{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ALR6F7WTHANJXJB2WZXR72C66G","short_pith_number":"pith:ALR6F7WT","canonical_record":{"source":{"id":"1507.08477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-30T12:27:21Z","cross_cats_sorted":[],"title_canon_sha256":"aaf14d56a618fdbfdc1d17f953db1224380300f56d669b5788444f5e8dcb0b2e","abstract_canon_sha256":"c996af74702bbf59a5e1b27612f7c26d0a944fd34f5e13831b16a3eb80b9d6f0"},"schema_version":"1.0"},"canonical_sha256":"02e3e2fed3381a9ba43ab66f1fe85ef191d0274f51e9c9f32482f391c2173067","source":{"kind":"arxiv","id":"1507.08477","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08477","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08477v1","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08477","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"ALR6F7WTHANJ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ALR6F7WTHANJXJB2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ALR6F7WT","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ALR6F7WTHANJXJB2WZXR72C66G","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-30T12:27:21Z","cross_cats_sorted":[],"title_canon_sha256":"aaf14d56a618fdbfdc1d17f953db1224380300f56d669b5788444f5e8dcb0b2e","abstract_canon_sha256":"c996af74702bbf59a5e1b27612f7c26d0a944fd34f5e13831b16a3eb80b9d6f0"},"schema_version":"1.0"},"canonical_sha256":"02e3e2fed3381a9ba43ab66f1fe85ef191d0274f51e9c9f32482f391c2173067","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:06.336503Z","signature_b64":"ZsDKAAKcUf4dq2SgDJGf4NDfiyxYesPU3lZOVhndbiFojURdO7E1zqfkZyWLtA3IjE0ZVDUS7Hx+f8/nNYtQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02e3e2fed3381a9ba43ab66f1fe85ef191d0274f51e9c9f32482f391c2173067","last_reissued_at":"2026-05-18T01:36:06.335906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:06.335906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08477","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":"2026-05-18T01:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6A0zekTqTWS6cAN3NGIN3Mm4J/s1SOIdlAoajxhBf54d6tGR35uxC3nZlqehRRhMQi76TeYILpGtqUy5ExtGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:32:48.716271Z"},"content_sha256":"35b0a369ab33751b631d6f5321381be028d81803045466dbcce58c402bc039a2","schema_version":"1.0","event_id":"sha256:35b0a369ab33751b631d6f5321381be028d81803045466dbcce58c402bc039a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ALR6F7WTHANJXJB2WZXR72C66G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unstructured spline spaces for isogeometric analysis based on spline manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Giancarlo Sangalli, Rafael V\\'azquez, Thomas Takacs","submitted_at":"2015-07-30T12:27:21Z","abstract_excerpt":"Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines, which was originally developed for structured"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08477","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":"2026-05-18T01:36:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"etfMFuDTtRMi7EVTBwWY0Wg3VIGJ4vuGFFCkg+qNkXZ+UrOs+5ZbEXSVqwCzTDIcTA1AF2l45nVKUzHW2shzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:32:48.716627Z"},"content_sha256":"48453720c842ce4a44cfda3f7cf2174a9f115bc71a1ef70081e3b1c118e9c690","schema_version":"1.0","event_id":"sha256:48453720c842ce4a44cfda3f7cf2174a9f115bc71a1ef70081e3b1c118e9c690"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ALR6F7WTHANJXJB2WZXR72C66G/bundle.json","state_url":"https://pith.science/pith/ALR6F7WTHANJXJB2WZXR72C66G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ALR6F7WTHANJXJB2WZXR72C66G/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":"2026-06-20T12:32:48Z","links":{"resolver":"https://pith.science/pith/ALR6F7WTHANJXJB2WZXR72C66G","bundle":"https://pith.science/pith/ALR6F7WTHANJXJB2WZXR72C66G/bundle.json","state":"https://pith.science/pith/ALR6F7WTHANJXJB2WZXR72C66G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ALR6F7WTHANJXJB2WZXR72C66G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ALR6F7WTHANJXJB2WZXR72C66G","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":"c996af74702bbf59a5e1b27612f7c26d0a944fd34f5e13831b16a3eb80b9d6f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-30T12:27:21Z","title_canon_sha256":"aaf14d56a618fdbfdc1d17f953db1224380300f56d669b5788444f5e8dcb0b2e"},"schema_version":"1.0","source":{"id":"1507.08477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08477","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08477v1","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08477","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"ALR6F7WTHANJ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ALR6F7WTHANJXJB2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ALR6F7WT","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:48453720c842ce4a44cfda3f7cf2174a9f115bc71a1ef70081e3b1c118e9c690","target":"graph","created_at":"2026-05-18T01:36:06Z","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":"Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines, which was originally developed for structured","authors_text":"Giancarlo Sangalli, Rafael V\\'azquez, Thomas Takacs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-30T12:27:21Z","title":"Unstructured spline spaces for isogeometric analysis based on spline manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08477","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":"sha256:35b0a369ab33751b631d6f5321381be028d81803045466dbcce58c402bc039a2","target":"record","created_at":"2026-05-18T01:36:06Z","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":"c996af74702bbf59a5e1b27612f7c26d0a944fd34f5e13831b16a3eb80b9d6f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-30T12:27:21Z","title_canon_sha256":"aaf14d56a618fdbfdc1d17f953db1224380300f56d669b5788444f5e8dcb0b2e"},"schema_version":"1.0","source":{"id":"1507.08477","kind":"arxiv","version":1}},"canonical_sha256":"02e3e2fed3381a9ba43ab66f1fe85ef191d0274f51e9c9f32482f391c2173067","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02e3e2fed3381a9ba43ab66f1fe85ef191d0274f51e9c9f32482f391c2173067","first_computed_at":"2026-05-18T01:36:06.335906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:06.335906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZsDKAAKcUf4dq2SgDJGf4NDfiyxYesPU3lZOVhndbiFojURdO7E1zqfkZyWLtA3IjE0ZVDUS7Hx+f8/nNYtQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:06.336503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35b0a369ab33751b631d6f5321381be028d81803045466dbcce58c402bc039a2","sha256:48453720c842ce4a44cfda3f7cf2174a9f115bc71a1ef70081e3b1c118e9c690"],"state_sha256":"5b0d2bc57a561cc1939a258763f8baa2a3fc236764ebd9895eb50ada798720c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0+EAB70ZRRJVG3PJXctCPeEvcYtMNzN+aVxk3xRIy1QqjoXLoUbVg/D8DnKgc0Ef8YZl8dAQBQk1p1KMgg+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T12:32:48.718412Z","bundle_sha256":"3826096d54cfd856e2ef4a01e5d4856a7a02160498f7779008006b7196a0360f"}}