{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:AW4UZIPG2C75YSGSRCEON5SHXA","short_pith_number":"pith:AW4UZIPG","schema_version":"1.0","canonical_sha256":"05b94ca1e6d0bfdc48d28888e6f647b82e6569855b5bbe5a9ce00c64dd3f8adf","source":{"kind":"arxiv","id":"2508.10125","version":1},"attestation_state":"computed","paper":{"title":"Concepts for Composing Finite Element Function Space Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.MS","authors_text":"Carsten Gr\\\"aser, Christian Engwer, Oliver Sander, Simon Praetorius, Steffen M\\\"uthing","submitted_at":"2025-08-13T18:40:07Z","abstract_excerpt":"Finite Element discretizations of coupled multi-physics partial differential equation models require the handling of composed function spaces. In this paper we discuss software concepts and abstractions to handle the composition of function spaces, based on a representation of product spaces as trees of simpler bases. From this description, many different numberings of degrees of freedom by multi-indices can be derived in a natural way, allowing to adapt the function spaces to very different data layouts, so that it opens the possibility to directly use the finite element code with very differ"},"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":"2508.10125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2025-08-13T18:40:07Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"d5303920d257d62a119b65af46d6ba74e5670725f13149c08180dcb793e91c3e","abstract_canon_sha256":"353b39bc3b1807d39f0bc3b3437bf115a11c493c0911fc7c712c2993a70ffb8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:53:32.052962Z","signature_b64":"Iwu/PBTgIOZ3M2skO69ki4U2RxF0P4sYSC4HYHCxhkncCP/7SghGkmdULEwX/O9JRqZFcIfFeMAaZ1poe7eVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05b94ca1e6d0bfdc48d28888e6f647b82e6569855b5bbe5a9ce00c64dd3f8adf","last_reissued_at":"2026-07-05T11:53:32.052456Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:53:32.052456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concepts for Composing Finite Element Function Space Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.MS","authors_text":"Carsten Gr\\\"aser, Christian Engwer, Oliver Sander, Simon Praetorius, Steffen M\\\"uthing","submitted_at":"2025-08-13T18:40:07Z","abstract_excerpt":"Finite Element discretizations of coupled multi-physics partial differential equation models require the handling of composed function spaces. In this paper we discuss software concepts and abstractions to handle the composition of function spaces, based on a representation of product spaces as trees of simpler bases. From this description, many different numberings of degrees of freedom by multi-indices can be derived in a natural way, allowing to adapt the function spaces to very different data layouts, so that it opens the possibility to directly use the finite element code with very differ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.10125","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/2508.10125/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":"2508.10125","created_at":"2026-07-05T11:53:32.052512+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.10125v1","created_at":"2026-07-05T11:53:32.052512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.10125","created_at":"2026-07-05T11:53:32.052512+00:00"},{"alias_kind":"pith_short_12","alias_value":"AW4UZIPG2C75","created_at":"2026-07-05T11:53:32.052512+00:00"},{"alias_kind":"pith_short_16","alias_value":"AW4UZIPG2C75YSGS","created_at":"2026-07-05T11:53:32.052512+00:00"},{"alias_kind":"pith_short_8","alias_value":"AW4UZIPG","created_at":"2026-07-05T11:53:32.052512+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/AW4UZIPG2C75YSGSRCEON5SHXA","json":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA.json","graph_json":"https://pith.science/api/pith-number/AW4UZIPG2C75YSGSRCEON5SHXA/graph.json","events_json":"https://pith.science/api/pith-number/AW4UZIPG2C75YSGSRCEON5SHXA/events.json","paper":"https://pith.science/paper/AW4UZIPG"},"agent_actions":{"view_html":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA","download_json":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA.json","view_paper":"https://pith.science/paper/AW4UZIPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.10125&json=true","fetch_graph":"https://pith.science/api/pith-number/AW4UZIPG2C75YSGSRCEON5SHXA/graph.json","fetch_events":"https://pith.science/api/pith-number/AW4UZIPG2C75YSGSRCEON5SHXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA/action/storage_attestation","attest_author":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA/action/author_attestation","sign_citation":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA/action/citation_signature","submit_replication":"https://pith.science/pith/AW4UZIPG2C75YSGSRCEON5SHXA/action/replication_record"}},"created_at":"2026-07-05T11:53:32.052512+00:00","updated_at":"2026-07-05T11:53:32.052512+00:00"}