{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TDWWWAQIO7T4TKBHHOFIEAM7FE","short_pith_number":"pith:TDWWWAQI","canonical_record":{"source":{"id":"1508.04897","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-20T07:14:30Z","cross_cats_sorted":[],"title_canon_sha256":"46a8f146d4d35e02fc02566709653ff74eae7886bd80180a0dde783c0ba020fc","abstract_canon_sha256":"5ee20a51aac328cd769dda9783bee7d9c58b9b1911987548b58695db9c08815e"},"schema_version":"1.0"},"canonical_sha256":"98ed6b020877e7c9a8273b8a82019f290e494480163b620baf8b89f7c8b7ded0","source":{"kind":"arxiv","id":"1508.04897","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04897","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04897v1","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04897","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"TDWWWAQIO7T4","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TDWWWAQIO7T4TKBH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TDWWWAQI","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TDWWWAQIO7T4TKBHHOFIEAM7FE","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04897","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-20T07:14:30Z","cross_cats_sorted":[],"title_canon_sha256":"46a8f146d4d35e02fc02566709653ff74eae7886bd80180a0dde783c0ba020fc","abstract_canon_sha256":"5ee20a51aac328cd769dda9783bee7d9c58b9b1911987548b58695db9c08815e"},"schema_version":"1.0"},"canonical_sha256":"98ed6b020877e7c9a8273b8a82019f290e494480163b620baf8b89f7c8b7ded0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:52.027948Z","signature_b64":"lX7D9y9+5G5V5Lcj08QK5LcM1fgq+Lv8Z331eGQFNcW00E9A6QBIbzY0R0/9cYK01tNK6HrzrOTLyreSml31CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98ed6b020877e7c9a8273b8a82019f290e494480163b620baf8b89f7c8b7ded0","last_reissued_at":"2026-05-18T01:32:52.027190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:52.027190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04897","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":"2026-05-18T01:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TOUXogo8pCvf+imnBKA5yNnGyWn1aOM5XqeUn2GFkRagN/S+ZCkBhaxUB6tQFdNWU1ZCfjZd9fzKGsOyBaJODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:09:26.190940Z"},"content_sha256":"aba7b9ce72f4d662708e42b4ecac302f480418da5cd00bd95a3060f5d520cbb2","schema_version":"1.0","event_id":"sha256:aba7b9ce72f4d662708e42b4ecac302f480418da5cd00bd95a3060f5d520cbb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TDWWWAQIO7T4TKBHHOFIEAM7FE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Voronovskaja type asymptotic approximation by general gamma type operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alok Kumar","submitted_at":"2015-08-20T07:14:30Z","abstract_excerpt":"In the present paper, we studied the voronovskaja type theorem for general Gamma type operators. Also, we obtain an error estimate for general Gamma type operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04897","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":"2026-05-18T01:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mm0fRIaQUXDgMHhgrLxvIsdDM0KBPeApq5g3VFLCsfP2CzM8dFFDqwDlvYOBx6Skemh5EuTjbF/MYutl/h/QAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:09:26.191310Z"},"content_sha256":"428f2d4598200871c89bb75a531a5f58f48b24aeaa0a95b68547b5780f7f9139","schema_version":"1.0","event_id":"sha256:428f2d4598200871c89bb75a531a5f58f48b24aeaa0a95b68547b5780f7f9139"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDWWWAQIO7T4TKBHHOFIEAM7FE/bundle.json","state_url":"https://pith.science/pith/TDWWWAQIO7T4TKBHHOFIEAM7FE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDWWWAQIO7T4TKBHHOFIEAM7FE/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":"2026-06-01T00:09:26Z","links":{"resolver":"https://pith.science/pith/TDWWWAQIO7T4TKBHHOFIEAM7FE","bundle":"https://pith.science/pith/TDWWWAQIO7T4TKBHHOFIEAM7FE/bundle.json","state":"https://pith.science/pith/TDWWWAQIO7T4TKBHHOFIEAM7FE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDWWWAQIO7T4TKBHHOFIEAM7FE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TDWWWAQIO7T4TKBHHOFIEAM7FE","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":"5ee20a51aac328cd769dda9783bee7d9c58b9b1911987548b58695db9c08815e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-20T07:14:30Z","title_canon_sha256":"46a8f146d4d35e02fc02566709653ff74eae7886bd80180a0dde783c0ba020fc"},"schema_version":"1.0","source":{"id":"1508.04897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04897","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04897v1","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04897","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"TDWWWAQIO7T4","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TDWWWAQIO7T4TKBH","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TDWWWAQI","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:428f2d4598200871c89bb75a531a5f58f48b24aeaa0a95b68547b5780f7f9139","target":"graph","created_at":"2026-05-18T01:32:52Z","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 the present paper, we studied the voronovskaja type theorem for general Gamma type operators. Also, we obtain an error estimate for general Gamma type operators.","authors_text":"Alok Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-20T07:14:30Z","title":"Voronovskaja type asymptotic approximation by general gamma type operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04897","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:aba7b9ce72f4d662708e42b4ecac302f480418da5cd00bd95a3060f5d520cbb2","target":"record","created_at":"2026-05-18T01:32:52Z","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":"5ee20a51aac328cd769dda9783bee7d9c58b9b1911987548b58695db9c08815e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-20T07:14:30Z","title_canon_sha256":"46a8f146d4d35e02fc02566709653ff74eae7886bd80180a0dde783c0ba020fc"},"schema_version":"1.0","source":{"id":"1508.04897","kind":"arxiv","version":1}},"canonical_sha256":"98ed6b020877e7c9a8273b8a82019f290e494480163b620baf8b89f7c8b7ded0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98ed6b020877e7c9a8273b8a82019f290e494480163b620baf8b89f7c8b7ded0","first_computed_at":"2026-05-18T01:32:52.027190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:52.027190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lX7D9y9+5G5V5Lcj08QK5LcM1fgq+Lv8Z331eGQFNcW00E9A6QBIbzY0R0/9cYK01tNK6HrzrOTLyreSml31CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:52.027948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aba7b9ce72f4d662708e42b4ecac302f480418da5cd00bd95a3060f5d520cbb2","sha256:428f2d4598200871c89bb75a531a5f58f48b24aeaa0a95b68547b5780f7f9139"],"state_sha256":"e2829d3d1570a2349c5844696a03937621b8b2a76ae28fe546f5ee2ecc63c0cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+wNLV1MxrSs1cU/SyxbsDr5VL6aT8be9CsoDK7gpTN+0rqOxntEku3AkMGFNHwN29WIkbi+3j3baq8YxBROCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:09:26.194340Z","bundle_sha256":"d8ed8310287804e1eda0acdf3077c5d4cbdfea8c291c5e8ca58c80c5029794ef"}}