{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AQLLWMGPAXCAYNVUJS5APU5Z2J","short_pith_number":"pith:AQLLWMGP","canonical_record":{"source":{"id":"1704.08190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-15T11:37:43Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"65305403f6cf140fed0b5c613f2e56f1ee3bda51c0c658b91e381679ebe93fb8","abstract_canon_sha256":"2daad425f6ace6f7a941645d8bc754c2208f1898ad02c617c73161f7098beec2"},"schema_version":"1.0"},"canonical_sha256":"0416bb30cf05c40c36b44cba07d3b9d265b9d7ef1058fc71e2cf676a958950eb","source":{"kind":"arxiv","id":"1704.08190","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08190","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08190v1","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08190","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"AQLLWMGPAXCA","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQLLWMGPAXCAYNVU","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQLLWMGP","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AQLLWMGPAXCAYNVUJS5APU5Z2J","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-15T11:37:43Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"65305403f6cf140fed0b5c613f2e56f1ee3bda51c0c658b91e381679ebe93fb8","abstract_canon_sha256":"2daad425f6ace6f7a941645d8bc754c2208f1898ad02c617c73161f7098beec2"},"schema_version":"1.0"},"canonical_sha256":"0416bb30cf05c40c36b44cba07d3b9d265b9d7ef1058fc71e2cf676a958950eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:30.968115Z","signature_b64":"ZZd5VOjGSTSgviguitQ+M5oSIw/lJj9yXWV+0eDuHXWLp33g3Lo/9F8vNJhZscV/79cbNcs11hcghZYAT8ZPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0416bb30cf05c40c36b44cba07d3b9d265b9d7ef1058fc71e2cf676a958950eb","last_reissued_at":"2026-05-18T00:45:30.967513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:30.967513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08190","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":"2026-05-18T00:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTVjInAlEG/AVc8uwS5sYMf2ln7zR3lFyHC0KJ86D+a2sy3Ws7xR+cZRs+rPsS+AxX1gmVS0rUOO6HDUhDYlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T07:56:52.845075Z"},"content_sha256":"7519ce256b0d11c19ec146f777205064f11f9a24bca01d8d90502271d972c9c0","schema_version":"1.0","event_id":"sha256:7519ce256b0d11c19ec146f777205064f11f9a24bca01d8d90502271d972c9c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AQLLWMGPAXCAYNVUJS5APU5Z2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Convex Functions and Their Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Adem Kilicman, Wedad Saleh","submitted_at":"2017-04-15T11:37:43Z","abstract_excerpt":"This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex functions and establish some their properties. Moreover, we give generalized $ s $-convex functions in the second sense and present some new inequalities of generalized Hermite-Hadamard type for the class of functions whose second local fractional derivatives of order $ \\alpha $ in absolute value at certain powers are generalized $ s $-convex functions in the seco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08190","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":"2026-05-18T00:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYBSc87cmSKiozXgxtYLKTv06d6a1r5U8EQ1mXsqN57R1z1os3yxnJNEyXH/P6G0CwrHGjsKrHusmmk8pL8+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T07:56:52.845759Z"},"content_sha256":"04b6cde6f4f793c51afd80efd9d4a0f3c97988b15163e6997d69a25c21aa5f6b","schema_version":"1.0","event_id":"sha256:04b6cde6f4f793c51afd80efd9d4a0f3c97988b15163e6997d69a25c21aa5f6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQLLWMGPAXCAYNVUJS5APU5Z2J/bundle.json","state_url":"https://pith.science/pith/AQLLWMGPAXCAYNVUJS5APU5Z2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQLLWMGPAXCAYNVUJS5APU5Z2J/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":"2026-06-08T07:56:52Z","links":{"resolver":"https://pith.science/pith/AQLLWMGPAXCAYNVUJS5APU5Z2J","bundle":"https://pith.science/pith/AQLLWMGPAXCAYNVUJS5APU5Z2J/bundle.json","state":"https://pith.science/pith/AQLLWMGPAXCAYNVUJS5APU5Z2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQLLWMGPAXCAYNVUJS5APU5Z2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AQLLWMGPAXCAYNVUJS5APU5Z2J","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":"2daad425f6ace6f7a941645d8bc754c2208f1898ad02c617c73161f7098beec2","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-15T11:37:43Z","title_canon_sha256":"65305403f6cf140fed0b5c613f2e56f1ee3bda51c0c658b91e381679ebe93fb8"},"schema_version":"1.0","source":{"id":"1704.08190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08190","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08190v1","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08190","created_at":"2026-05-18T00:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"AQLLWMGPAXCA","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQLLWMGPAXCAYNVU","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQLLWMGP","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:04b6cde6f4f793c51afd80efd9d4a0f3c97988b15163e6997d69a25c21aa5f6b","target":"graph","created_at":"2026-05-18T00:45:30Z","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":"This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex functions and establish some their properties. Moreover, we give generalized $ s $-convex functions in the second sense and present some new inequalities of generalized Hermite-Hadamard type for the class of functions whose second local fractional derivatives of order $ \\alpha $ in absolute value at certain powers are generalized $ s $-convex functions in the seco","authors_text":"Adem Kilicman, Wedad Saleh","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-15T11:37:43Z","title":"Generalized Convex Functions and Their Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08190","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":"sha256:7519ce256b0d11c19ec146f777205064f11f9a24bca01d8d90502271d972c9c0","target":"record","created_at":"2026-05-18T00:45:30Z","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":"2daad425f6ace6f7a941645d8bc754c2208f1898ad02c617c73161f7098beec2","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-15T11:37:43Z","title_canon_sha256":"65305403f6cf140fed0b5c613f2e56f1ee3bda51c0c658b91e381679ebe93fb8"},"schema_version":"1.0","source":{"id":"1704.08190","kind":"arxiv","version":1}},"canonical_sha256":"0416bb30cf05c40c36b44cba07d3b9d265b9d7ef1058fc71e2cf676a958950eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0416bb30cf05c40c36b44cba07d3b9d265b9d7ef1058fc71e2cf676a958950eb","first_computed_at":"2026-05-18T00:45:30.967513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:30.967513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZZd5VOjGSTSgviguitQ+M5oSIw/lJj9yXWV+0eDuHXWLp33g3Lo/9F8vNJhZscV/79cbNcs11hcghZYAT8ZPCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:30.968115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7519ce256b0d11c19ec146f777205064f11f9a24bca01d8d90502271d972c9c0","sha256:04b6cde6f4f793c51afd80efd9d4a0f3c97988b15163e6997d69a25c21aa5f6b"],"state_sha256":"ec0b4525ffaefd5e7abb98f7d525539cd0922899b2d22f3d92ea42843bd3df74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYhIfRD+xDWZ6OuYg/lJ4PJWE39OLXlXIdp3z4bdlLTE3QIAgmB/NO2yz/Y2KR2Yn/G7inR/z07hGKyAhG0MBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T07:56:52.849814Z","bundle_sha256":"102fcb68fc9cb93c31a388e903de2dabebf7b024490229f3b4f3b22a53fe60d3"}}