{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TEGVDRIYYO6F7CIKGPDYKOLWIK","short_pith_number":"pith:TEGVDRIY","canonical_record":{"source":{"id":"1205.4158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-18T13:52:44Z","cross_cats_sorted":[],"title_canon_sha256":"a1f51e8b8a6f14f4825f02022458a7bc026968fc88e4bec3f9dfe05f1a515f8c","abstract_canon_sha256":"832a81c0fa60992e912a3404656fbaa00215ebef6da3d977276c75f59bac6aa0"},"schema_version":"1.0"},"canonical_sha256":"990d51c518c3bc5f890a33c785397642bf1a49117f1532745483a7f8a4d76d52","source":{"kind":"arxiv","id":"1205.4158","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4158","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4158v2","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4158","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"TEGVDRIYYO6F","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TEGVDRIYYO6F7CIK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TEGVDRIY","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TEGVDRIYYO6F7CIKGPDYKOLWIK","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-18T13:52:44Z","cross_cats_sorted":[],"title_canon_sha256":"a1f51e8b8a6f14f4825f02022458a7bc026968fc88e4bec3f9dfe05f1a515f8c","abstract_canon_sha256":"832a81c0fa60992e912a3404656fbaa00215ebef6da3d977276c75f59bac6aa0"},"schema_version":"1.0"},"canonical_sha256":"990d51c518c3bc5f890a33c785397642bf1a49117f1532745483a7f8a4d76d52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:54.064219Z","signature_b64":"F+9S8uKRxnfOrxDsXuXN8cn/KgZrPbModb9a+ssgXfKZYxGJt9twAt6Q5zWwdFe7YHs3MErmj1/he0UEOlhlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"990d51c518c3bc5f890a33c785397642bf1a49117f1532745483a7f8a4d76d52","last_reissued_at":"2026-05-18T03:53:54.063792Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:54.063792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4158","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pmEs6X04T8qfTPKq/cVq6qp+MWA7+vPJsdsyfnz7OHk09Pz9s9rwmZ45U96srLuj0FZitydZMu2epAkzZWurDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:49:27.223392Z"},"content_sha256":"4d43f928bf803600495850c861e51bbae4c21f5943fbaabc03124716fbc64f48","schema_version":"1.0","event_id":"sha256:4d43f928bf803600495850c861e51bbae4c21f5943fbaabc03124716fbc64f48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TEGVDRIYYO6F7CIKGPDYKOLWIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ostrowski's Type Inequalities for Strongly-Convex Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Ocak Akdemir, Erhan Set, M.Emin Ozdemir, M.Zeki Sarikaya","submitted_at":"2012-05-18T13:52:44Z","abstract_excerpt":"In this paper, we establish Ostrowski's type inequalities for strongly-convex functions where c>0 by using some classical inequalities and elemantery analysis. We also give some results for product of two strongly-convex functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4158","kind":"arxiv","version":2},"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":"2026-05-18T03:53:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cqqvGBJN+8EKfkWZAIqNtf2u5ydtDF4NbJWiWssFrCMWNUmotg6wXY7cyVQnxD/C+EP/8jJlLy+tJ2ZW2YI4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:49:27.223742Z"},"content_sha256":"869801f0dd5ecf7487329c56ef4ea533ef2efcf7bc1b1f1590709b13eaf622e0","schema_version":"1.0","event_id":"sha256:869801f0dd5ecf7487329c56ef4ea533ef2efcf7bc1b1f1590709b13eaf622e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEGVDRIYYO6F7CIKGPDYKOLWIK/bundle.json","state_url":"https://pith.science/pith/TEGVDRIYYO6F7CIKGPDYKOLWIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEGVDRIYYO6F7CIKGPDYKOLWIK/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":"2026-06-22T14:49:27Z","links":{"resolver":"https://pith.science/pith/TEGVDRIYYO6F7CIKGPDYKOLWIK","bundle":"https://pith.science/pith/TEGVDRIYYO6F7CIKGPDYKOLWIK/bundle.json","state":"https://pith.science/pith/TEGVDRIYYO6F7CIKGPDYKOLWIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEGVDRIYYO6F7CIKGPDYKOLWIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TEGVDRIYYO6F7CIKGPDYKOLWIK","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":"832a81c0fa60992e912a3404656fbaa00215ebef6da3d977276c75f59bac6aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-18T13:52:44Z","title_canon_sha256":"a1f51e8b8a6f14f4825f02022458a7bc026968fc88e4bec3f9dfe05f1a515f8c"},"schema_version":"1.0","source":{"id":"1205.4158","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4158","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4158v2","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4158","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"TEGVDRIYYO6F","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TEGVDRIYYO6F7CIK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TEGVDRIY","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:869801f0dd5ecf7487329c56ef4ea533ef2efcf7bc1b1f1590709b13eaf622e0","target":"graph","created_at":"2026-05-18T03:53:54Z","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, we establish Ostrowski's type inequalities for strongly-convex functions where c>0 by using some classical inequalities and elemantery analysis. We also give some results for product of two strongly-convex functions.","authors_text":"A. Ocak Akdemir, Erhan Set, M.Emin Ozdemir, M.Zeki Sarikaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-18T13:52:44Z","title":"Ostrowski's Type Inequalities for Strongly-Convex Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4158","kind":"arxiv","version":2},"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":"sha256:4d43f928bf803600495850c861e51bbae4c21f5943fbaabc03124716fbc64f48","target":"record","created_at":"2026-05-18T03:53:54Z","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":"832a81c0fa60992e912a3404656fbaa00215ebef6da3d977276c75f59bac6aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-05-18T13:52:44Z","title_canon_sha256":"a1f51e8b8a6f14f4825f02022458a7bc026968fc88e4bec3f9dfe05f1a515f8c"},"schema_version":"1.0","source":{"id":"1205.4158","kind":"arxiv","version":2}},"canonical_sha256":"990d51c518c3bc5f890a33c785397642bf1a49117f1532745483a7f8a4d76d52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"990d51c518c3bc5f890a33c785397642bf1a49117f1532745483a7f8a4d76d52","first_computed_at":"2026-05-18T03:53:54.063792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:54.063792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F+9S8uKRxnfOrxDsXuXN8cn/KgZrPbModb9a+ssgXfKZYxGJt9twAt6Q5zWwdFe7YHs3MErmj1/he0UEOlhlBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:54.064219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4158","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d43f928bf803600495850c861e51bbae4c21f5943fbaabc03124716fbc64f48","sha256:869801f0dd5ecf7487329c56ef4ea533ef2efcf7bc1b1f1590709b13eaf622e0"],"state_sha256":"ef5227472853d0c4da8e72a908b855d4af301bf476ce8154fe4a96b3796fdcca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ky29o142uAylgbx6Qqv/Gz88e5HMIHiM2ct1RVvx/gh5WjxKGpe6pVknbhPGYyHmmPQpJkTxKIYfZ0ypuSFiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:49:27.225865Z","bundle_sha256":"a49f7e10f3c0db6f63a85e9b4b910984e2fb9b974820af5870e93fa46355fb82"}}