{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UBJRN6ZKKOGDU5YL6LZ2FC5EAI","short_pith_number":"pith:UBJRN6ZK","canonical_record":{"source":{"id":"1512.07272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-22T21:45:15Z","cross_cats_sorted":[],"title_canon_sha256":"12fc9290828abe9f798be7d753ff6fd90b5220cb9a5d140a832285fd69cd62a3","abstract_canon_sha256":"7be824554f0f11dc0d45cbadb2d422967df9995ea2cbaf00327a4da41dbf15ad"},"schema_version":"1.0"},"canonical_sha256":"a05316fb2a538c3a770bf2f3a28ba4021a5babfb79488051697fdec441d187dd","source":{"kind":"arxiv","id":"1512.07272","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07272","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07272v1","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07272","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"pith_short_12","alias_value":"UBJRN6ZKKOGD","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UBJRN6ZKKOGDU5YL","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UBJRN6ZK","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UBJRN6ZKKOGDU5YL6LZ2FC5EAI","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-22T21:45:15Z","cross_cats_sorted":[],"title_canon_sha256":"12fc9290828abe9f798be7d753ff6fd90b5220cb9a5d140a832285fd69cd62a3","abstract_canon_sha256":"7be824554f0f11dc0d45cbadb2d422967df9995ea2cbaf00327a4da41dbf15ad"},"schema_version":"1.0"},"canonical_sha256":"a05316fb2a538c3a770bf2f3a28ba4021a5babfb79488051697fdec441d187dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:50.206802Z","signature_b64":"+oIj1Z8hexoEO9bNZC+mOSEVJIT64BAnXWll24Hgo1jaHyNFa5FRdUaekYiRRoxB7mvL3XvE+mx3n0lVgMVzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a05316fb2a538c3a770bf2f3a28ba4021a5babfb79488051697fdec441d187dd","last_reissued_at":"2026-05-18T01:23:50.206295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:50.206295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07272","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q58G0QuNIP4O1cve5ZGBJVNybJF64FDJbeqNccm7HS8GNb5wqQ9VMgZwkO8PqzV0hBap0HJBgObyh5bIoAlyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:08:44.873642Z"},"content_sha256":"83371005cba361ed78f0a21ffd151bb8d7fc2fbc36d48e9b07b70c4c9e46083a","schema_version":"1.0","event_id":"sha256:83371005cba361ed78f0a21ffd151bb8d7fc2fbc36d48e9b07b70c4c9e46083a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UBJRN6ZKKOGDU5YL6LZ2FC5EAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convexity with respect to families of means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Gyula Maksa, Zsolt P\\'ales","submitted_at":"2015-12-22T21:45:15Z","abstract_excerpt":"In this paper we investigate continuity properties of functions $f:\\mathbb{R}_+\\to\\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\\big(H_p(x,y)\\big)\\leq H_q(f(x),f(y)) \\qquad(x,y>0), $$ where $H_p$ stands for the $p$th power (or H\\\"older) mean. One of the main results shows that there exist discontinuous multiplicative functions that are $(p,p)$-Jensen convex for all positive rational number $p$. A counterpart of this result states that if $f$ is $(p,p)$-Jensen convex for all $p\\in P\\subseteq\\mathbb{R}_+$, where $P$ is a set of positive Lebesgue measure, then $f$ must be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07272","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ypwsz83L/Ot4ZP+nkMQ4UsECpRWN5qvoEOJpPI39RGvFHIBjPdwUtNXw+hVc1jpAuzqNr/h9CjokFrZUymCMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:08:44.874280Z"},"content_sha256":"51094a136c554ee82011763bc2c0962c6130250858716047b121967bd3e7f067","schema_version":"1.0","event_id":"sha256:51094a136c554ee82011763bc2c0962c6130250858716047b121967bd3e7f067"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UBJRN6ZKKOGDU5YL6LZ2FC5EAI/bundle.json","state_url":"https://pith.science/pith/UBJRN6ZKKOGDU5YL6LZ2FC5EAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