{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AKZBZHDF3QLMTKRBCM5UASD7ZA","short_pith_number":"pith:AKZBZHDF","canonical_record":{"source":{"id":"1902.01230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-04T14:51:30Z","cross_cats_sorted":[],"title_canon_sha256":"d8db1c63d205c15323b9db6d8446a0c9abd2ed588cd8c447a3bd91257e72bb78","abstract_canon_sha256":"de1944feab78dfad7d020b901b7eeeede95b0ba93120c2e6343b2340777b0979"},"schema_version":"1.0"},"canonical_sha256":"02b21c9c65dc16c9aa21133b40487fc82b6d8ea7797d64b9757aa08f7877dacf","source":{"kind":"arxiv","id":"1902.01230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01230","created_at":"2026-05-17T23:54:49Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01230v1","created_at":"2026-05-17T23:54:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01230","created_at":"2026-05-17T23:54:49Z"},{"alias_kind":"pith_short_12","alias_value":"AKZBZHDF3QLM","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AKZBZHDF3QLMTKRB","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AKZBZHDF","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AKZBZHDF3QLMTKRBCM5UASD7ZA","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-04T14:51:30Z","cross_cats_sorted":[],"title_canon_sha256":"d8db1c63d205c15323b9db6d8446a0c9abd2ed588cd8c447a3bd91257e72bb78","abstract_canon_sha256":"de1944feab78dfad7d020b901b7eeeede95b0ba93120c2e6343b2340777b0979"},"schema_version":"1.0"},"canonical_sha256":"02b21c9c65dc16c9aa21133b40487fc82b6d8ea7797d64b9757aa08f7877dacf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:49.362075Z","signature_b64":"Ctv/SWxa96lkFGRME1YCGy8rAuLDW/3sJk1CrZdhnYFyZlaHrESylnZWKgrZdoEcGPglzZfn5PJgHfu+/qgGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02b21c9c65dc16c9aa21133b40487fc82b6d8ea7797d64b9757aa08f7877dacf","last_reissued_at":"2026-05-17T23:54:49.361248Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:49.361248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01230","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":"2026-05-17T23:54:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4w0epbqJGpyMFzIqToXuTc+GNmnMcEzZSbEYNQdUUncYx6fisWQ5NC0karBGOGoXl1QpTBrRrPOO8gCcLL0jCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:51:40.328595Z"},"content_sha256":"953e9e91adc3b2e38fe4265227db9ce09221eb36a79bf65be0ca62d8894c3565","schema_version":"1.0","event_id":"sha256:953e9e91adc3b2e38fe4265227db9ce09221eb36a79bf65be0ca62d8894c3565"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AKZBZHDF3QLMTKRBCM5UASD7ZA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On generalized stochastic fractional integrals and related inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"H\\\"useyin Budak, Mehmet Zeki Sarikaya","submitted_at":"2019-02-04T14:51:30Z","abstract_excerpt":"The generalized mean-square fractional integrals $\\mathcal{J}_{\\rho,\\lambda,u+;\\omega}^{\\sigma}$ and $\\mathcal{J}_{\\rho,\\lambda,v-;\\omega}^{\\sigma}$ of the stochastic process $X$ are introduced. Then, for Jensen-convex and strongly convex stochastic proceses, the generalized fractional Hermite--Hadamard inequality is establish via generalized stochastic fractional integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01230","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":"2026-05-17T23:54:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TyViDU3BogJksTyyv+zQCG5wxUsEgOWV5n9NdFbmdcHreGp9BBRJvZpZzDpQ9eXde7h4esqIRpnu8egtDdQvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:51:40.328946Z"},"content_sha256":"a73ec2eaa0d987b8f66bb4e48329fbf7c01723c060a2030eb2ac44c162d67e3b","schema_version":"1.0","event_id":"sha256:a73ec2eaa0d987b8f66bb4e48329fbf7c01723c060a2030eb2ac44c162d67e3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKZBZHDF3QLMTKRBCM5UASD7ZA/bundle.json","state_url":"https://pith.science/pith/AKZBZHDF3QLMTKRBCM5UASD7ZA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKZBZHDF3QLMTKRBCM5UASD7ZA/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":"2026-06-22T18:51:40Z","links":{"resolver":"https://pith.science/pith/AKZBZHDF3QLMTKRBCM5UASD7ZA","bundle":"https://pith.science/pith/AKZBZHDF3QLMTKRBCM5UASD7ZA/bundle.json","state":"https://pith.science/pith/AKZBZHDF3QLMTKRBCM5UASD7ZA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKZBZHDF3QLMTKRBCM5UASD7ZA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AKZBZHDF3QLMTKRBCM5UASD7ZA","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":"de1944feab78dfad7d020b901b7eeeede95b0ba93120c2e6343b2340777b0979","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-04T14:51:30Z","title_canon_sha256":"d8db1c63d205c15323b9db6d8446a0c9abd2ed588cd8c447a3bd91257e72bb78"},"schema_version":"1.0","source":{"id":"1902.01230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01230","created_at":"2026-05-17T23:54:49Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01230v1","created_at":"2026-05-17T23:54:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01230","created_at":"2026-05-17T23:54:49Z"},{"alias_kind":"pith_short_12","alias_value":"AKZBZHDF3QLM","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"AKZBZHDF3QLMTKRB","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"AKZBZHDF","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:a73ec2eaa0d987b8f66bb4e48329fbf7c01723c060a2030eb2ac44c162d67e3b","target":"graph","created_at":"2026-05-17T23:54:49Z","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 generalized mean-square fractional integrals $\\mathcal{J}_{\\rho,\\lambda,u+;\\omega}^{\\sigma}$ and $\\mathcal{J}_{\\rho,\\lambda,v-;\\omega}^{\\sigma}$ of the stochastic process $X$ are introduced. Then, for Jensen-convex and strongly convex stochastic proceses, the generalized fractional Hermite--Hadamard inequality is establish via generalized stochastic fractional integrals.","authors_text":"H\\\"useyin Budak, Mehmet Zeki Sarikaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-04T14:51:30Z","title":"On generalized stochastic fractional integrals and related inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01230","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":"sha256:953e9e91adc3b2e38fe4265227db9ce09221eb36a79bf65be0ca62d8894c3565","target":"record","created_at":"2026-05-17T23:54:49Z","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":"de1944feab78dfad7d020b901b7eeeede95b0ba93120c2e6343b2340777b0979","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-04T14:51:30Z","title_canon_sha256":"d8db1c63d205c15323b9db6d8446a0c9abd2ed588cd8c447a3bd91257e72bb78"},"schema_version":"1.0","source":{"id":"1902.01230","kind":"arxiv","version":1}},"canonical_sha256":"02b21c9c65dc16c9aa21133b40487fc82b6d8ea7797d64b9757aa08f7877dacf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02b21c9c65dc16c9aa21133b40487fc82b6d8ea7797d64b9757aa08f7877dacf","first_computed_at":"2026-05-17T23:54:49.361248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:49.361248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ctv/SWxa96lkFGRME1YCGy8rAuLDW/3sJk1CrZdhnYFyZlaHrESylnZWKgrZdoEcGPglzZfn5PJgHfu+/qgGBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:49.362075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:953e9e91adc3b2e38fe4265227db9ce09221eb36a79bf65be0ca62d8894c3565","sha256:a73ec2eaa0d987b8f66bb4e48329fbf7c01723c060a2030eb2ac44c162d67e3b"],"state_sha256":"5a87ba47a7cb2ccac8ca1b9e3952743c61f66c4c747dde9f579df0d27a490a24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgOlmkeB/I1ZyY6l5mcT8R9wLPPpX2C6jb36/rwIiv4rPQ8fusiswJekwyI1UIw2c0AXs5EtI1wtyUpH5y4GAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:51:40.330886Z","bundle_sha256":"6b865e4f746d38df3021e36f551b235ecc03473e808b3024f7934bacb6751d37"}}