{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HIJ5QD7KNXOCDGSYMQ4MZGQ76B","short_pith_number":"pith:HIJ5QD7K","canonical_record":{"source":{"id":"1508.05852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-21T09:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"a3eac70038da333952665eec06bb43b4758d43bbe795fa2840179c7e1a902221","abstract_canon_sha256":"26e6b97719c86cfacf37c5dd124743ff8ef886d643ac73ff73d3e8857650e553"},"schema_version":"1.0"},"canonical_sha256":"3a13d80fea6ddc219a586438cc9a1ff05aa4d189cf4b90fa15f09a281fd612d1","source":{"kind":"arxiv","id":"1508.05852","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05852","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05852v1","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05852","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"HIJ5QD7KNXOC","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HIJ5QD7KNXOCDGSY","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HIJ5QD7K","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HIJ5QD7KNXOCDGSYMQ4MZGQ76B","target":"record","payload":{"canonical_record":{"source":{"id":"1508.05852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-21T09:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"a3eac70038da333952665eec06bb43b4758d43bbe795fa2840179c7e1a902221","abstract_canon_sha256":"26e6b97719c86cfacf37c5dd124743ff8ef886d643ac73ff73d3e8857650e553"},"schema_version":"1.0"},"canonical_sha256":"3a13d80fea6ddc219a586438cc9a1ff05aa4d189cf4b90fa15f09a281fd612d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:51.528572Z","signature_b64":"mfZxhHaaW1yk81K4GDYOUZJifmfF+t19wkeYtjH2IuIYOaae/MiJvPskZUtIUtRX3qIbWeDP6NTIPzYwqFqcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a13d80fea6ddc219a586438cc9a1ff05aa4d189cf4b90fa15f09a281fd612d1","last_reissued_at":"2026-05-18T01:34:51.528088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:51.528088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.05852","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":"2026-05-18T01:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/m6t/0xwVl8fv6eL8FQxbwONvWXlqxwhXWIxFJqo0wtFlzKo2tR+hBbt0b75iAf7/mO1MoGRF5RFk5PLlA0HCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:24:48.715686Z"},"content_sha256":"8442c82a7303c2b611258abc630ba4ee759be2e696f9f5e152f07e41f97107ff","schema_version":"1.0","event_id":"sha256:8442c82a7303c2b611258abc630ba4ee759be2e696f9f5e152f07e41f97107ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HIJ5QD7KNXOCDGSYMQ4MZGQ76B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On q-analogue of modified Kantorovich-type discrete-Beta operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Preeti Sharma, Vishnu Narayan Mishra","submitted_at":"2015-08-21T09:11:26Z","abstract_excerpt":"The present paper deals with the Stancu type generalization of the Kantorovich discrete $q$-Beta operators. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05852","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":"2026-05-18T01:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pC2BZtZSww9H1QwUm7RkN5yLydXBw59t0oBTK/ZZkPiI/zMY5BdTTwoELapf8AS3tPORdOCMcT53vHy19LSWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:24:48.716468Z"},"content_sha256":"0698ad422e2e955453cd1474f8944b77d247f986e91a6182d4fafa6020bfa38c","schema_version":"1.0","event_id":"sha256:0698ad422e2e955453cd1474f8944b77d247f986e91a6182d4fafa6020bfa38c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HIJ5QD7KNXOCDGSYMQ4MZGQ76B/bundle.json","state_url":"https://pith.science/pith/HIJ5QD7KNXOCDGSYMQ4MZGQ76B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HIJ5QD7KNXOCDGSYMQ4MZGQ76B/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":"2026-05-31T10:24:48Z","links":{"resolver":"https://pith.science/pith/HIJ5QD7KNXOCDGSYMQ4MZGQ76B","bundle":"https://pith.science/pith/HIJ5QD7KNXOCDGSYMQ4MZGQ76B/bundle.json","state":"https://pith.science/pith/HIJ5QD7KNXOCDGSYMQ4MZGQ76B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HIJ5QD7KNXOCDGSYMQ4MZGQ76B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HIJ5QD7KNXOCDGSYMQ4MZGQ76B","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":"26e6b97719c86cfacf37c5dd124743ff8ef886d643ac73ff73d3e8857650e553","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-21T09:11:26Z","title_canon_sha256":"a3eac70038da333952665eec06bb43b4758d43bbe795fa2840179c7e1a902221"},"schema_version":"1.0","source":{"id":"1508.05852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05852","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05852v1","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05852","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"HIJ5QD7KNXOC","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HIJ5QD7KNXOCDGSY","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HIJ5QD7K","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:0698ad422e2e955453cd1474f8944b77d247f986e91a6182d4fafa6020bfa38c","target":"graph","created_at":"2026-05-18T01:34:51Z","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":"The present paper deals with the Stancu type generalization of the Kantorovich discrete $q$-Beta operators. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation.","authors_text":"Preeti Sharma, Vishnu Narayan Mishra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-21T09:11:26Z","title":"On q-analogue of modified Kantorovich-type discrete-Beta operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05852","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":"sha256:8442c82a7303c2b611258abc630ba4ee759be2e696f9f5e152f07e41f97107ff","target":"record","created_at":"2026-05-18T01:34:51Z","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":"26e6b97719c86cfacf37c5dd124743ff8ef886d643ac73ff73d3e8857650e553","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-21T09:11:26Z","title_canon_sha256":"a3eac70038da333952665eec06bb43b4758d43bbe795fa2840179c7e1a902221"},"schema_version":"1.0","source":{"id":"1508.05852","kind":"arxiv","version":1}},"canonical_sha256":"3a13d80fea6ddc219a586438cc9a1ff05aa4d189cf4b90fa15f09a281fd612d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a13d80fea6ddc219a586438cc9a1ff05aa4d189cf4b90fa15f09a281fd612d1","first_computed_at":"2026-05-18T01:34:51.528088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:51.528088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mfZxhHaaW1yk81K4GDYOUZJifmfF+t19wkeYtjH2IuIYOaae/MiJvPskZUtIUtRX3qIbWeDP6NTIPzYwqFqcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:51.528572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8442c82a7303c2b611258abc630ba4ee759be2e696f9f5e152f07e41f97107ff","sha256:0698ad422e2e955453cd1474f8944b77d247f986e91a6182d4fafa6020bfa38c"],"state_sha256":"b091ebd8aa0237d19ce9705ab290a54d9ea293183e8afc73edfc0b96c20a0fee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/0BbfMNQSAu02MTsNHuSFxUi9u/SqHfmeZvU32gnuj+TOsTkCNNPv5h98XnzTWdF7GBYFaPbgX+NjI3L5VwvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:24:48.720235Z","bundle_sha256":"71fc35b0f9790b0836380ac79c14cc9b76c0e3036000c07396c1ab5b5f75901a"}}