UBJRN6ZKKOGDU5YL6LZ2FC5EAI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T08:08:44Z","links":{"resolver":"https://pith.science/pith/UBJRN6ZKKOGDU5YL6LZ2FC5EAI","bundle":"https://pith.science/pith/UBJRN6ZKKOGDU5YL6LZ2FC5EAI/bundle.json","state":"https://pith.science/pith/UBJRN6ZKKOGDU5YL6LZ2FC5EAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UBJRN6ZKKOGDU5YL6LZ2FC5EAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UBJRN6ZKKOGDU5YL6LZ2FC5EAI","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":"7be824554f0f11dc0d45cbadb2d422967df9995ea2cbaf00327a4da41dbf15ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-22T21:45:15Z","title_canon_sha256":"12fc9290828abe9f798be7d753ff6fd90b5220cb9a5d140a832285fd69cd62a3"},"schema_version":"1.0","source":{"id":"1512.07272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07272","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07272v1","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07272","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"pith_short_12","alias_value":"UBJRN6ZKKOGD","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UBJRN6ZKKOGDU5YL","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UBJRN6ZK","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:51094a136c554ee82011763bc2c0962c6130250858716047b121967bd3e7f067","target":"graph","created_at":"2026-05-18T01:23:50Z","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 investigate continuity properties of functions $f:\\mathbb{R}_+\\to\\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\\big(H_p(x,y)\\big)\\leq H_q(f(x),f(y)) \\qquad(x,y>0), $$ where $H_p$ stands for the $p$th power (or H\\\"older) mean. One of the main results shows that there exist discontinuous multiplicative functions that are $(p,p)$-Jensen convex for all positive rational number $p$. A counterpart of this result states that if $f$ is $(p,p)$-Jensen convex for all $p\\in P\\subseteq\\mathbb{R}_+$, where $P$ is a set of positive Lebesgue measure, then $f$ must be","authors_text":"Gyula Maksa, Zsolt P\\'ales","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-22T21:45:15Z","title":"Convexity with respect to families of means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07272","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":"sha256:83371005cba361ed78f0a21ffd151bb8d7fc2fbc36d48e9b07b70c4c9e46083a","target":"record","created_at":"2026-05-18T01:23:50Z","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":"7be824554f0f11dc0d45cbadb2d422967df9995ea2cbaf00327a4da41dbf15ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-12-22T21:45:15Z","title_canon_sha256":"12fc9290828abe9f798be7d753ff6fd90b5220cb9a5d140a832285fd69cd62a3"},"schema_version":"1.0","source":{"id":"1512.07272","kind":"arxiv","version":1}},"canonical_sha256":"a05316fb2a538c3a770bf2f3a28ba4021a5babfb79488051697fdec441d187dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a05316fb2a538c3a770bf2f3a28ba4021a5babfb79488051697fdec441d187dd","first_computed_at":"2026-05-18T01:23:50.206295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:50.206295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+oIj1Z8hexoEO9bNZC+mOSEVJIT64BAnXWll24Hgo1jaHyNFa5FRdUaekYiRRoxB7mvL3XvE+mx3n0lVgMVzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:50.206802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83371005cba361ed78f0a21ffd151bb8d7fc2fbc36d48e9b07b70c4c9e46083a","sha256:51094a136c554ee82011763bc2c0962c6130250858716047b121967bd3e7f067"],"state_sha256":"9539a8cd89b18cfee1c41ecf0f05685fc340bd5297195fb962aa0f3fd49d02f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaqA02ChWoV7y/giNFL4E0YNpz8WLqbtIOXRLqJXJVEhwlqUalWIspSNweOMGf76lS8wqVq9aUENoA9EU/sTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:08:44.878412Z","bundle_sha256":"d52c435225c19c44f18b559e2a6d1933ca68e5902e62138a9092a377abdad3a3"}}