{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:75FITWWUTG3BPSR2JJ6KYU6JGX","short_pith_number":"pith:75FITWWU","schema_version":"1.0","canonical_sha256":"ff4a89dad499b617ca3a4a7cac53c935ca9750d42a9fff775726e54e3e97b77d","source":{"kind":"arxiv","id":"1309.5521","version":1},"attestation_state":"computed","paper":{"title":"More Jordan type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. Aharonov, U. Elias","submitted_at":"2013-09-21T19:30:51Z","abstract_excerpt":"The function $ \\tan(\\pi x / 2) / (\\pi x / 2) $ is expanded into a Laurent series of $ 1 - x^2 $, where the coefficients are given explicitly as combinations of zeta function of even integers. This is used to achieve a sequence of upper and lower bounds which are very precise even at the poles $ x = 1, -1 $.\n  Similar results are obtained for other trigonometric functions with poles."},"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":"1309.5521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-09-21T19:30:51Z","cross_cats_sorted":[],"title_canon_sha256":"477e2106ac4532e307b96945ffb93c2aca390ac2c722f79e8a619057055d2d62","abstract_canon_sha256":"fa49f25927e33ff22d716ee034841aa430773af19d7612175a5101a50e2b6b87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:36.064124Z","signature_b64":"TFpA5zwTUt0egSiTedkg39Gdz2nqu7IwaYWVEApfNvL8qW6Z3889KhP5Nr+lLMJEu+bgRD0lWKKGdOjMDdNIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff4a89dad499b617ca3a4a7cac53c935ca9750d42a9fff775726e54e3e97b77d","last_reissued_at":"2026-05-18T03:12:36.063436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:36.063436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"More Jordan type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. Aharonov, U. Elias","submitted_at":"2013-09-21T19:30:51Z","abstract_excerpt":"The function $ \\tan(\\pi x / 2) / (\\pi x / 2) $ is expanded into a Laurent series of $ 1 - x^2 $, where the coefficients are given explicitly as combinations of zeta function of even integers. This is used to achieve a sequence of upper and lower bounds which are very precise even at the poles $ x = 1, -1 $.\n  Similar results are obtained for other trigonometric functions with poles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5521","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":"1309.5521","created_at":"2026-05-18T03:12:36.063535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.5521v1","created_at":"2026-05-18T03:12:36.063535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5521","created_at":"2026-05-18T03:12:36.063535+00:00"},{"alias_kind":"pith_short_12","alias_value":"75FITWWUTG3B","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"75FITWWUTG3BPSR2","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"75FITWWU","created_at":"2026-05-18T12:27:36.564083+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/75FITWWUTG3BPSR2JJ6KYU6JGX","json":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX.json","graph_json":"https://pith.science/api/pith-number/75FITWWUTG3BPSR2JJ6KYU6JGX/graph.json","events_json":"https://pith.science/api/pith-number/75FITWWUTG3BPSR2JJ6KYU6JGX/events.json","paper":"https://pith.science/paper/75FITWWU"},"agent_actions":{"view_html":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX","download_json":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX.json","view_paper":"https://pith.science/paper/75FITWWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.5521&json=true","fetch_graph":"https://pith.science/api/pith-number/75FITWWUTG3BPSR2JJ6KYU6JGX/graph.json","fetch_events":"https://pith.science/api/pith-number/75FITWWUTG3BPSR2JJ6KYU6JGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX/action/storage_attestation","attest_author":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX/action/author_attestation","sign_citation":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX/action/citation_signature","submit_replication":"https://pith.science/pith/75FITWWUTG3BPSR2JJ6KYU6JGX/action/replication_record"}},"created_at":"2026-05-18T03:12:36.063535+00:00","updated_at":"2026-05-18T03:12:36.063535+00:00"}