1$ isogeometric spline space fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09088","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":"2026-05-17T23:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HD94wyhxFjrX2X2Y0VT1YuT3H38886TUbnOZIbcYhZfY8S3oCSEDpSe4ulx9nlM3i+1oDgqcOv/RwHJ7y8NrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T07:02:39.553167Z"},"content_sha256":"b10f6b074075b5d331ae0b66f5757b24c6b09d9510905d2866d83438d4f1bb68","schema_version":"1.0","event_id":"sha256:b10f6b074075b5d331ae0b66f5757b24c6b09d9510905d2866d83438d4f1bb68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIAJAUYSH5EBMMDBNKYPZHZKMH/bundle.json","state_url":"https://pith.science/pith/NIAJAUYSH5EBMMDBNKYPZHZKMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIAJAUYSH5EBMMDBNKYPZHZKMH/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":"2026-07-05T07:02:39Z","links":{"resolver":"https://pith.science/pith/NIAJAUYSH5EBMMDBNKYPZHZKMH","bundle":"https://pith.science/pith/NIAJAUYSH5EBMMDBNKYPZHZKMH/bundle.json","state":"https://pith.science/pith/NIAJAUYSH5EBMMDBNKYPZHZKMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIAJAUYSH5EBMMDBNKYPZHZKMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NIAJAUYSH5EBMMDBNKYPZHZKMH","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":"2e76a4e4c1355aeaf03e19b1b340a541606082cc7ccd9ff45109305b76ab8c15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-21T12:46:55Z","title_canon_sha256":"d5def9ca85993ebcf5fbdc307f0dfe8839d24d6b826d964a25a63e089ced5c01"},"schema_version":"1.0","source":{"id":"1812.09088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09088","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09088v1","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09088","created_at":"2026-05-17T23:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"NIAJAUYSH5EB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NIAJAUYSH5EBMMDB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NIAJAUYS","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:b10f6b074075b5d331ae0b66f5757b24c6b09d9510905d2866d83438d4f1bb68","target":"graph","created_at":"2026-05-17T23:57:45Z","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 the context of isogeometric analysis, globally $C^1$ isogeometric spaces over unstructured quadrilateral meshes allow the direct solution of fourth order partial differential equations on complex geometries via their Galerkin discretization. The design of such smooth spaces has been intensively studied in the last five years, in particular for the case of planar domains, and is still task of current research. In this paper, we first give a short survey of the developed methods and especially focus on the approach [26]. There, the construction of a specific $C^1$ isogeometric spline space fo","authors_text":"Giancarlo Sangalli, Mario Kapl, Thomas Takacs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-21T12:46:55Z","title":"Isogeometric analysis with $C^1$ functions on unstructured quadrilateral meshes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09088","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":"sha256:101d05859f4f4e3b5909f5067244151fc1aac1542e51125f48c6ecde0e69b055","target":"record","created_at":"2026-05-17T23:57:45Z","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":"2e76a4e4c1355aeaf03e19b1b340a541606082cc7ccd9ff45109305b76ab8c15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-12-21T12:46:55Z","title_canon_sha256":"d5def9ca85993ebcf5fbdc307f0dfe8839d24d6b826d964a25a63e089ced5c01"},"schema_version":"1.0","source":{"id":"1812.09088","kind":"arxiv","version":1}},"canonical_sha256":"6a009053123f481630616ab0fc9f2a61ebc8830fec371fe7d82bf09886ba234f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a009053123f481630616ab0fc9f2a61ebc8830fec371fe7d82bf09886ba234f","first_computed_at":"2026-05-17T23:57:45.451388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:45.451388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5h8qv7yWTQM3nCUyqyDUXXw8bivjCa3mPiRyMt6QcNsmymVm28wToYUNiF4urjYuwxfMHTGjeaaUiaZA+2ZDAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:45.452026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:101d05859f4f4e3b5909f5067244151fc1aac1542e51125f48c6ecde0e69b055","sha256:b10f6b074075b5d331ae0b66f5757b24c6b09d9510905d2866d83438d4f1bb68"],"state_sha256":"50249209b2401074c6d4e25e1a1119f7fbfe017ce5efa2e99a02fdc2aa9319e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6aYl7VqlIdhxZY5F/y1wpK9XTeA8nRIUveQBDuNkJRYmYVYs8ugDG+4SGpHcTNm1ry+g7bn0PJ9L9s1PUYtvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T07:02:39.555118Z","bundle_sha256":"0667b4ea07a668967264102a95f9e76131c72972031106c909aca1e9c2aa2de8"}}