{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DS5XMEWZ5F66ZTWGLZ3E4FMDQL","short_pith_number":"pith:DS5XMEWZ","schema_version":"1.0","canonical_sha256":"1cbb7612d9e97deccec65e764e158382eddb4bb3968d08f44ac2a8554dab803b","source":{"kind":"arxiv","id":"1311.0028","version":1},"attestation_state":"computed","paper":{"title":"Legendre-Gauss-Lobatto grids and associated nested dyadic grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claudio Canuto, Kolja Brix, Wolfgang Dahmen","submitted_at":"2013-10-31T20:32:08Z","abstract_excerpt":"Legendre-Gauss-Lobatto (LGL) grids play a pivotal role in nodal spectral methods for the numerical solution of partial differential equations. They not only provide efficient high-order quadrature rules, but give also rise to norm equivalences that could eventually lead to efficient preconditioning techniques in high-order methods. Unfortunately, a serious obstruction to fully exploiting the potential of such concepts is the fact that LGL grids of different degree are not nested. This affects, on the one hand, the choice and analysis of suitable auxiliary spaces, when applying the auxiliary sp"},"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":"1311.0028","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-31T20:32:08Z","cross_cats_sorted":[],"title_canon_sha256":"1d9454013a74c3fdba29f3d2f18a928e747459f1197e8cd56390c542d4d29ffb","abstract_canon_sha256":"e6691d2a5e0924e0effe95e04c06cd50a2a935c567ecc7525b3bb1a3083543b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:16.240184Z","signature_b64":"qX25fx0BQ5hgEM6hbwXjgjm2MxdRWcBWAh36w9VY1odmYQAyZqoiRGWwdHQrskjMi4FgsFlZh9MONK61Ys1MDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cbb7612d9e97deccec65e764e158382eddb4bb3968d08f44ac2a8554dab803b","last_reissued_at":"2026-05-18T03:08:16.239708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:16.239708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Legendre-Gauss-Lobatto grids and associated nested dyadic grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claudio Canuto, Kolja Brix, Wolfgang Dahmen","submitted_at":"2013-10-31T20:32:08Z","abstract_excerpt":"Legendre-Gauss-Lobatto (LGL) grids play a pivotal role in nodal spectral methods for the numerical solution of partial differential equations. They not only provide efficient high-order quadrature rules, but give also rise to norm equivalences that could eventually lead to efficient preconditioning techniques in high-order methods. Unfortunately, a serious obstruction to fully exploiting the potential of such concepts is the fact that LGL grids of different degree are not nested. This affects, on the one hand, the choice and analysis of suitable auxiliary spaces, when applying the auxiliary sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0028","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":""},"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":"1311.0028","created_at":"2026-05-18T03:08:16.239769+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.0028v1","created_at":"2026-05-18T03:08:16.239769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0028","created_at":"2026-05-18T03:08:16.239769+00:00"},{"alias_kind":"pith_short_12","alias_value":"DS5XMEWZ5F66","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DS5XMEWZ5F66ZTWG","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DS5XMEWZ","created_at":"2026-05-18T12:27:43.054852+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/DS5XMEWZ5F66ZTWGLZ3E4FMDQL","json":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL.json","graph_json":"https://pith.science/api/pith-number/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/graph.json","events_json":"https://pith.science/api/pith-number/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/events.json","paper":"https://pith.science/paper/DS5XMEWZ"},"agent_actions":{"view_html":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL","download_json":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL.json","view_paper":"https://pith.science/paper/DS5XMEWZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.0028&json=true","fetch_graph":"https://pith.science/api/pith-number/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/graph.json","fetch_events":"https://pith.science/api/pith-number/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/action/storage_attestation","attest_author":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/action/author_attestation","sign_citation":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/action/citation_signature","submit_replication":"https://pith.science/pith/DS5XMEWZ5F66ZTWGLZ3E4FMDQL/action/replication_record"}},"created_at":"2026-05-18T03:08:16.239769+00:00","updated_at":"2026-05-18T03:08:16.239769+00:00"}