{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UCFV4EHPU5USBYRXBDQS5HGI6K","short_pith_number":"pith:UCFV4EHP","schema_version":"1.0","canonical_sha256":"a08b5e10efa76920e23708e12e9cc8f289934949312dc9125e0a307d0912da2b","source":{"kind":"arxiv","id":"1301.6768","version":2},"attestation_state":"computed","paper":{"title":"Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claudio Canuto, Kolja Brix, Martin Campos Pinto, Wolfgang Dahmen","submitted_at":"2013-01-28T21:03:24Z","abstract_excerpt":"This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of the condition numbers that is logarithmic in the polynomial degrees when all degrees are equal and quadratic otherwise, our main objective is to realize full robustness with respect to arbitrarily large locally varying polynomial degrees degrees, i.e., under mild grading constraints condition numbers stay uniformly bounded with respect to the mesh size and va"},"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":"1301.6768","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-28T21:03:24Z","cross_cats_sorted":[],"title_canon_sha256":"f07a1507ecc9bbacaa11b7dcad81af15359ff249d734f52db96c1aaea01f30b4","abstract_canon_sha256":"198b4018fcde38104bb93ab331156845fd38ddcac674bbb077135d4349d7457d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:04.294779Z","signature_b64":"xaUj4czJck9pBQUHl2Hi/wAuBteZsnTtWrx9xmDx+20hmaGjH5WExDIhwdVrb2eHvP3IfgL6ykwQayzlOS/IDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a08b5e10efa76920e23708e12e9cc8f289934949312dc9125e0a307d0912da2b","last_reissued_at":"2026-05-18T02:52:04.294345Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:04.294345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claudio Canuto, Kolja Brix, Martin Campos Pinto, Wolfgang Dahmen","submitted_at":"2013-01-28T21:03:24Z","abstract_excerpt":"This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of the condition numbers that is logarithmic in the polynomial degrees when all degrees are equal and quadratic otherwise, our main objective is to realize full robustness with respect to arbitrarily large locally varying polynomial degrees degrees, i.e., under mild grading constraints condition numbers stay uniformly bounded with respect to the mesh size and va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6768","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.6768","created_at":"2026-05-18T02:52:04.294429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6768v2","created_at":"2026-05-18T02:52:04.294429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6768","created_at":"2026-05-18T02:52:04.294429+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCFV4EHPU5US","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCFV4EHPU5USBYRX","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCFV4EHP","created_at":"2026-05-18T12:28:02.375192+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/UCFV4EHPU5USBYRXBDQS5HGI6K","json":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K.json","graph_json":"https://pith.science/api/pith-number/UCFV4EHPU5USBYRXBDQS5HGI6K/graph.json","events_json":"https://pith.science/api/pith-number/UCFV4EHPU5USBYRXBDQS5HGI6K/events.json","paper":"https://pith.science/paper/UCFV4EHP"},"agent_actions":{"view_html":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K","download_json":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K.json","view_paper":"https://pith.science/paper/UCFV4EHP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6768&json=true","fetch_graph":"https://pith.science/api/pith-number/UCFV4EHPU5USBYRXBDQS5HGI6K/graph.json","fetch_events":"https://pith.science/api/pith-number/UCFV4EHPU5USBYRXBDQS5HGI6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K/action/storage_attestation","attest_author":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K/action/author_attestation","sign_citation":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K/action/citation_signature","submit_replication":"https://pith.science/pith/UCFV4EHPU5USBYRXBDQS5HGI6K/action/replication_record"}},"created_at":"2026-05-18T02:52:04.294429+00:00","updated_at":"2026-05-18T02:52:04.294429+00:00"}