{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4WZ2BJUNIVF7GE35KEVXN5ZCD5","short_pith_number":"pith:4WZ2BJUN","schema_version":"1.0","canonical_sha256":"e5b3a0a68d454bf3137d512b76f7221f5ae82d70a2f6b13698d04dbedc48346a","source":{"kind":"arxiv","id":"1701.06030","version":4},"attestation_state":"computed","paper":{"title":"Fourth-order time-stepping for stiff PDEs on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hadrien Montanelli, Yuji Nakatsukasa","submitted_at":"2017-01-21T14:10:14Z","abstract_excerpt":"We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with multiplication matrices that differ from the usual ones, and implicit-explicit time-stepping schemes. Operating in coefficient space with these new matrices allows one to use a sparse direct solver, avoids the coordinate singularity and maintains smoothness at the poles, while implicit-explicit schemes circumvent severe restrictions on the time-steps due to stif"},"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":"1701.06030","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-21T14:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"c0bb001d167350f52e71e3f02324404802bb806171ec449bc1afa787816bbfb7","abstract_canon_sha256":"b7fe9b382a8c908dc84f2eb1e4140445cd2f17800bb05cd532a6cb47deb7e901"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:21.820669Z","signature_b64":"dwu9Wrw7GLhqyspbViZsOUsKJFjzazSCQRNwfHyLAustdYvR0gCLwA2FSCxBmqA1wxVjW/c2UQ2z+rP3bhJXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5b3a0a68d454bf3137d512b76f7221f5ae82d70a2f6b13698d04dbedc48346a","last_reissued_at":"2026-05-18T00:27:21.820036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:21.820036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourth-order time-stepping for stiff PDEs on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hadrien Montanelli, Yuji Nakatsukasa","submitted_at":"2017-01-21T14:10:14Z","abstract_excerpt":"We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with multiplication matrices that differ from the usual ones, and implicit-explicit time-stepping schemes. Operating in coefficient space with these new matrices allows one to use a sparse direct solver, avoids the coordinate singularity and maintains smoothness at the poles, while implicit-explicit schemes circumvent severe restrictions on the time-steps due to stif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06030","kind":"arxiv","version":4},"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":"1701.06030","created_at":"2026-05-18T00:27:21.820133+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.06030v4","created_at":"2026-05-18T00:27:21.820133+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06030","created_at":"2026-05-18T00:27:21.820133+00:00"},{"alias_kind":"pith_short_12","alias_value":"4WZ2BJUNIVF7","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4WZ2BJUNIVF7GE35","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4WZ2BJUN","created_at":"2026-05-18T12:31:00.734936+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/4WZ2BJUNIVF7GE35KEVXN5ZCD5","json":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5.json","graph_json":"https://pith.science/api/pith-number/4WZ2BJUNIVF7GE35KEVXN5ZCD5/graph.json","events_json":"https://pith.science/api/pith-number/4WZ2BJUNIVF7GE35KEVXN5ZCD5/events.json","paper":"https://pith.science/paper/4WZ2BJUN"},"agent_actions":{"view_html":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5","download_json":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5.json","view_paper":"https://pith.science/paper/4WZ2BJUN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.06030&json=true","fetch_graph":"https://pith.science/api/pith-number/4WZ2BJUNIVF7GE35KEVXN5ZCD5/graph.json","fetch_events":"https://pith.science/api/pith-number/4WZ2BJUNIVF7GE35KEVXN5ZCD5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/action/storage_attestation","attest_author":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/action/author_attestation","sign_citation":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/action/citation_signature","submit_replication":"https://pith.science/pith/4WZ2BJUNIVF7GE35KEVXN5ZCD5/action/replication_record"}},"created_at":"2026-05-18T00:27:21.820133+00:00","updated_at":"2026-05-18T00:27:21.820133+00:00"}