{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:L3FAQM273DNBVEQUCPRDL4Q6RJ","short_pith_number":"pith:L3FAQM27","schema_version":"1.0","canonical_sha256":"5eca08335fd8da1a921413e235f21e8a7242451bf890bac9195eace3485547f3","source":{"kind":"arxiv","id":"1712.06893","version":1},"attestation_state":"computed","paper":{"title":"Wider contours and adaptive contours","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Kevin Burrage, Shev MacNamara, William McLean","submitted_at":"2017-12-19T12:16:07Z","abstract_excerpt":"Contour integrals in the complex plane are the basis of effective numerical methods for computing matrix functions, such as the matrix exponential and the Mittag-Leffler function. These methods provide successful ways to solve partial differential equations, such as convection--diffusion models. Part of the success of these methods comes from exploiting the freedom to choose the contour, by appealing to Cauchy's theorem. However, the pseudospectra of non-normal matrices or operators present a challenge for these methods: if the contour is too close to regions where the norm of the resolvent ma"},"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":"1712.06893","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-19T12:16:07Z","cross_cats_sorted":["cs.NA","math.PR"],"title_canon_sha256":"afb17501f7ba9b77092e4bf97d4c8a459fa4845786340daf2b53d16c147e7206","abstract_canon_sha256":"2615a135413a0af535511de5f329e3c4a044eebdaf6ee8fdedcc38833a531729"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:11:21.290697Z","signature_b64":"2XJmOHL02bQG6Jn/gp/+HZaa5mCShSyTt1zEWEHJ8B6HlDWfQmb3BERfkx4+jwjduKiWOD1Ktrqx27O2JZXRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5eca08335fd8da1a921413e235f21e8a7242451bf890bac9195eace3485547f3","last_reissued_at":"2026-06-04T19:11:21.290250Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:11:21.290250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wider contours and adaptive contours","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.PR"],"primary_cat":"math.NA","authors_text":"Kevin Burrage, Shev MacNamara, William McLean","submitted_at":"2017-12-19T12:16:07Z","abstract_excerpt":"Contour integrals in the complex plane are the basis of effective numerical methods for computing matrix functions, such as the matrix exponential and the Mittag-Leffler function. These methods provide successful ways to solve partial differential equations, such as convection--diffusion models. Part of the success of these methods comes from exploiting the freedom to choose the contour, by appealing to Cauchy's theorem. However, the pseudospectra of non-normal matrices or operators present a challenge for these methods: if the contour is too close to regions where the norm of the resolvent ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06893","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/1712.06893/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":"1712.06893","created_at":"2026-06-04T19:11:21.290307+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.06893v1","created_at":"2026-06-04T19:11:21.290307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06893","created_at":"2026-06-04T19:11:21.290307+00:00"},{"alias_kind":"pith_short_12","alias_value":"L3FAQM273DNB","created_at":"2026-06-04T19:11:21.290307+00:00"},{"alias_kind":"pith_short_16","alias_value":"L3FAQM273DNBVEQU","created_at":"2026-06-04T19:11:21.290307+00:00"},{"alias_kind":"pith_short_8","alias_value":"L3FAQM27","created_at":"2026-06-04T19:11:21.290307+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/L3FAQM273DNBVEQUCPRDL4Q6RJ","json":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ.json","graph_json":"https://pith.science/api/pith-number/L3FAQM273DNBVEQUCPRDL4Q6RJ/graph.json","events_json":"https://pith.science/api/pith-number/L3FAQM273DNBVEQUCPRDL4Q6RJ/events.json","paper":"https://pith.science/paper/L3FAQM27"},"agent_actions":{"view_html":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ","download_json":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ.json","view_paper":"https://pith.science/paper/L3FAQM27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.06893&json=true","fetch_graph":"https://pith.science/api/pith-number/L3FAQM273DNBVEQUCPRDL4Q6RJ/graph.json","fetch_events":"https://pith.science/api/pith-number/L3FAQM273DNBVEQUCPRDL4Q6RJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ/action/storage_attestation","attest_author":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ/action/author_attestation","sign_citation":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ/action/citation_signature","submit_replication":"https://pith.science/pith/L3FAQM273DNBVEQUCPRDL4Q6RJ/action/replication_record"}},"created_at":"2026-06-04T19:11:21.290307+00:00","updated_at":"2026-06-04T19:11:21.290307+00:00"}