{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TV45M73KBJ576CDFEN26RJUN5G","short_pith_number":"pith:TV45M73K","schema_version":"1.0","canonical_sha256":"9d79d67f6a0a7bff08652375e8a68de99345e2e8fbed76fecdff7eebf931b24e","source":{"kind":"arxiv","id":"2606.05615","version":1},"attestation_state":"computed","paper":{"title":"Weighted hp-Uniform Decompositions for H^k-Type Tensor-Product Spaces in Arbitrary Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Situan Li, Weiying Zheng","submitted_at":"2026-06-04T02:36:42Z","abstract_excerpt":"We establish weighted hp-uniform vertex-patch decompositions in arbitrary space dimension d >= 1 for tensor-product discretizations of H^k-type conforming and nonconforming spaces, with arbitrary fixed Sobolev order k >= 1, on fitted interface meshes. The cells are coordinate-compatible cuboids, the local spaces are Q_{p_K}(K) with arbitrary elementwise degrees satisfying p_K >= 2k-1, and the coefficient may have arbitrarily large jumps across material interfaces. Under local coefficient oscillation bounds and a local high-side connectivity condition, both the conforming H^k space and the nonc"},"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":"2606.05615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-04T02:36:42Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"79f09425e735b7c6d8fb48e8d17ec5ee0b5e1ddab9840f214823cd12a249727d","abstract_canon_sha256":"0daa6ecec89e540aadec0f989246015cef76eb098054ef3a28836baf2f8e002b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:14:56.506490Z","signature_b64":"jBoQsEHgYhwaFbf8AgslYLXuNOplnVQHmQ0OmyExsTU4zLytcypDECNzRP2H2pZFnV4eZMJKtVdXhfn0x6yMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d79d67f6a0a7bff08652375e8a68de99345e2e8fbed76fecdff7eebf931b24e","last_reissued_at":"2026-06-05T01:14:56.505989Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:14:56.505989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted hp-Uniform Decompositions for H^k-Type Tensor-Product Spaces in Arbitrary Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Situan Li, Weiying Zheng","submitted_at":"2026-06-04T02:36:42Z","abstract_excerpt":"We establish weighted hp-uniform vertex-patch decompositions in arbitrary space dimension d >= 1 for tensor-product discretizations of H^k-type conforming and nonconforming spaces, with arbitrary fixed Sobolev order k >= 1, on fitted interface meshes. The cells are coordinate-compatible cuboids, the local spaces are Q_{p_K}(K) with arbitrary elementwise degrees satisfying p_K >= 2k-1, and the coefficient may have arbitrarily large jumps across material interfaces. Under local coefficient oscillation bounds and a local high-side connectivity condition, both the conforming H^k space and the nonc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05615","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/2606.05615/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":"2606.05615","created_at":"2026-06-05T01:14:56.506058+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.05615v1","created_at":"2026-06-05T01:14:56.506058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.05615","created_at":"2026-06-05T01:14:56.506058+00:00"},{"alias_kind":"pith_short_12","alias_value":"TV45M73KBJ57","created_at":"2026-06-05T01:14:56.506058+00:00"},{"alias_kind":"pith_short_16","alias_value":"TV45M73KBJ576CDF","created_at":"2026-06-05T01:14:56.506058+00:00"},{"alias_kind":"pith_short_8","alias_value":"TV45M73K","created_at":"2026-06-05T01:14:56.506058+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/TV45M73KBJ576CDFEN26RJUN5G","json":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G.json","graph_json":"https://pith.science/api/pith-number/TV45M73KBJ576CDFEN26RJUN5G/graph.json","events_json":"https://pith.science/api/pith-number/TV45M73KBJ576CDFEN26RJUN5G/events.json","paper":"https://pith.science/paper/TV45M73K"},"agent_actions":{"view_html":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G","download_json":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G.json","view_paper":"https://pith.science/paper/TV45M73K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.05615&json=true","fetch_graph":"https://pith.science/api/pith-number/TV45M73KBJ576CDFEN26RJUN5G/graph.json","fetch_events":"https://pith.science/api/pith-number/TV45M73KBJ576CDFEN26RJUN5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G/action/storage_attestation","attest_author":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G/action/author_attestation","sign_citation":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G/action/citation_signature","submit_replication":"https://pith.science/pith/TV45M73KBJ576CDFEN26RJUN5G/action/replication_record"}},"created_at":"2026-06-05T01:14:56.506058+00:00","updated_at":"2026-06-05T01:14:56.506058+00:00"}