{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PDRTPO5XFKNR4FRMCWQDMKZK7Q","short_pith_number":"pith:PDRTPO5X","canonical_record":{"source":{"id":"1604.01380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-21T16:31:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b895649bde4d55f485bdae4dd74957814b12f1d8104d02b3d01d302ff13c0bbc","abstract_canon_sha256":"0505f0805c62e451f1c522cb8d0d4fc46608912fc11993e62990f1b0451d551b"},"schema_version":"1.0"},"canonical_sha256":"78e337bbb72a9b1e162c15a0362b2afc18aab110dbb5e3a12a4e01979bcdd230","source":{"kind":"arxiv","id":"1604.01380","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01380","created_at":"2026-05-18T01:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01380v1","created_at":"2026-05-18T01:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01380","created_at":"2026-05-18T01:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"PDRTPO5XFKNR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PDRTPO5XFKNR4FRM","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PDRTPO5X","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PDRTPO5XFKNR4FRMCWQDMKZK7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-21T16:31:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b895649bde4d55f485bdae4dd74957814b12f1d8104d02b3d01d302ff13c0bbc","abstract_canon_sha256":"0505f0805c62e451f1c522cb8d0d4fc46608912fc11993e62990f1b0451d551b"},"schema_version":"1.0"},"canonical_sha256":"78e337bbb72a9b1e162c15a0362b2afc18aab110dbb5e3a12a4e01979bcdd230","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:38.331247Z","signature_b64":"YV9Lt2832BcZA3ny9lB+WEiQmEOlexBvEHibVO+ryxFmnv9Eyu8+v0tc4BKb8qBwxQSuqcrjJX4U7yAnbL+ZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78e337bbb72a9b1e162c15a0362b2afc18aab110dbb5e3a12a4e01979bcdd230","last_reissued_at":"2026-05-18T01:17:38.330550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:38.330550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01380","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":"2026-05-18T01:17:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NuTNhJ2H1Wa0C4CcUwM+sboi6JdtD+pcQ413peYk5jcZFStNwy3ADphmIZjWpnX+t3y8CR/s6hPFdd1BPGCmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:52.154406Z"},"content_sha256":"b0efa5da462a95c2d98e0586e2e55d3887ffaf33bc21184d24c3a22fb8c3bc08","schema_version":"1.0","event_id":"sha256:b0efa5da462a95c2d98e0586e2e55d3887ffaf33bc21184d24c3a22fb8c3bc08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PDRTPO5XFKNR4FRMCWQDMKZK7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modified Stancu-type Dunkl generalization of Szasz- Kantorovich-operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Md. Nasiruzzaman, M. Mursaleen","submitted_at":"2016-03-21T16:31:58Z","abstract_excerpt":"In this paper, we introduce a modification of the Szasz-Mirakjan-Kantorovich operators as well as Stancu operators [9] (or a Dunkl generalization of modified Szasz-Mirakjan-Kantrovich operators [5]) which preserve the linear functions. These types of operators modification enables better error estimation than the classical Dunkl Szasz-MirakjanKantrovich as well as Stancu operators. We obtain some approximation results via well known Korovkin's type theorem, weighted Korovkin's type theorem convergence properties by using the modulus of continuity and the rate of convergence of the operators fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01380","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":"2026-05-18T01:17:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bFL+BUvCtaI9Yzpcj4PBxEGv2hmniy5FgxI2u4+xaTse9aMn4wxUGzRbAhW2d6ap2dDchfUGYLFNmPZdfAzQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:19:52.154969Z"},"content_sha256":"f9e2689d24813433999e8c7f46facee23d1072d96307cbc7dfeb7c75686ffdff","schema_version":"1.0","event_id":"sha256:f9e2689d24813433999e8c7f46facee23d1072d96307cbc7dfeb7c75686ffdff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDRTPO5XFKNR4FRMCWQDMKZK7Q/bundle.json","state_url":"https://pith.science/pith