{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:E3RBPNJKUYAIJL6NZLDYMJAQXZ","short_pith_number":"pith:E3RBPNJK","canonical_record":{"source":{"id":"1203.3698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-03-16T13:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"aec145cb3d3eb01b9ef38a263ed280807a0c03fffd8209c1db46edeea7bf5a56","abstract_canon_sha256":"56d88c4631756276a0e2b6a256806ac5fcf5b7206e295cd6b61127d4223c64ca"},"schema_version":"1.0"},"canonical_sha256":"26e217b52aa60084afcdcac7862410be480ac681df8fdb8d28759d88eb13dede","source":{"kind":"arxiv","id":"1203.3698","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3698","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3698v1","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3698","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"pith_short_12","alias_value":"E3RBPNJKUYAI","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3RBPNJKUYAIJL6N","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3RBPNJK","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:E3RBPNJKUYAIJL6NZLDYMJAQXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-03-16T13:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"aec145cb3d3eb01b9ef38a263ed280807a0c03fffd8209c1db46edeea7bf5a56","abstract_canon_sha256":"56d88c4631756276a0e2b6a256806ac5fcf5b7206e295cd6b61127d4223c64ca"},"schema_version":"1.0"},"canonical_sha256":"26e217b52aa60084afcdcac7862410be480ac681df8fdb8d28759d88eb13dede","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:50.151896Z","signature_b64":"49O2QRL4ovTGWadONZIkMyRrnC8F3NSMhWhSFJR3iAoNpapXMzzhVFWkGFG7D6YqPUFZV2b7EmdX/TzOSg3HBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26e217b52aa60084afcdcac7862410be480ac681df8fdb8d28759d88eb13dede","last_reissued_at":"2026-05-18T03:59:50.151262Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:50.151262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3698","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":"2026-05-18T03:59:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bk/uHjSzlBrpQgqkpdt7rEl76Q09low1wmOskDOnj0IGIL0ug98icsc9eXkO0l7U+QWWRb6WA1Zd5hQnLRkFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:00:56.738128Z"},"content_sha256":"7b2580d40cd135534a208ea58f5de175fa103b1b1c17075fe0a1592fc65b9f9d","schema_version":"1.0","event_id":"sha256:7b2580d40cd135534a208ea58f5de175fa103b1b1c17075fe0a1592fc65b9f9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:E3RBPNJKUYAIJL6NZLDYMJAQXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some New Inequalities for (h-s)_{1,2}-convex Functions via Further Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ahmet Ocak Akdemir, M. Emin Ozdemir, Mevlut Tunc","submitted_at":"2012-03-16T13:23:08Z","abstract_excerpt":"In this paper, we establish some new inequalities of the Hermite-Hadamard like for class of (h-s)_{1,2}-convex functions which are ordinary, super-multiplicative or similarly ordered and nonnegative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3698","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":"2026-05-18T03:59:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdR9LDe1MVruID4RCh02e+B12CcJhd+z/qY4GvFByWLckMMWHRN1Lik4klsxJ+Kz12ZoSSKLtE8YrP98uJeqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:00:56.738489Z"},"content_sha256":"1f57a89bdd1c104be4afa6de9448f8b71d45fa3e86c74da44e32505356670d70","schema_version":"1.0","event_id":"sha256:1f57a89bdd1c104be4afa6de9448f8b71d45fa3e86c74da44e32505356670d70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3RBPNJKUYAIJL6NZLDYMJAQXZ/bundle.json","state_url":"https://pith.science/pith/E3RBPNJKUYAIJL6NZLDYMJAQXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3RBPNJKUYAIJL6NZLDYMJAQXZ/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":"2026-06-22T16:00:56Z","links":{"resolver":"https://pith.science/pith/E3RBPNJKUYAIJL6NZLDYMJAQXZ","bundle":"https://pith.science/pith/E3RBPNJKUYAIJL6NZLDYMJAQXZ/bundle.json","state":"https://pith.science/pith/E3RBPNJKUYAIJL6NZLDYMJAQXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3RBPNJKUYAIJL6NZLDYMJAQXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E3RBPNJKUYAIJL6NZLDYMJAQXZ","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":"56d88c4631756276a0e2b6a256806ac5fcf5b7206e295cd6b61127d4223c64ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-03-16T13:23:08Z","title_canon_sha256":"aec145cb3d3eb01b9ef38a263ed280807a0c03fffd8209c1db46edeea7bf5a56"},"schema_version":"1.0","source":{"id":"1203.3698","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3698","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3698v1","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3698","created_at":"2026-05-18T03:59:50Z"},{"alias_kind":"pith_short_12","alias_value":"E3RBPNJKUYAI","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3RBPNJKUYAIJL6N","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3RBPNJK","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:1f57a89bdd1c104be4afa6de9448f8b71d45fa3e86c74da44e32505356670d70","target":"graph","created_at":"2026-05-18T03:59:50Z","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 some new inequalities of the Hermite-Hadamard like for class of (h-s)_{1,2}-convex functions which are ordinary, super-multiplicative or similarly ordered and nonnegative.","authors_text":"Ahmet Ocak Akdemir, M. Emin Ozdemir, Mevlut Tunc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-03-16T13:23:08Z","title":"Some New Inequalities for (h-s)_{1,2}-convex Functions via Further Properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3698","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":"sha256:7b2580d40cd135534a208ea58f5de175fa103b1b1c17075fe0a1592fc65b9f9d","target":"record","created_at":"2026-05-18T03:59:50Z","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":"56d88c4631756276a0e2b6a256806ac5fcf5b7206e295cd6b61127d4223c64ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-03-16T13:23:08Z","title_canon_sha256":"aec145cb3d3eb01b9ef38a263ed280807a0c03fffd8209c1db46edeea7bf5a56"},"schema_version":"1.0","source":{"id":"1203.3698","kind":"arxiv","version":1}},"canonical_sha256":"26e217b52aa60084afcdcac7862410be480ac681df8fdb8d28759d88eb13dede","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26e217b52aa60084afcdcac7862410be480ac681df8fdb8d28759d88eb13dede","first_computed_at":"2026-05-18T03:59:50.151262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:50.151262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"49O2QRL4ovTGWadONZIkMyRrnC8F3NSMhWhSFJR3iAoNpapXMzzhVFWkGFG7D6YqPUFZV2b7EmdX/TzOSg3HBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:50.151896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3698","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b2580d40cd135534a208ea58f5de175fa103b1b1c17075fe0a1592fc65b9f9d","sha256:1f57a89bdd1c104be4afa6de9448f8b71d45fa3e86c74da44e32505356670d70"],"state_sha256":"7bb2864f501ddbfbcef4ae3082c672dafec2b5f4b110ebdb917e21fb9e50ad88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9B7HKMPQAcEsL3AfZlWQU5N4RICn6uWGeZt6RD7KHv3hDK15d7DFGsulaeu140fRVCe6HkY4bnvgsJkRETyACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:00:56.740465Z","bundle_sha256":"daacc42c6ae41a17c0ae214c8f2b5f3af87082566ed626234c83f60789b8402b"}}