{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GWXFBNKE3IHADQMDX7QZSDTFQB","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":"08fbf4c2faef51873972ff763f8273c82bebd8dfb1dea9f5e97b88ff9f854e11","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-27T15:45:52Z","title_canon_sha256":"ebc43f445633ea34f980fcab64b0e47ad33819263686b01dd0ffc06c9d4bf78d"},"schema_version":"1.0","source":{"id":"1207.6577","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6577","created_at":"2026-05-18T03:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6577v2","created_at":"2026-05-18T03:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6577","created_at":"2026-05-18T03:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"GWXFBNKE3IHA","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GWXFBNKE3IHADQMD","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GWXFBNKE","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:0bc6c1f41ed31460f4df048681e65888177347b217f31dcb78e7ae913f3c61d7","target":"graph","created_at":"2026-05-18T03:42:33Z","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 obtain some companions of Ostrowski type inequality for absolutely continuous functions whose second derivatives absolute value are convex and concave.Finally, we gave some applications for special means.","authors_text":"M. Emin \\\"Ozdemir, Merve Avci Ardic","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-27T15:45:52Z","title":"Some Companions of Ostrowski type inequality for functions whose second derivatives are convex and concave with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6577","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":"sha256:4a28cff9cc0a77b37fd4af1257fd36294ceb24a337f26053a4cbc6f1f322477c","target":"record","created_at":"2026-05-18T03:42:33Z","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":"08fbf4c2faef51873972ff763f8273c82bebd8dfb1dea9f5e97b88ff9f854e11","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-27T15:45:52Z","title_canon_sha256":"ebc43f445633ea34f980fcab64b0e47ad33819263686b01dd0ffc06c9d4bf78d"},"schema_version":"1.0","source":{"id":"1207.6577","kind":"arxiv","version":2}},"canonical_sha256":"35ae50b544da0e01c183bfe1990e65804577334fdea733d3edf78fb2b38058a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35ae50b544da0e01c183bfe1990e65804577334fdea733d3edf78fb2b38058a6","first_computed_at":"2026-05-18T03:42:33.714955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:33.714955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uj3fc59qeW1Gf51uYmrTAcu6xwiWsmd8gRInY/osuuQx5lmFEaI4fTS2Qp+sknmxwbIwclzX1InLvCQKbR+oCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:33.715579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6577","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a28cff9cc0a77b37fd4af1257fd36294ceb24a337f26053a4cbc6f1f322477c","sha256:0bc6c1f41ed31460f4df048681e65888177347b217f31dcb78e7ae913f3c61d7"],"state_sha256":"2b85eedf4f5c33c7b953905e92b705f0529793a1a9d9bed4a430e4c86bb75d56"}