{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6I7XT5GMVKSHLFF4M6E6PVNIYE","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":"a644c1e16b9a47b9ea440ad178ed303b61a363839dbe3903e270355f4103288d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-11-09T09:20:34Z","title_canon_sha256":"8bfbafbfc58c69719e268b5f387014217524206bb0d360cb97d3f6db2f5643e5"},"schema_version":"1.0","source":{"id":"1811.03827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03827","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03827v1","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03827","created_at":"2026-05-18T00:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"6I7XT5GMVKSH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6I7XT5GMVKSHLFF4","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6I7XT5GM","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:25d6e04c1ec962f85e074aac4476a30a415b150228d325d174ad5b412908bd7d","target":"graph","created_at":"2026-05-18T00:01:11Z","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":"We give necessary and sufficient conditions for Borel measures to satisfy the inequality introduced by Komisarski, Rajba (2018). This inequality is a generalization of the convex order inequality for binomial distributions, which was proved by Mrowiec, Rajba, W\\k{a}sowicz (2017), as a probabilistic version of the inequality for convex functions, that was conjectured as an old open problem by I.~Ra\\c{s}a. We present also further generalizations using convex order inequalities between convolution polynomials of finite Borel measures. We generalize recent results obtained by B.~Gavrea (2018) in t","authors_text":"Andrzej Komisarski, Teresa Rajba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-11-09T09:20:34Z","title":"Convex order for convolution polynomials of Borel measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03827","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:d960ddf7bfe74a1236ecec9b04374b2ad9c6f76b77343f8ebc74cf232062b5a9","target":"record","created_at":"2026-05-18T00:01:11Z","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":"a644c1e16b9a47b9ea440ad178ed303b61a363839dbe3903e270355f4103288d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-11-09T09:20:34Z","title_canon_sha256":"8bfbafbfc58c69719e268b5f387014217524206bb0d360cb97d3f6db2f5643e5"},"schema_version":"1.0","source":{"id":"1811.03827","kind":"arxiv","version":1}},"canonical_sha256":"f23f79f4ccaaa47594bc6789e7d5a8c11fab639cc9b9fa502ad1c8945ff57794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f23f79f4ccaaa47594bc6789e7d5a8c11fab639cc9b9fa502ad1c8945ff57794","first_computed_at":"2026-05-18T00:01:11.879719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:11.879719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l1H537k2vsuRFwPBWBUPIFvzJEy7Y1q0odTD618tvwv2+CxwWJfnCDobuLPEpBWSDfngoa+P+DyrIdNcVhviCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:11.880408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d960ddf7bfe74a1236ecec9b04374b2ad9c6f76b77343f8ebc74cf232062b5a9","sha256:25d6e04c1ec962f85e074aac4476a30a415b150228d325d174ad5b412908bd7d"],"state_sha256":"13f66e8e11cac74180f9da80504c0262835727a8baa7680332d7d32baa4ccad5"}