{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SA4JQAB44I63WJSOWSGSE4TQMI","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":"1dc38024ef0e6fdbc7a4efae03f38e84d7be6c0cd819266baa927c1541395110","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-06-02T22:41:59Z","title_canon_sha256":"2ce01e5f48411c829654127ba5ec7e8331e1992c93701c2a673b4b298f31f238"},"schema_version":"1.0","source":{"id":"1306.0259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0259","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0259v1","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0259","created_at":"2026-05-18T03:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"SA4JQAB44I63","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SA4JQAB44I63WJSO","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SA4JQAB4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:a094c21a6a1b09da1de7102048e27304c0d74b98253d660dbda560ba9b0ede39","target":"graph","created_at":"2026-05-18T03:21:55Z","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 study, we define g-convex dominated functions on the co-ordinates and prove some Hadamard-type, Fejer-type inequalities for this new class of functions. We also give some results related to the functional H.","authors_text":"Alper Ekinci, A. Ocak Akdemir, M. Emin \\\"Ozdemir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-06-02T22:41:59Z","title":"On The Coordinated g-convex Dominated Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0259","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":"sha256:5705df4ad29c10a9685744081c4eec14bee6dab00e96b7795c57e59760dc20be","target":"record","created_at":"2026-05-18T03:21:55Z","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":"1dc38024ef0e6fdbc7a4efae03f38e84d7be6c0cd819266baa927c1541395110","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-06-02T22:41:59Z","title_canon_sha256":"2ce01e5f48411c829654127ba5ec7e8331e1992c93701c2a673b4b298f31f238"},"schema_version":"1.0","source":{"id":"1306.0259","kind":"arxiv","version":1}},"canonical_sha256":"903898003ce23dbb264eb48d227270620f08e02114a3fe73130a225ff6332300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"903898003ce23dbb264eb48d227270620f08e02114a3fe73130a225ff6332300","first_computed_at":"2026-05-18T03:21:55.660049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:55.660049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cLuEWM8nEdQamMnf09cAj4ownsRGCRlr6Aa1Ffg8gCFj4G8wDwt4jprdz+SzMEHBw+w4Jp6qBOg3vefigfm9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:55.660526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5705df4ad29c10a9685744081c4eec14bee6dab00e96b7795c57e59760dc20be","sha256:a094c21a6a1b09da1de7102048e27304c0d74b98253d660dbda560ba9b0ede39"],"state_sha256":"dd249214847c8f2599125ffd12579721666a50d7c352d4ef4bec5125ae0ff281"}