{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SFW4NXAXR6RBSDG3RRP3IPR4ZH","short_pith_number":"pith:SFW4NXAX","canonical_record":{"source":{"id":"1102.1585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T12:25:01Z","cross_cats_sorted":[],"title_canon_sha256":"6351db568a9a38219325f58241798dfca02fc8aa759e8163e969b5af99843640","abstract_canon_sha256":"94c25e41f1c307b23ab831098caa82d83ae0d58eaf3cc8fc526ec991a407c293"},"schema_version":"1.0"},"canonical_sha256":"916dc6dc178fa2190cdb8c5fb43e3cc9edcdbad1e5e5e44a85474551b41602ea","source":{"kind":"arxiv","id":"1102.1585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1585","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1585v1","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1585","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"SFW4NXAXR6RB","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SFW4NXAXR6RBSDG3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SFW4NXAX","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SFW4NXAXR6RBSDG3RRP3IPR4ZH","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T12:25:01Z","cross_cats_sorted":[],"title_canon_sha256":"6351db568a9a38219325f58241798dfca02fc8aa759e8163e969b5af99843640","abstract_canon_sha256":"94c25e41f1c307b23ab831098caa82d83ae0d58eaf3cc8fc526ec991a407c293"},"schema_version":"1.0"},"canonical_sha256":"916dc6dc178fa2190cdb8c5fb43e3cc9edcdbad1e5e5e44a85474551b41602ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:52.913023Z","signature_b64":"BI/4XhvEoz3b/d9PWb3O4X6asWTd8DbXBtYiItKR94/5inoY8kaSgyi5zXi1FzUeRI0ZrSQ3FYW3kV9EEqUNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"916dc6dc178fa2190cdb8c5fb43e3cc9edcdbad1e5e5e44a85474551b41602ea","last_reissued_at":"2026-05-18T04:29:52.912572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:52.912572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1585","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":"2026-05-18T04:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVo4w/+wOnk/AnSrwjE0ow5dl9aDhylB4IEUd9Wie/6uGogGfyDMHRL6co8RFIZw00u1xi8It4R30AXT1aF1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:11:23.530689Z"},"content_sha256":"79b182c5293e2d90c43af7a758b7d3c47b0193c9d6d71e80d2bbd76f6a87a096","schema_version":"1.0","event_id":"sha256:79b182c5293e2d90c43af7a758b7d3c47b0193c9d6d71e80d2bbd76f6a87a096"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SFW4NXAXR6RBSDG3RRP3IPR4ZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Quantum Generalized Mittag-Leffler Function Via Caputo q-Fractional Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bet\\\"ul Benli, Thabet Abdeljawad","submitted_at":"2011-02-08T12:25:01Z","abstract_excerpt":"Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1585","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":"2026-05-18T04:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E0yaUaTNe8NUoUzCXO1Zu1Rwv/kCYB4gei4q8y6pg0zrLnlyM7iaT3MlB8xrP1+uRvlJfcR7wqX/Dqi4HwmEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:11:23.531032Z"},"content_sha256":"b82867147bbc43fa26d0dbad66a70fcb8e84db8668dfefc36973c782b9fedec2","schema_version":"1.0","event_id":"sha256:b82867147bbc43fa26d0dbad66a70fcb8e84db8668dfefc36973c782b9fedec2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFW4NXAXR6RBSDG3RRP3IPR4ZH/bundle.json","state_url":"https://pith.science/pith/SFW4NXAXR6RBSDG3RRP3IPR4ZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFW4NXAXR6RBSDG3RRP3IPR4ZH/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":"2026-06-26T07:11:23Z","links":{"resolver":"https://pith.science/pith/SFW4NXAXR6RBSDG3RRP3IPR4ZH","bundle":"https://pith.science/pith/SFW4NXAXR6RBSDG3RRP3IPR4ZH/bundle.json","state":"https://pith.science/pith/SFW4NXAXR6RBSDG3RRP3IPR4ZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFW4NXAXR6RBSDG3RRP3IPR4ZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SFW4NXAXR6RBSDG3RRP3IPR4ZH","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":"94c25e41f1c307b23ab831098caa82d83ae0d58eaf3cc8fc526ec991a407c293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T12:25:01Z","title_canon_sha256":"6351db568a9a38219325f58241798dfca02fc8aa759e8163e969b5af99843640"},"schema_version":"1.0","source":{"id":"1102.1585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1585","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1585v1","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1585","created_at":"2026-05-18T04:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"SFW4NXAXR6RB","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SFW4NXAXR6RBSDG3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SFW4NXAX","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:b82867147bbc43fa26d0dbad66a70fcb8e84db8668dfefc36973c782b9fedec2","target":"graph","created_at":"2026-05-18T04:29:52Z","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":"Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo.","authors_text":"Bet\\\"ul Benli, Thabet Abdeljawad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T12:25:01Z","title":"A Quantum Generalized Mittag-Leffler Function Via Caputo q-Fractional Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1585","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":"sha256:79b182c5293e2d90c43af7a758b7d3c47b0193c9d6d71e80d2bbd76f6a87a096","target":"record","created_at":"2026-05-18T04:29:52Z","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":"94c25e41f1c307b23ab831098caa82d83ae0d58eaf3cc8fc526ec991a407c293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-08T12:25:01Z","title_canon_sha256":"6351db568a9a38219325f58241798dfca02fc8aa759e8163e969b5af99843640"},"schema_version":"1.0","source":{"id":"1102.1585","kind":"arxiv","version":1}},"canonical_sha256":"916dc6dc178fa2190cdb8c5fb43e3cc9edcdbad1e5e5e44a85474551b41602ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"916dc6dc178fa2190cdb8c5fb43e3cc9edcdbad1e5e5e44a85474551b41602ea","first_computed_at":"2026-05-18T04:29:52.912572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:52.912572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BI/4XhvEoz3b/d9PWb3O4X6asWTd8DbXBtYiItKR94/5inoY8kaSgyi5zXi1FzUeRI0ZrSQ3FYW3kV9EEqUNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:52.913023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79b182c5293e2d90c43af7a758b7d3c47b0193c9d6d71e80d2bbd76f6a87a096","sha256:b82867147bbc43fa26d0dbad66a70fcb8e84db8668dfefc36973c782b9fedec2"],"state_sha256":"9ccdbf6e9eca535544c266ed92894c964a496bfa324cd3442cd8e7f9a26eaba0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qdkIvZzzirlOgmH3GqznVI7WB4Z4O3bFEmDfypz5PV0XRq5N62EURL88ZAOpw0LTbK9OJ8oQaLTP6rRBJ+Q0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:11:23.532987Z","bundle_sha256":"8d6caa31ae120bdf2329749895670d6c6435f6e4accacc73e056877b3d6fbd57"}}