{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:C3W7VV7TRSG6UEPPU2ADPB7SVP","short_pith_number":"pith:C3W7VV7T","canonical_record":{"source":{"id":"1202.2207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T08:23:29Z","cross_cats_sorted":[],"title_canon_sha256":"b7d117a3c99f54b43f963fa9368d14d27a7e92873ba49f278d08dc385345d66b","abstract_canon_sha256":"62ba2bb32bad9e3f71cc3a5d1f4ef48b3ca4119c568880d4adbe8b8f77b86f35"},"schema_version":"1.0"},"canonical_sha256":"16edfad7f38c8dea11efa6803787f2abf0cc0950450016dfe8ba42296538425f","source":{"kind":"arxiv","id":"1202.2207","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2207","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2207v1","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2207","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"C3W7VV7TRSG6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3W7VV7TRSG6UEPP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3W7VV7T","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:C3W7VV7TRSG6UEPPU2ADPB7SVP","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T08:23:29Z","cross_cats_sorted":[],"title_canon_sha256":"b7d117a3c99f54b43f963fa9368d14d27a7e92873ba49f278d08dc385345d66b","abstract_canon_sha256":"62ba2bb32bad9e3f71cc3a5d1f4ef48b3ca4119c568880d4adbe8b8f77b86f35"},"schema_version":"1.0"},"canonical_sha256":"16edfad7f38c8dea11efa6803787f2abf0cc0950450016dfe8ba42296538425f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:36.910719Z","signature_b64":"FAhcoCYtwZoqiQgRgxtp+/QcAGqg37kiSjHYIEJMM776PaBMAltDXrdYtG8KkHh9Ljv3Z+O1Tr+5Ks2lfbPsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16edfad7f38c8dea11efa6803787f2abf0cc0950450016dfe8ba42296538425f","last_reissued_at":"2026-05-18T04:02:36.910114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:36.910114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2207","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":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eowlTU7pSH3rnDvZkyWpwC0WXZSp8jylxBTpQMBKD1UPsIQTa9mIK/q1cpE0hiybGLyLYI+hFK1/qfiIujarDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:28:27.017089Z"},"content_sha256":"84326f1cf1fae4faaf4bd355385c40bd251e84b96de4a45ab2cdc3dc3b1314e1","schema_version":"1.0","event_id":"sha256:84326f1cf1fae4faaf4bd355385c40bd251e84b96de4a45ab2cdc3dc3b1314e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:C3W7VV7TRSG6UEPPU2ADPB7SVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Estimations for h-convex Functions via Further Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Huseyin Yildirim, Mevlut Tunc","submitted_at":"2012-02-10T08:23:29Z","abstract_excerpt":"In this paper, some new inequalities of the Hermite-Hadamard type for h- convex functions whose modulus of the derivatives are h-convex and applications for special means are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2207","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":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YV12SjvaYZIUbPgWwsFoQO/smgmCFXGjPtr5Ipg8YPgSOaHMfWTce4m+LgNWAwzP61XHAPSM6DQG9MyvGSpSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:28:27.017441Z"},"content_sha256":"4027d7eab0331872d0469c1dd03b69ddb294765cfc38de3284431257d6b9d24c","schema_version":"1.0","event_id":"sha256:4027d7eab0331872d0469c1dd03b69ddb294765cfc38de3284431257d6b9d24c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3W7VV7TRSG6UEPPU2ADPB7SVP/bundle.json","state_url":"https://pith.science/pith/C3W7VV7TRSG6UEPPU2ADPB7SVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3W7VV7TRSG6UEPPU2ADPB7SVP/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":"2026-06-22T15:28:27Z","links":{"resolver":"https://pith.science/pith/C3W7VV7TRSG6UEPPU2ADPB7SVP","bundle":"https://pith.science/pith/C3W7VV7TRSG6UEPPU2ADPB7SVP/bundle.json","state":"https://pith.science/pith/C3W7VV7TRSG6UEPPU2ADPB7SVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3W7VV7TRSG6UEPPU2ADPB7SVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C3W7VV7TRSG6UEPPU2ADPB7SVP","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":"62ba2bb32bad9e3f71cc3a5d1f4ef48b3ca4119c568880d4adbe8b8f77b86f35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T08:23:29Z","title_canon_sha256":"b7d117a3c99f54b43f963fa9368d14d27a7e92873ba49f278d08dc385345d66b"},"schema_version":"1.0","source":{"id":"1202.2207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2207","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2207v1","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2207","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"C3W7VV7TRSG6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C3W7VV7TRSG6UEPP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C3W7VV7T","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:4027d7eab0331872d0469c1dd03b69ddb294765cfc38de3284431257d6b9d24c","target":"graph","created_at":"2026-05-18T04:02:36Z","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, some new inequalities of the Hermite-Hadamard type for h- convex functions whose modulus of the derivatives are h-convex and applications for special means are given.","authors_text":"Huseyin Yildirim, Mevlut Tunc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T08:23:29Z","title":"New Estimations for h-convex Functions via Further Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2207","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":"sha256:84326f1cf1fae4faaf4bd355385c40bd251e84b96de4a45ab2cdc3dc3b1314e1","target":"record","created_at":"2026-05-18T04:02:36Z","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":"62ba2bb32bad9e3f71cc3a5d1f4ef48b3ca4119c568880d4adbe8b8f77b86f35","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-02-10T08:23:29Z","title_canon_sha256":"b7d117a3c99f54b43f963fa9368d14d27a7e92873ba49f278d08dc385345d66b"},"schema_version":"1.0","source":{"id":"1202.2207","kind":"arxiv","version":1}},"canonical_sha256":"16edfad7f38c8dea11efa6803787f2abf0cc0950450016dfe8ba42296538425f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16edfad7f38c8dea11efa6803787f2abf0cc0950450016dfe8ba42296538425f","first_computed_at":"2026-05-18T04:02:36.910114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:36.910114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FAhcoCYtwZoqiQgRgxtp+/QcAGqg37kiSjHYIEJMM776PaBMAltDXrdYtG8KkHh9Ljv3Z+O1Tr+5Ks2lfbPsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:36.910719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84326f1cf1fae4faaf4bd355385c40bd251e84b96de4a45ab2cdc3dc3b1314e1","sha256:4027d7eab0331872d0469c1dd03b69ddb294765cfc38de3284431257d6b9d24c"],"state_sha256":"4736bd7018ea79d071d4baa3e32cf0768fb56051be02fa0a37976536603705b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7pQqUVqcb4UVEdqiSkDZWNA77UoF0tc+ZZ2o91iV5DCoZTrnPKmHOkdhO09dVheDd7gUez2c39BV6evZQX1rCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:28:27.019327Z","bundle_sha256":"23acad8381414b9490db0aeac5ed478f71bc8207d04b82188806d96955ebd4ea"}}