{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XIQCG7EFBQQDIW3SPYF57BQLRQ","short_pith_number":"pith:XIQCG7EF","schema_version":"1.0","canonical_sha256":"ba20237c850c20345b727e0bdf860b8c1e913bdea77af76df6a6a181ec05b39a","source":{"kind":"arxiv","id":"2606.12656","version":1},"attestation_state":"computed","paper":{"title":"On the completeness of generalized hierarchical spline spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ahmed Oufqir, Carla Manni, Hendrik Speleers","submitted_at":"2026-06-10T20:30:26Z","abstract_excerpt":"We introduce a general theoretical approach to hierarchical spline spaces that replaces the classical constructive definition - based on basis selection - with a descriptive formulation in terms of regularity constraints. Specifically, we define generalized hierarchical spline spaces on multi-level domains as collections of piecewise functions satisfying hierarchical contact conditions across interfaces between refinement levels. The proposed framework applies to a broad class of local function spaces and relies on a minimal abstract requirement, the extension assumption, rather than on specif"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.12656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-10T20:30:26Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"e03cbffa72630033f8951a2148f238e27119e290d4c454fa0c3c3f285c7cde80","abstract_canon_sha256":"d737a201e2457831611a479bb9c8dee57c2ff095f47867ec499dd4f3adfdbc2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:08:42.976244Z","signature_b64":"rRBMdkK9IbyHVUmuRhSOBqOMOZDXEBP164Fp0Y8cHB8+Vdajn2+7waBOWoYyQZdJ5UeVc0wrmlhQ2ZldiP0eCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba20237c850c20345b727e0bdf860b8c1e913bdea77af76df6a6a181ec05b39a","last_reissued_at":"2026-06-12T01:08:42.975366Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:08:42.975366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the completeness of generalized hierarchical spline spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Ahmed Oufqir, Carla Manni, Hendrik Speleers","submitted_at":"2026-06-10T20:30:26Z","abstract_excerpt":"We introduce a general theoretical approach to hierarchical spline spaces that replaces the classical constructive definition - based on basis selection - with a descriptive formulation in terms of regularity constraints. Specifically, we define generalized hierarchical spline spaces on multi-level domains as collections of piecewise functions satisfying hierarchical contact conditions across interfaces between refinement levels. The proposed framework applies to a broad class of local function spaces and relies on a minimal abstract requirement, the extension assumption, rather than on specif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12656","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.12656/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.12656","created_at":"2026-06-12T01:08:42.975508+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.12656v1","created_at":"2026-06-12T01:08:42.975508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12656","created_at":"2026-06-12T01:08:42.975508+00:00"},{"alias_kind":"pith_short_12","alias_value":"XIQCG7EFBQQD","created_at":"2026-06-12T01:08:42.975508+00:00"},{"alias_kind":"pith_short_16","alias_value":"XIQCG7EFBQQDIW3S","created_at":"2026-06-12T01:08:42.975508+00:00"},{"alias_kind":"pith_short_8","alias_value":"XIQCG7EF","created_at":"2026-06-12T01:08:42.975508+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ","json":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ.json","graph_json":"https://pith.science/api/pith-number/XIQCG7EFBQQDIW3SPYF57BQLRQ/graph.json","events_json":"https://pith.science/api/pith-number/XIQCG7EFBQQDIW3SPYF57BQLRQ/events.json","paper":"https://pith.science/paper/XIQCG7EF"},"agent_actions":{"view_html":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ","download_json":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ.json","view_paper":"https://pith.science/paper/XIQCG7EF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.12656&json=true","fetch_graph":"https://pith.science/api/pith-number/XIQCG7EFBQQDIW3SPYF57BQLRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/XIQCG7EFBQQDIW3SPYF57BQLRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ/action/storage_attestation","attest_author":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ/action/author_attestation","sign_citation":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ/action/citation_signature","submit_replication":"https://pith.science/pith/XIQCG7EFBQQDIW3SPYF57BQLRQ/action/replication_record"}},"created_at":"2026-06-12T01:08:42.975508+00:00","updated_at":"2026-06-12T01:08:42.975508+00:00"}