{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TTCO33PENWJA67THZGQRANKWXJ","short_pith_number":"pith:TTCO33PE","schema_version":"1.0","canonical_sha256":"9cc4edede46d920f7e67c9a1103556ba5424aac8ec376d803fe353e4cf56d684","source":{"kind":"arxiv","id":"1903.03897","version":1},"attestation_state":"computed","paper":{"title":"Sharp Bounds for the Arc Lemniscate Sine Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Horst Alzer, Man Kam Kwong","submitted_at":"2019-03-10T01:17:20Z","abstract_excerpt":"The arc lemniscate sine function is given by $$ \\mbox{arcsl}(x)=\\int_0^x \\frac{1}{\\sqrt{1-t^4}}dt. $$ In 2017, Mahmoud and Agarwal presented bounds for $\\mbox{arcsl}$ in terms of the Lerch zeta function $$ \\Phi(z,s,a)=\\sum_{k=0}^\\infty \\frac {z^k}{(k+a)^s}. $$ They proved $$ \\frac{1}{8} \\, x \\, \\Phi(x^4, 3/2, 1/4) < \\mbox{arcsl}(x)< \\frac{1}{4} \\, x \\, \\Phi(x^4,3/2,1/4)\\qquad{(0<x<1)}. $$ We %use the monotone form of l'Hopital's rule to show that the factor $1/4$ can be replaced by $\\mbox{arcsl}(1)/\\Phi(1,3/2,1/4)=0.12836...$. This constant is best possible."},"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":"1903.03897","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-03-10T01:17:20Z","cross_cats_sorted":[],"title_canon_sha256":"60ade0bddef3464d7588b16f236c624177411b30f3d3da852e9cb90a0ab2b07a","abstract_canon_sha256":"fba0c990b890dd5ad581b2c512cb5d4a163b21e512b53e55b0568b7b75c4fe7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:40.672882Z","signature_b64":"+rUGtpSYQocEnx6mekH3I422L+5Vl5ixFRBf6jAwmn9CeiziMbnNOtXLlpBuf3pPoQNNVaze+Zk79E71yO51Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cc4edede46d920f7e67c9a1103556ba5424aac8ec376d803fe353e4cf56d684","last_reissued_at":"2026-05-17T23:51:40.672369Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:40.672369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Bounds for the Arc Lemniscate Sine Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Horst Alzer, Man Kam Kwong","submitted_at":"2019-03-10T01:17:20Z","abstract_excerpt":"The arc lemniscate sine function is given by $$ \\mbox{arcsl}(x)=\\int_0^x \\frac{1}{\\sqrt{1-t^4}}dt. $$ In 2017, Mahmoud and Agarwal presented bounds for $\\mbox{arcsl}$ in terms of the Lerch zeta function $$ \\Phi(z,s,a)=\\sum_{k=0}^\\infty \\frac {z^k}{(k+a)^s}. $$ They proved $$ \\frac{1}{8} \\, x \\, \\Phi(x^4, 3/2, 1/4) < \\mbox{arcsl}(x)< \\frac{1}{4} \\, x \\, \\Phi(x^4,3/2,1/4)\\qquad{(0<x<1)}. $$ We %use the monotone form of l'Hopital's rule to show that the factor $1/4$ can be replaced by $\\mbox{arcsl}(1)/\\Phi(1,3/2,1/4)=0.12836...$. This constant is best possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03897","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":"1903.03897","created_at":"2026-05-17T23:51:40.672450+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.03897v1","created_at":"2026-05-17T23:51:40.672450+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03897","created_at":"2026-05-17T23:51:40.672450+00:00"},{"alias_kind":"pith_short_12","alias_value":"TTCO33PENWJA","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"TTCO33PENWJA67TH","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"TTCO33PE","created_at":"2026-05-18T12:33:30.264802+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/TTCO33PENWJA67THZGQRANKWXJ","json":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ.json","graph_json":"https://pith.science/api/pith-number/TTCO33PENWJA67THZGQRANKWXJ/graph.json","events_json":"https://pith.science/api/pith-number/TTCO33PENWJA67THZGQRANKWXJ/events.json","paper":"https://pith.science/paper/TTCO33PE"},"agent_actions":{"view_html":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ","download_json":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ.json","view_paper":"https://pith.science/paper/TTCO33PE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.03897&json=true","fetch_graph":"https://pith.science/api/pith-number/TTCO33PENWJA67THZGQRANKWXJ/graph.json","fetch_events":"https://pith.science/api/pith-number/TTCO33PENWJA67THZGQRANKWXJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ/action/storage_attestation","attest_author":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ/action/author_attestation","sign_citation":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ/action/citation_signature","submit_replication":"https://pith.science/pith/TTCO33PENWJA67THZGQRANKWXJ/action/replication_record"}},"created_at":"2026-05-17T23:51:40.672450+00:00","updated_at":"2026-05-17T23:51:40.672450+00:00"}