{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:34KTANW3OCSJ4JNAKOJCUAHWYS","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":"35ac13049781a2158330f4feaf7b0f6b72f0b3ddcb08c09e1766b827d61f4dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T07:51:42Z","title_canon_sha256":"46232688d37542dfb7d4d6e7f78d36f18e730e2ad10e06e57d62af7985142d67"},"schema_version":"1.0","source":{"id":"1601.06123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06123","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06123v1","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06123","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"34KTANW3OCSJ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"34KTANW3OCSJ4JNA","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"34KTANW3","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:37ab562deed48184e4846637204ad1ca9c9c8bdd396b01a1fe8e784f8ee9f6d1","target":"graph","created_at":"2026-05-18T01:22:09Z","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 give the refinement of an extension of Jensen's inequality to affine combinations. Furthermore, we present the functional form of Jensen's inequality for continuous 3-convex functions of one variable at a point.","authors_text":"Imran Abbas Baloch, Silvestru Sever Dragomir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T07:51:42Z","title":"Affine and Functional Form of Jensen's Inequalitiy for $3$-convex Functions at a Point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06123","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:b5b702e04c0f0eaac3bad818ab182fdaa0f378c43f56d23f1ae12e18de9ab333","target":"record","created_at":"2026-05-18T01:22:09Z","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":"35ac13049781a2158330f4feaf7b0f6b72f0b3ddcb08c09e1766b827d61f4dd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-15T07:51:42Z","title_canon_sha256":"46232688d37542dfb7d4d6e7f78d36f18e730e2ad10e06e57d62af7985142d67"},"schema_version":"1.0","source":{"id":"1601.06123","kind":"arxiv","version":1}},"canonical_sha256":"df153036db70a49e25a053922a00f6c4b2d19e2b096286a37487ce0639326699","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df153036db70a49e25a053922a00f6c4b2d19e2b096286a37487ce0639326699","first_computed_at":"2026-05-18T01:22:09.226213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:09.226213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCNrvAw1FEcrfg+Tf/O+rnIpKfm0gtOfeWRT+saJ75kclfsgjodBNbcXhVeNHYsnxkGmFjDDTcg8ZfEQbkmsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:09.226828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b702e04c0f0eaac3bad818ab182fdaa0f378c43f56d23f1ae12e18de9ab333","sha256:37ab562deed48184e4846637204ad1ca9c9c8bdd396b01a1fe8e784f8ee9f6d1"],"state_sha256":"cb3f2fc9e05925247363c9b3147911561dbfc459434924a84059f514031aae27"}