{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SXCAHTOCWDUW3M4YRNKOXLASBW","short_pith_number":"pith:SXCAHTOC","canonical_record":{"source":{"id":"1705.00965","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-28T02:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"1597996f29e9b809735031ec874d036b4f6cba6c0f991e7e6e13ec5f7bd7946a","abstract_canon_sha256":"476ce3f2d2e5ab377e655425a295ae1d588eb3ccfbff1e41fd2c34d56ecb07e7"},"schema_version":"1.0"},"canonical_sha256":"95c403cdc2b0e96db3988b54ebac120dbf5fff55e7600071d3366dce1e781cb9","source":{"kind":"arxiv","id":"1705.00965","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00965","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00965v3","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00965","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"pith_short_12","alias_value":"SXCAHTOCWDUW","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SXCAHTOCWDUW3M4Y","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SXCAHTOC","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SXCAHTOCWDUW3M4YRNKOXLASBW","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00965","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-28T02:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"1597996f29e9b809735031ec874d036b4f6cba6c0f991e7e6e13ec5f7bd7946a","abstract_canon_sha256":"476ce3f2d2e5ab377e655425a295ae1d588eb3ccfbff1e41fd2c34d56ecb07e7"},"schema_version":"1.0"},"canonical_sha256":"95c403cdc2b0e96db3988b54ebac120dbf5fff55e7600071d3366dce1e781cb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:04.559520Z","signature_b64":"5TylYsfior/Zc6W8VAGsiU3wyQFe8Jg2CZcDL6zY66ToQRJ2M/maL3IfbODElSO0c/7fom1hKUc/V3lb/rX6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95c403cdc2b0e96db3988b54ebac120dbf5fff55e7600071d3366dce1e781cb9","last_reissued_at":"2026-05-18T00:42:04.558832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:04.558832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00965","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IF9KkzjSwLlh0IufVbwgb9jNXtKQngzyd9/rSEiybmSLDJnyOvphzRtN/ZiAs+Ym6ZDSzFrZZju6paCPNy7aBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:51:13.415230Z"},"content_sha256":"cdd9ac27634654575bf75d4c888720039f0e5cbdeb9d27978cd3aae47b9cda5c","schema_version":"1.0","event_id":"sha256:cdd9ac27634654575bf75d4c888720039f0e5cbdeb9d27978cd3aae47b9cda5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SXCAHTOCWDUW3M4YRNKOXLASBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gruss-type inequality by mean of a fractional integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. S. Oliveira, E. Capelas de Oliveira, J. Vanterler da C. Sousa","submitted_at":"2017-04-28T02:51:42Z","abstract_excerpt":"In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove others inequalities associated with these fractional operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00965","kind":"arxiv","version":3},"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":"2026-05-18T00:42:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GAd4yqYyupBKZjs4riBp/m1Rqoh9/O1lnVD/FLOxVe+D4rrYWLq8e/3apl/1R3mCeuEz4ykL6TfX3zomfuW0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:51:13.415582Z"},"content_sha256":"4ba06d36fa00e13c33ad66561fa6bb3c430da98cc0dd58005df25695b741bedf","schema_version":"1.0","event_id":"sha256:4ba06d36fa00e13c33ad66561fa6bb3c430da98cc0dd58005df25695b741bedf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXCAHTOCWDUW3M4YRNKOXLASBW/bundle.json","state_url":"https://pith.science/pith/SXCAHTOCWDUW3M4YRNKOXLASBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXCAHTOCWDUW3M4YRNKOXLASBW/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":"2026-06-03T16:51:13Z","links":{"resolver":"https://pith.science/pith/SXCAHTOCWDUW3M4YRNKOXLASBW","bundle":"https://pith.science/pith/SXCAHTOCWDUW3M4YRNKOXLASBW/bundle.json","state":"https://pith.science/pith/SXCAHTOCWDUW3M4YRNKOXLASBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXCAHTOCWDUW3M4YRNKOXLASBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SXCAHTOCWDUW3M4YRNKOXLASBW","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":"476ce3f2d2e5ab377e655425a295ae1d588eb3ccfbff1e41fd2c34d56ecb07e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-28T02:51:42Z","title_canon_sha256":"1597996f29e9b809735031ec874d036b4f6cba6c0f991e7e6e13ec5f7bd7946a"},"schema_version":"1.0","source":{"id":"1705.00965","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00965","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00965v3","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00965","created_at":"2026-05-18T00:42:04Z"},{"alias_kind":"pith_short_12","alias_value":"SXCAHTOCWDUW","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SXCAHTOCWDUW3M4Y","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SXCAHTOC","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:4ba06d36fa00e13c33ad66561fa6bb3c430da98cc0dd58005df25695b741bedf","target":"graph","created_at":"2026-05-18T00:42:04Z","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, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove others inequalities associated with these fractional operator.","authors_text":"D. S. Oliveira, E. Capelas de Oliveira, J. Vanterler da C. Sousa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-28T02:51:42Z","title":"Gruss-type inequality by mean of a fractional integral"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00965","kind":"arxiv","version":3},"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:cdd9ac27634654575bf75d4c888720039f0e5cbdeb9d27978cd3aae47b9cda5c","target":"record","created_at":"2026-05-18T00:42:04Z","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":"476ce3f2d2e5ab377e655425a295ae1d588eb3ccfbff1e41fd2c34d56ecb07e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-28T02:51:42Z","title_canon_sha256":"1597996f29e9b809735031ec874d036b4f6cba6c0f991e7e6e13ec5f7bd7946a"},"schema_version":"1.0","source":{"id":"1705.00965","kind":"arxiv","version":3}},"canonical_sha256":"95c403cdc2b0e96db3988b54ebac120dbf5fff55e7600071d3366dce1e781cb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95c403cdc2b0e96db3988b54ebac120dbf5fff55e7600071d3366dce1e781cb9","first_computed_at":"2026-05-18T00:42:04.558832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:04.558832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5TylYsfior/Zc6W8VAGsiU3wyQFe8Jg2CZcDL6zY66ToQRJ2M/maL3IfbODElSO0c/7fom1hKUc/V3lb/rX6Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:04.559520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00965","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd9ac27634654575bf75d4c888720039f0e5cbdeb9d27978cd3aae47b9cda5c","sha256:4ba06d36fa00e13c33ad66561fa6bb3c430da98cc0dd58005df25695b741bedf"],"state_sha256":"9c3c6cca0db00ca19c8f9e47505f8e74578efed89863fe40116ff61a55ad8aae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sK0ajKZ5Dw04wbVVrYbydX+4CDzEJsjXSYon/RfCK8Bgiz3DOGVFH+iTH02de0wWoaoxvEiH66+8roUTMsO7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:51:13.417664Z","bundle_sha256":"5e3fd03b01deaec704f1f658e48b39c9a45352087b7c78152337db129713c858"}}