{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VBR32PH2YB26JDEE2IONURV7Q5","short_pith_number":"pith:VBR32PH2","canonical_record":{"source":{"id":"1711.11529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T17:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"c69635269b7ce78249275bcd6ee40afd3155a0eedbacd2b6b22036b99039659a","abstract_canon_sha256":"f8c00c376f2f7be78843f72c80b7169ccf9ad803bb6802aa39c1ed2d9bf5c670"},"schema_version":"1.0"},"canonical_sha256":"a863bd3cfac075e48c84d21cda46bf875feba35966587073024135e898be0e8f","source":{"kind":"arxiv","id":"1711.11529","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11529","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11529v1","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11529","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"VBR32PH2YB26","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VBR32PH2YB26JDEE","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VBR32PH2","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VBR32PH2YB26JDEE2IONURV7Q5","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T17:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"c69635269b7ce78249275bcd6ee40afd3155a0eedbacd2b6b22036b99039659a","abstract_canon_sha256":"f8c00c376f2f7be78843f72c80b7169ccf9ad803bb6802aa39c1ed2d9bf5c670"},"schema_version":"1.0"},"canonical_sha256":"a863bd3cfac075e48c84d21cda46bf875feba35966587073024135e898be0e8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:11.352615Z","signature_b64":"CBwX5N0yB9YRYjeN5+Yp/DfRzX5IeVc/pT0ivtzajWLDJl3sojzMnOKUoXC6kcFg1Vca0UchQd5biL4j/OqlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a863bd3cfac075e48c84d21cda46bf875feba35966587073024135e898be0e8f","last_reissued_at":"2026-05-18T00:29:11.352006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:11.352006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11529","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":"2026-05-18T00:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PPCjROyXA/Gou63Pcx333oCWd98Vpt0T12kDqB+Eg+rOc2msN/NU34HxAjQIFf1ll7TT+tWfisvxltciD90mBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:04:09.022688Z"},"content_sha256":"9586f6657f0f2d441080dfa5eb31cf375a9b714f4d9ffefffdaefd38f06fe833","schema_version":"1.0","event_id":"sha256:9586f6657f0f2d441080dfa5eb31cf375a9b714f4d9ffefffdaefd38f06fe833"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VBR32PH2YB26JDEE2IONURV7Q5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuity properties of weakly monotone Orlicz-Sobolev functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andrea Cianchi, Menita Carozza","submitted_at":"2017-11-30T17:38:07Z","abstract_excerpt":"The notion of weakly monotone functions extends the classical definition of monotone function, that can be traced back to H.Lebesgue. It was introduced, in the setting of Sobolev spaces, by J.Manfredi, and thoroughly investigated in the more general framework of Orlicz-Sobolev spaces by diverse authors, including T.Iwaniec, J.Kauhanen, P.Koskela, J.Maly, J.Onninen, X.Zhong. The present paper complements and augments the available theory of pointwise regularity properties of weakly monotone functions in Orlicz-Sobolev spaces. In particular, a variant is proposed in a customary condition ensurin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11529","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":"2026-05-18T00:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52/Pq8Ik02pYGS5EaJZa8VVv07w9rkxIZbtFvkWQXpbUL75oJ7Z2NArmkBXNjp1c3CXTxX72vrlVUcN+zN04Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:04:09.023053Z"},"content_sha256":"01d6fc026752b61a7b41022021f983bb7dad2ee0e21e20eafbf98c979d29c218","schema_version":"1.0","event_id":"sha256:01d6fc026752b61a7b41022021f983bb7dad2ee0e21e20eafbf98c979d29c218"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBR32PH2YB26JDEE2IONURV7Q5/bundle.json","state_url":"https://pith.science/pith/VBR32PH2YB26JDEE2IONURV7Q5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBR32PH2YB26JDEE2IONURV7Q5/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":"2026-06-25T20:04:09Z","links":{"resolver":"https://pith.science/pith/VBR32PH2YB26JDEE2IONURV7Q5","bundle":"https://pith.science/pith/VBR32PH2YB26JDEE2IONURV7Q5/bundle.json","state":"https://pith.science/pith/VBR32PH2YB26JDEE2IONURV7Q5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBR32PH2YB26JDEE2IONURV7Q5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VBR32PH2YB26JDEE2IONURV7Q5","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":"f8c00c376f2f7be78843f72c80b7169ccf9ad803bb6802aa39c1ed2d9bf5c670","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T17:38:07Z","title_canon_sha256":"c69635269b7ce78249275bcd6ee40afd3155a0eedbacd2b6b22036b99039659a"},"schema_version":"1.0","source":{"id":"1711.11529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11529","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11529v1","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11529","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"VBR32PH2YB26","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VBR32PH2YB26JDEE","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VBR32PH2","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:01d6fc026752b61a7b41022021f983bb7dad2ee0e21e20eafbf98c979d29c218","target":"graph","created_at":"2026-05-18T00:29:11Z","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":"The notion of weakly monotone functions extends the classical definition of monotone function, that can be traced back to H.Lebesgue. It was introduced, in the setting of Sobolev spaces, by J.Manfredi, and thoroughly investigated in the more general framework of Orlicz-Sobolev spaces by diverse authors, including T.Iwaniec, J.Kauhanen, P.Koskela, J.Maly, J.Onninen, X.Zhong. The present paper complements and augments the available theory of pointwise regularity properties of weakly monotone functions in Orlicz-Sobolev spaces. In particular, a variant is proposed in a customary condition ensurin","authors_text":"Andrea Cianchi, Menita Carozza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T17:38:07Z","title":"Continuity properties of weakly monotone Orlicz-Sobolev functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11529","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":"sha256:9586f6657f0f2d441080dfa5eb31cf375a9b714f4d9ffefffdaefd38f06fe833","target":"record","created_at":"2026-05-18T00:29:11Z","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":"f8c00c376f2f7be78843f72c80b7169ccf9ad803bb6802aa39c1ed2d9bf5c670","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T17:38:07Z","title_canon_sha256":"c69635269b7ce78249275bcd6ee40afd3155a0eedbacd2b6b22036b99039659a"},"schema_version":"1.0","source":{"id":"1711.11529","kind":"arxiv","version":1}},"canonical_sha256":"a863bd3cfac075e48c84d21cda46bf875feba35966587073024135e898be0e8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a863bd3cfac075e48c84d21cda46bf875feba35966587073024135e898be0e8f","first_computed_at":"2026-05-18T00:29:11.352006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:11.352006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CBwX5N0yB9YRYjeN5+Yp/DfRzX5IeVc/pT0ivtzajWLDJl3sojzMnOKUoXC6kcFg1Vca0UchQd5biL4j/OqlDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:11.352615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9586f6657f0f2d441080dfa5eb31cf375a9b714f4d9ffefffdaefd38f06fe833","sha256:01d6fc026752b61a7b41022021f983bb7dad2ee0e21e20eafbf98c979d29c218"],"state_sha256":"eda00678492ec8e1ee116d3f53cd44c5e636b6bdb0d02ad1b8c051db7481419b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63WxlRBJLwqZg1jY/CuecAa/I//S+YEUwRryInsmuQI85twK/pzOhdw/jz6sg28Q29dIk3SJI8jS13AUPVxSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:04:09.025026Z","bundle_sha256":"2ce6d530689a623adf3c75b91f636f5b182e72b9de09ff39872c9dd5f6fc0980"}}