{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TIJ46TBIKKWE23AEW2T6R2BZN5","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":"6cf1831f857836b55aaa95d6ff8e3e912718c89d8266e3c3252dd742adefac8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-28T15:17:54Z","title_canon_sha256":"3069c30fd31b53d1a1afa6f404b42e2132191d4353c5c7f78fad7f4e56a03e0a"},"schema_version":"1.0","source":{"id":"1611.09174","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09174","created_at":"2026-05-18T00:56:28Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09174v1","created_at":"2026-05-18T00:56:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09174","created_at":"2026-05-18T00:56:28Z"},{"alias_kind":"pith_short_12","alias_value":"TIJ46TBIKKWE","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIJ46TBIKKWE23AE","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIJ46TBI","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:3114b1d7c5ba2600311506d87a142cd62ddc4d1aec9b2c17dd3fb6191107a591","target":"graph","created_at":"2026-05-18T00:56:28Z","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":"Recently Nikodem, Rajba and W\\k{a}sowicz compared the classes of n-Wright-convex functions and n-Jensen-convex functions by showing that the first one is a proper subclass of the latter one, whenever n is an odd natural number. Till now the case of even n was an open problem. In this paper the complete solution is given: it is shown that the inclusion is proper for any natural n. The classes of strongly n-Wright-convex and strongly n-Jensen-convex functions are also compared (with the same assertion).","authors_text":"Jacek Mrowiec, Szymon W\\k{a}sowicz, Teresa Rajba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-28T15:17:54Z","title":"On the classes of higher-order Jensen-convex functions and Wright-convex functions, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09174","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:c5f9f60e21135d99ccb9c80f6fb5f33451b09a8294f5f17714fbce3bcff45a6c","target":"record","created_at":"2026-05-18T00:56:28Z","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":"6cf1831f857836b55aaa95d6ff8e3e912718c89d8266e3c3252dd742adefac8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-11-28T15:17:54Z","title_canon_sha256":"3069c30fd31b53d1a1afa6f404b42e2132191d4353c5c7f78fad7f4e56a03e0a"},"schema_version":"1.0","source":{"id":"1611.09174","kind":"arxiv","version":1}},"canonical_sha256":"9a13cf4c2852ac4d6c04b6a7e8e8396f5dc0598c716b8c7e2ae27fa72d97f1d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a13cf4c2852ac4d6c04b6a7e8e8396f5dc0598c716b8c7e2ae27fa72d97f1d9","first_computed_at":"2026-05-18T00:56:28.917654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:28.917654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/tD6VoaTWx8EyTk/SUxeoSCNF5WS3a/JnuLIj/+3TePpQpx7HoKJPNwAuT6qs/H1f4RRDHPw5b69GxQ3xMcKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:28.918344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09174","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5f9f60e21135d99ccb9c80f6fb5f33451b09a8294f5f17714fbce3bcff45a6c","sha256:3114b1d7c5ba2600311506d87a142cd62ddc4d1aec9b2c17dd3fb6191107a591"],"state_sha256":"59e98def87f5a44092ae8e993503d75d2fd47c4e4277fb13e4f0e0d80e6614d0"}