{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:EL32L35N7WTZUH7TYF33Z77SHB","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":"430a3e03b51acd56765d7b1bb38a12c1b7459eb2e73c0f1f6ac59f71212a98fa","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2023-03-09T03:46:46Z","title_canon_sha256":"6429fa57ece172805de98258a62cb914a6eb5a48a09d60d4a8f6122ba0d263c4"},"schema_version":"1.0","source":{"id":"2303.05020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.05020","created_at":"2026-07-05T05:49:36Z"},{"alias_kind":"arxiv_version","alias_value":"2303.05020v1","created_at":"2026-07-05T05:49:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.05020","created_at":"2026-07-05T05:49:36Z"},{"alias_kind":"pith_short_12","alias_value":"EL32L35N7WTZ","created_at":"2026-07-05T05:49:36Z"},{"alias_kind":"pith_short_16","alias_value":"EL32L35N7WTZUH7T","created_at":"2026-07-05T05:49:36Z"},{"alias_kind":"pith_short_8","alias_value":"EL32L35N","created_at":"2026-07-05T05:49:36Z"}],"graph_snapshots":[{"event_id":"sha256:6fc016a263b84c1d3478a704a7b26e84fcd315815a8d40f183885535e49c1462","target":"graph","created_at":"2026-07-05T05:49:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.05020/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce a new family of orthogonal systems, termed as the M\\\"{u}ntz ball polynomials (MBPs), which are orthogonal with respect to the weight function: $\\|x\\|^{2\\theta+2\\mu-2} (1-\\|x\\|^{2\\theta})^{\\alpha}$ with the parameters $\\alpha>-1, \\mu>- 1/2$ and $\\theta>0$ in the $d$-dimensional unit ball $x\\in {\\mathbb B}^d=\\big\\{x\\in\\mathbb{R}^d: r=\\|x\\|\\leq1\\big\\}$. We then develop efficient and spectrally accurate MBP spectral-Galerkin methods for singular eigenvalue problems including degenerating elliptic problems with perturbed ellipticity and Schr\\\"odinger's operators with fra","authors_text":"Changtao Sheng, Huiyuan Li, Li-Lian Wang, Xiu Yang","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2023-03-09T03:46:46Z","title":"M\\\"untz ball polynomials and M\\\"untz spectral-Galerkin methods for singular eigenvalue problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.05020","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":"sha256:3dea27c329b7cfa7c22bdb342b269e376d89a642edc6d39a89dd50892ae691bf","target":"record","created_at":"2026-07-05T05:49:36Z","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":"430a3e03b51acd56765d7b1bb38a12c1b7459eb2e73c0f1f6ac59f71212a98fa","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2023-03-09T03:46:46Z","title_canon_sha256":"6429fa57ece172805de98258a62cb914a6eb5a48a09d60d4a8f6122ba0d263c4"},"schema_version":"1.0","source":{"id":"2303.05020","kind":"arxiv","version":1}},"canonical_sha256":"22f7a5efadfda79a1ff3c177bcfff23856ac7e96daf49dbd070b62f7a09251d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22f7a5efadfda79a1ff3c177bcfff23856ac7e96daf49dbd070b62f7a09251d3","first_computed_at":"2026-07-05T05:49:36.389434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:49:36.389434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j94bgs/UjK/FyYJb/Q0BM7l0dwNMSxsOXExvMB+1v/Jn95L0Dm4q20lh6zGY4XY5p8pyHOtQaQ03CsdWij3KAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:49:36.389856Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.05020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dea27c329b7cfa7c22bdb342b269e376d89a642edc6d39a89dd50892ae691bf","sha256:6fc016a263b84c1d3478a704a7b26e84fcd315815a8d40f183885535e49c1462"],"state_sha256":"575a73470de38392b59e857af92ba672ad8b405f500e4f9ceaa1bb6b6540ae9f"}