{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GKIAOXBDDJIXVBR42AMZMDXAPE","short_pith_number":"pith:GKIAOXBD","schema_version":"1.0","canonical_sha256":"3290075c231a517a863cd019960ee079138fb60bc0f85255c80c57d7892f872a","source":{"kind":"arxiv","id":"1801.03654","version":1},"attestation_state":"computed","paper":{"title":"Proving some identities of Gosper on $q$-trigonometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mohamed El Bachraoui","submitted_at":"2018-01-11T07:58:34Z","abstract_excerpt":"Gosper introduced the functions $\\sin_q z$ and $\\cos_q z$ as $q$-analogues for the trigonometric functions $\\sin z$ and $\\cos z$ respectively. He stated but did not prove a variety of identities involving these two $q$-trigonometric functions. In this paper, we shall use the theory of elliptic functions to prove three formulas from the list of Gosper on the functions $\\sin_q z$ and $\\cos_q z$."},"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":"1801.03654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-01-11T07:58:34Z","cross_cats_sorted":[],"title_canon_sha256":"80397d0b5aa92adaff7e8e8da4d4d0be846322a593ebce33194af351fa3e64b8","abstract_canon_sha256":"00b4bf409c1eeb1dd72181d745cfd84f1b0c6485c1b540f827b0033da4bfa8ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:13.739097Z","signature_b64":"Xq7nkauzg2PSF9Ok0C4NGtEk2eD8roNHyHz6V+Hft7jg4IB4YqVDWxgF/yVecxbhiLGkXwEnetPxD39r9IjIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3290075c231a517a863cd019960ee079138fb60bc0f85255c80c57d7892f872a","last_reissued_at":"2026-05-18T00:26:13.738625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:13.738625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proving some identities of Gosper on $q$-trigonometric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mohamed El Bachraoui","submitted_at":"2018-01-11T07:58:34Z","abstract_excerpt":"Gosper introduced the functions $\\sin_q z$ and $\\cos_q z$ as $q$-analogues for the trigonometric functions $\\sin z$ and $\\cos z$ respectively. He stated but did not prove a variety of identities involving these two $q$-trigonometric functions. In this paper, we shall use the theory of elliptic functions to prove three formulas from the list of Gosper on the functions $\\sin_q z$ and $\\cos_q z$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03654","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":"1801.03654","created_at":"2026-05-18T00:26:13.738692+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.03654v1","created_at":"2026-05-18T00:26:13.738692+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03654","created_at":"2026-05-18T00:26:13.738692+00:00"},{"alias_kind":"pith_short_12","alias_value":"GKIAOXBDDJIX","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GKIAOXBDDJIXVBR4","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GKIAOXBD","created_at":"2026-05-18T12:32:25.280505+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/GKIAOXBDDJIXVBR42AMZMDXAPE","json":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE.json","graph_json":"https://pith.science/api/pith-number/GKIAOXBDDJIXVBR42AMZMDXAPE/graph.json","events_json":"https://pith.science/api/pith-number/GKIAOXBDDJIXVBR42AMZMDXAPE/events.json","paper":"https://pith.science/paper/GKIAOXBD"},"agent_actions":{"view_html":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE","download_json":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE.json","view_paper":"https://pith.science/paper/GKIAOXBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.03654&json=true","fetch_graph":"https://pith.science/api/pith-number/GKIAOXBDDJIXVBR42AMZMDXAPE/graph.json","fetch_events":"https://pith.science/api/pith-number/GKIAOXBDDJIXVBR42AMZMDXAPE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE/action/storage_attestation","attest_author":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE/action/author_attestation","sign_citation":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE/action/citation_signature","submit_replication":"https://pith.science/pith/GKIAOXBDDJIXVBR42AMZMDXAPE/action/replication_record"}},"created_at":"2026-05-18T00:26:13.738692+00:00","updated_at":"2026-05-18T00:26:13.738692+00:00"}