{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CMWKA73KT7AFIZEF4EN4T3AJJI","short_pith_number":"pith:CMWKA73K","canonical_record":{"source":{"id":"1810.13362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-31T16:00:27Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"368282efd171edcab53c04e19225457fd433bce85e0a6e5a49f225cfc4bac3ec","abstract_canon_sha256":"3fbca67286517e4285b9a52f6bef853eb3418a0bc0528fa9e1ccd5707597b4d5"},"schema_version":"1.0"},"canonical_sha256":"132ca07f6a9fc0546485e11bc9ec094a3117a926b6ba6f98c3adeaf82c08f895","source":{"kind":"arxiv","id":"1810.13362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.13362","created_at":"2026-05-18T00:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.13362v2","created_at":"2026-05-18T00:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.13362","created_at":"2026-05-18T00:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"CMWKA73KT7AF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CMWKA73KT7AFIZEF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CMWKA73K","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CMWKA73KT7AFIZEF4EN4T3AJJI","target":"record","payload":{"canonical_record":{"source":{"id":"1810.13362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-31T16:00:27Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"368282efd171edcab53c04e19225457fd433bce85e0a6e5a49f225cfc4bac3ec","abstract_canon_sha256":"3fbca67286517e4285b9a52f6bef853eb3418a0bc0528fa9e1ccd5707597b4d5"},"schema_version":"1.0"},"canonical_sha256":"132ca07f6a9fc0546485e11bc9ec094a3117a926b6ba6f98c3adeaf82c08f895","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:14.487583Z","signature_b64":"X9q/nK3+rtr4F08Dk5F0wCKulntSNPqlLw3s9VcFrDlsYefC72yVdsDkbjm+mhjsSvzujg/FVDpOukF2Mh0HBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"132ca07f6a9fc0546485e11bc9ec094a3117a926b6ba6f98c3adeaf82c08f895","last_reissued_at":"2026-05-18T00:01:14.486995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:14.486995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.13362","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ji5os+QXA4OLSFFDXB3RrMT8pgHIV+xtbUQ3i6drGY0nRR0n1J6hjjAP6MWC6sfDPC1rAUIDQ3WUNBvK3DhDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T08:29:25.964910Z"},"content_sha256":"23ab7a6d3875cdb6682672c8b3c42ce61863d6bee2144de542831d902e4c2868","schema_version":"1.0","event_id":"sha256:23ab7a6d3875cdb6682672c8b3c42ce61863d6bee2144de542831d902e4c2868"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CMWKA73KT7AFIZEF4EN4T3AJJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The UMD property for Musielak--Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Ivan Yaroslavtsev, Mark Veraar, Nick Lindemulder","submitted_at":"2018-10-31T16:00:27Z","abstract_excerpt":"In this paper we show that Musielak--Orlicz spaces are UMD spaces under the so-called $\\Delta_2$ condition on the generalized Young function and its complemented function. We also prove that if the measure space is divisible, then a Musielak--Orlicz space has the UMD property if and only if it is reflexive. As a consequence we show that reflexive variable Lebesgue spaces $L^{p(\\cdot)}$ are UMD spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13362","kind":"arxiv","version":2},"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":"2026-05-18T00:01:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NdRwQou5Vgh/kUqk2+08vRlkvI2P4pjGd0cZEnoejEiyCovWe+gQYdOSVIs6CE5hB3n39FciwexYiMPmf3R6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T08:29:25.965638Z"},"content_sha256":"3305ae6fcf95bd4d4a06c3c4a92842a475cfecb8397a6352858c4363d4763a47","schema_version":"1.0","event_id":"sha256:3305ae6fcf95bd4d4a06c3c4a92842a475cfecb8397a6352858c4363d4763a47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CMWKA73KT7AFIZEF4EN4T3AJJI/bundle.json","state_url":"https://pith.science/pith/CMWKA73KT7AFIZEF4EN4T3AJJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CMWKA73KT7AFIZEF4EN4T3AJJI/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":"2026-05-19T08:29:25Z","links":{"resolver":"https://pith.science/pith/CMWKA73KT7AFIZEF4EN4T3AJJI","bundle":"https://pith.science/pith/CMWKA73KT7AFIZEF4EN4T3AJJI/bundle.json","state":"https://pith.science/pith/CMWKA73KT7AFIZEF4EN4T3AJJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CMWKA73KT7AFIZEF4EN4T3AJJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CMWKA73KT7AFIZEF4EN4T3AJJI","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":"3fbca67286517e4285b9a52f6bef853eb3418a0bc0528fa9e1ccd5707597b4d5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-31T16:00:27Z","title_canon_sha256":"368282efd171edcab53c04e19225457fd433bce85e0a6e5a49f225cfc4bac3ec"},"schema_version":"1.0","source":{"id":"1810.13362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.13362","created_at":"2026-05-18T00:01:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.13362v2","created_at":"2026-05-18T00:01:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.13362","created_at":"2026-05-18T00:01:14Z"},{"alias_kind":"pith_short_12","alias_value":"CMWKA73KT7AF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CMWKA73KT7AFIZEF","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CMWKA73K","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:3305ae6fcf95bd4d4a06c3c4a92842a475cfecb8397a6352858c4363d4763a47","target":"graph","created_at":"2026-05-18T00:01:14Z","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 show that Musielak--Orlicz spaces are UMD spaces under the so-called $\\Delta_2$ condition on the generalized Young function and its complemented function. We also prove that if the measure space is divisible, then a Musielak--Orlicz space has the UMD property if and only if it is reflexive. As a consequence we show that reflexive variable Lebesgue spaces $L^{p(\\cdot)}$ are UMD spaces.","authors_text":"Ivan Yaroslavtsev, Mark Veraar, Nick Lindemulder","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-31T16:00:27Z","title":"The UMD property for Musielak--Orlicz spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13362","kind":"arxiv","version":2},"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":"sha256:23ab7a6d3875cdb6682672c8b3c42ce61863d6bee2144de542831d902e4c2868","target":"record","created_at":"2026-05-18T00:01:14Z","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":"3fbca67286517e4285b9a52f6bef853eb3418a0bc0528fa9e1ccd5707597b4d5","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-31T16:00:27Z","title_canon_sha256":"368282efd171edcab53c04e19225457fd433bce85e0a6e5a49f225cfc4bac3ec"},"schema_version":"1.0","source":{"id":"1810.13362","kind":"arxiv","version":2}},"canonical_sha256":"132ca07f6a9fc0546485e11bc9ec094a3117a926b6ba6f98c3adeaf82c08f895","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"132ca07f6a9fc0546485e11bc9ec094a3117a926b6ba6f98c3adeaf82c08f895","first_computed_at":"2026-05-18T00:01:14.486995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:14.486995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X9q/nK3+rtr4F08Dk5F0wCKulntSNPqlLw3s9VcFrDlsYefC72yVdsDkbjm+mhjsSvzujg/FVDpOukF2Mh0HBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:14.487583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.13362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23ab7a6d3875cdb6682672c8b3c42ce61863d6bee2144de542831d902e4c2868","sha256:3305ae6fcf95bd4d4a06c3c4a92842a475cfecb8397a6352858c4363d4763a47"],"state_sha256":"becb3a76b0cbbcbd9ba4093f7654a5f7e07011ecdca1cccf584435c157efeea8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dI0nQWeTjYCbVtfFh2AcuUV121WrN7vQO3AztllCvt05unp4l66UjiKX5nQpND6e1RC+QNb0R69Ea+CSeIyLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T08:29:25.968965Z","bundle_sha256":"747fd1c47fd57410f719346982ee0e0252f1eed5834159a937d3984ea4fa6067"}}