{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:W2M6GLD5PLW5MK5KKNO6RWZXEY","short_pith_number":"pith:W2M6GLD5","schema_version":"1.0","canonical_sha256":"b699e32c7d7aedd62baa535de8db37262087de9de01de9fcc405f6e650aa3757","source":{"kind":"arxiv","id":"1303.6651","version":1},"attestation_state":"computed","paper":{"title":"Rational functions with maximal radius of absolute monotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David I. Ketcheson, Lajos Loczi","submitted_at":"2013-03-26T20:26:41Z","abstract_excerpt":"We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parame"},"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":"1303.6651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-03-26T20:26:41Z","cross_cats_sorted":[],"title_canon_sha256":"add9fab2fc41768750ae052dbe5de1a9cf9d4caed1d9f24e33321ce7716aa993","abstract_canon_sha256":"e8d8df8421291f7b532cd93c3263630b47dffa5127c5099400ad67990150dd4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.750068Z","signature_b64":"/De+udr/zw1TIlwPjR7509jW3WwdYFkL7GzeoYYf+FUM4EL/zM2k4M1xkb+flv77LLJOAQ3lg3sVUAHRZjaeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b699e32c7d7aedd62baa535de8db37262087de9de01de9fcc405f6e650aa3757","last_reissued_at":"2026-05-17T23:53:17.749342Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.749342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational functions with maximal radius of absolute monotonicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"David I. Ketcheson, Lajos Loczi","submitted_at":"2013-03-26T20:26:41Z","abstract_excerpt":"We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions arise in the application of implicit s-stage, order p Runge-Kutta methods for initial value problems and the radius of absolute monotonicity governs the numerical preservation of properties like positivity and maximum-norm contractivity. We construct a function with p=2 and R>2s, disproving a conjecture of van de Griend and Kraaijevanger. We determine the maximum attainable radius for functions in several one-parame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6651","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":"1303.6651","created_at":"2026-05-17T23:53:17.749457+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.6651v1","created_at":"2026-05-17T23:53:17.749457+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6651","created_at":"2026-05-17T23:53:17.749457+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2M6GLD5PLW5","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2M6GLD5PLW5MK5K","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2M6GLD5","created_at":"2026-05-18T12:28:04.890932+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/W2M6GLD5PLW5MK5KKNO6RWZXEY","json":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY.json","graph_json":"https://pith.science/api/pith-number/W2M6GLD5PLW5MK5KKNO6RWZXEY/graph.json","events_json":"https://pith.science/api/pith-number/W2M6GLD5PLW5MK5KKNO6RWZXEY/events.json","paper":"https://pith.science/paper/W2M6GLD5"},"agent_actions":{"view_html":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY","download_json":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY.json","view_paper":"https://pith.science/paper/W2M6GLD5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.6651&json=true","fetch_graph":"https://pith.science/api/pith-number/W2M6GLD5PLW5MK5KKNO6RWZXEY/graph.json","fetch_events":"https://pith.science/api/pith-number/W2M6GLD5PLW5MK5KKNO6RWZXEY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY/action/storage_attestation","attest_author":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY/action/author_attestation","sign_citation":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY/action/citation_signature","submit_replication":"https://pith.science/pith/W2M6GLD5PLW5MK5KKNO6RWZXEY/action/replication_record"}},"created_at":"2026-05-17T23:53:17.749457+00:00","updated_at":"2026-05-17T23:53:17.749457+00:00"}