/PDRTPO5XFKNR4FRMCWQDMKZK7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDRTPO5XFKNR4FRMCWQDMKZK7Q/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":"2026-06-02T22:19:52Z","links":{"resolver":"https://pith.science/pith/PDRTPO5XFKNR4FRMCWQDMKZK7Q","bundle":"https://pith.science/pith/PDRTPO5XFKNR4FRMCWQDMKZK7Q/bundle.json","state":"https://pith.science/pith/PDRTPO5XFKNR4FRMCWQDMKZK7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDRTPO5XFKNR4FRMCWQDMKZK7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PDRTPO5XFKNR4FRMCWQDMKZK7Q","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":"0505f0805c62e451f1c522cb8d0d4fc46608912fc11993e62990f1b0451d551b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-21T16:31:58Z","title_canon_sha256":"b895649bde4d55f485bdae4dd74957814b12f1d8104d02b3d01d302ff13c0bbc"},"schema_version":"1.0","source":{"id":"1604.01380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01380","created_at":"2026-05-18T01:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01380v1","created_at":"2026-05-18T01:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01380","created_at":"2026-05-18T01:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"PDRTPO5XFKNR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PDRTPO5XFKNR4FRM","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PDRTPO5X","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:f9e2689d24813433999e8c7f46facee23d1072d96307cbc7dfeb7c75686ffdff","target":"graph","created_at":"2026-05-18T01:17:38Z","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":"In this paper, we introduce a modification of the Szasz-Mirakjan-Kantorovich operators as well as Stancu operators [9] (or a Dunkl generalization of modified Szasz-Mirakjan-Kantrovich operators [5]) which preserve the linear functions. These types of operators modification enables better error estimation than the classical Dunkl Szasz-MirakjanKantrovich as well as Stancu operators. We obtain some approximation results via well known Korovkin's type theorem, weighted Korovkin's type theorem convergence properties by using the modulus of continuity and the rate of convergence of the operators fo","authors_text":"Md. Nasiruzzaman, M. Mursaleen","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-21T16:31:58Z","title":"Modified Stancu-type Dunkl generalization of Szasz- Kantorovich-operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01380","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:b0efa5da462a95c2d98e0586e2e55d3887ffaf33bc21184d24c3a22fb8c3bc08","target":"record","created_at":"2026-05-18T01:17:38Z","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":"0505f0805c62e451f1c522cb8d0d4fc46608912fc11993e62990f1b0451d551b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-21T16:31:58Z","title_canon_sha256":"b895649bde4d55f485bdae4dd74957814b12f1d8104d02b3d01d302ff13c0bbc"},"schema_version":"1.0","source":{"id":"1604.01380","kind":"arxiv","version":1}},"canonical_sha256":"78e337bbb72a9b1e162c15a0362b2afc18aab110dbb5e3a12a4e01979bcdd230","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78e337bbb72a9b1e162c15a0362b2afc18aab110dbb5e3a12a4e01979bcdd230","first_computed_at":"2026-05-18T01:17:38.330550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:38.330550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YV9Lt2832BcZA3ny9lB+WEiQmEOlexBvEHibVO+ryxFmnv9Eyu8+v0tc4BKb8qBwxQSuqcrjJX4U7yAnbL+ZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:38.331247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0efa5da462a95c2d98e0586e2e55d3887ffaf33bc21184d24c3a22fb8c3bc08","sha256:f9e2689d24813433999e8c7f46facee23d1072d96307cbc7dfeb7c75686ffdff"],"state_sha256":"7c7f889fefb1c216cf33a567375a4474fe157509c27a583b04c064b6cd597342"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IMDngFg1fNFgl8vx6mtmgdLeUnHNBIIrJnvW43B2dwLie9+/xoNJDclSJsZa0yjl2ItsPdGinsTBg19AIiGgBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:19:52.157678Z","bundle_sha256":"0d6c56565980533a171055b8c93d9d132ed086293d977b25a4c4b26f6681ffb2"}}