{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MUUXJ2QURKD2O2GU5EKG7MNS7W","short_pith_number":"pith:MUUXJ2QU","canonical_record":{"source":{"id":"1603.05716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-14T07:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"ca693bcd5186cfafaade61d7d5196b798acbb0766c2fb336ef3a34e4ba7a14a7","abstract_canon_sha256":"8a55288e61a98542f8e1cd9993681b89a62b2e687c6207b4950c2b616a947102"},"schema_version":"1.0"},"canonical_sha256":"652974ea148a87a768d4e9146fb1b2fd9c988b43f9961d19af23effd24dcfe0e","source":{"kind":"arxiv","id":"1603.05716","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05716","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05716v1","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05716","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"MUUXJ2QURKD2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MUUXJ2QURKD2O2GU","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MUUXJ2QU","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MUUXJ2QURKD2O2GU5EKG7MNS7W","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05716","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-14T07:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"ca693bcd5186cfafaade61d7d5196b798acbb0766c2fb336ef3a34e4ba7a14a7","abstract_canon_sha256":"8a55288e61a98542f8e1cd9993681b89a62b2e687c6207b4950c2b616a947102"},"schema_version":"1.0"},"canonical_sha256":"652974ea148a87a768d4e9146fb1b2fd9c988b43f9961d19af23effd24dcfe0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:53.695696Z","signature_b64":"K7JGf7Kggzn8PK9jS/xn6IAOQYRvIPFzpSGwXEGHMrgiNND6WmLvj1WMsnfNj5sLw3cwIQclL9KFHR6pRt0eAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"652974ea148a87a768d4e9146fb1b2fd9c988b43f9961d19af23effd24dcfe0e","last_reissued_at":"2026-05-18T01:18:53.695144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:53.695144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05716","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAxbuOBTffcJP0S3Ol7PjJIlbuGWBZIGEHr4zr+k/1mC46EVig6gRB0OZ//QR1dOqHGAncAl0iGeSK3uXIFCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:33:44.399604Z"},"content_sha256":"a5afe002d295eab3d150390a00fa18b6ed90e53e52b045ae2d04bf9673da704b","schema_version":"1.0","event_id":"sha256:a5afe002d295eab3d150390a00fa18b6ed90e53e52b045ae2d04bf9673da704b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MUUXJ2QURKD2O2GU5EKG7MNS7W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation properties on q -Szasz-Mirakjan-Kantrovich Stancu type operators via Dunkl generalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Md. Nasiruzzaman, M. Mursaleen","submitted_at":"2016-03-14T07:17:04Z","abstract_excerpt":"This paper is devoted to study the approximation properties and rate of approximation of the Szasz-Mirakjan-Kantrovich-Stancu type polynomials generated by the Dunkl generalization of the exponential function with respect to q -calculus. We present approximation properties with the help of well-known Korovkin's theorem and determine the rat e of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Moreover, we obtain the approximation results for Bivariate case for these operators"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05716","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yaQm3saXA+wAW66JL6Yj3EyuLJYsycI6J72t3We7Cox+bnCzZWxcNKpQXLJm2H5P3/e0AeE8SSlClpXJsTnPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:33:44.399951Z"},"content_sha256":"5f12aaa31f75c4bcb4c0853b0115c9d37318a18f64975d590b995dd2075374b4","schema_version":"1.0","event_id":"sha256:5f12aaa31f75c4bcb4c0853b0115c9d37318a18f64975d590b995dd2075374b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUUXJ2QURKD2O2GU5EKG7MNS7W/bundle.json","state_url":"https://pith.science/pith/MUUXJ2QURKD2O2GU5EKG7MNS7W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUUXJ2QURKD2O2GU5EKG7MNS7W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T05:33:44Z","links":{"resolver":"https://pith.science/pith/MUUXJ2QURKD2O2GU5EKG7MNS7W","bundle":"https://pith.science/pith/MUUXJ2QURKD2O2GU5EKG7MNS7W/bundle.json","state":"https://pith.science/pith/MUUXJ2QURKD2O2GU5EKG7MNS7W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUUXJ2QURKD2O2GU5EKG7MNS7W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MUUXJ2QURKD2O2GU5EKG7MNS7W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8a55288e61a98542f8e1cd9993681b89a62b2e687c6207b4950c2b616a947102","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-14T07:17:04Z","title_canon_sha256":"ca693bcd5186cfafaade61d7d5196b798acbb0766c2fb336ef3a34e4ba7a14a7"},"schema_version":"1.0","source":{"id":"1603.05716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05716","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05716v1","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05716","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"MUUXJ2QURKD2","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MUUXJ2QURKD2O2GU","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MUUXJ2QU","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:5f12aaa31f75c4bcb4c0853b0115c9d37318a18f64975d590b995dd2075374b4","target":"graph","created_at":"2026-05-18T01:18:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is devoted to study the approximation properties and rate of approximation of the Szasz-Mirakjan-Kantrovich-Stancu type polynomials generated by the Dunkl generalization of the exponential function with respect to q -calculus. We present approximation properties with the help of well-known Korovkin's theorem and determine the rat e of convergence in terms of classical modulus of continuity, the class of Lipschitz functions, Peetre's K-functional, and the second-order modulus of continuity. Moreover, we obtain the approximation results for Bivariate case for these operators","authors_text":"Md. Nasiruzzaman, M. Mursaleen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-14T07:17:04Z","title":"Approximation properties on q -Szasz-Mirakjan-Kantrovich Stancu type operators via Dunkl generalization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05716","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a5afe002d295eab3d150390a00fa18b6ed90e53e52b045ae2d04bf9673da704b","target":"record","created_at":"2026-05-18T01:18:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8a55288e61a98542f8e1cd9993681b89a62b2e687c6207b4950c2b616a947102","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-14T07:17:04Z","title_canon_sha256":"ca693bcd5186cfafaade61d7d5196b798acbb0766c2fb336ef3a34e4ba7a14a7"},"schema_version":"1.0","source":{"id":"1603.05716","kind":"arxiv","version":1}},"canonical_sha256":"652974ea148a87a768d4e9146fb1b2fd9c988b43f9961d19af23effd24dcfe0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"652974ea148a87a768d4e9146fb1b2fd9c988b43f9961d19af23effd24dcfe0e","first_computed_at":"2026-05-18T01:18:53.695144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:53.695144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K7JGf7Kggzn8PK9jS/xn6IAOQYRvIPFzpSGwXEGHMrgiNND6WmLvj1WMsnfNj5sLw3cwIQclL9KFHR6pRt0eAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:53.695696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5afe002d295eab3d150390a00fa18b6ed90e53e52b045ae2d04bf9673da704b","sha256:5f12aaa31f75c4bcb4c0853b0115c9d37318a18f64975d590b995dd2075374b4"],"state_sha256":"9fe0d4fe0d65bb5c5016d7e81f03b2c2d5126b4c9fd9d75eeb4784638511a785"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"olacIejvNAjoy946KMk2AvCv8jvdCSfCDY5An1lezLPg0xNlDDeRBxDN4lTsIcKrq0FquzD+AbqG8bL4marhDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:33:44.402065Z","bundle_sha256":"2214412d970619f5a074914fd284fce441032d5937f279efce411a06e1bad5df"}}