{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JIAXJCAOIZVWJ3Q6PGH7MKPJCQ","short_pith_number":"pith:JIAXJCAO","canonical_record":{"source":{"id":"1511.00940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-03T15:14:00Z","cross_cats_sorted":[],"title_canon_sha256":"7f220b9e6a82e5dd3ce366a4283927167695c147ff9ff6429b3b0118631fd78f","abstract_canon_sha256":"064e4945cff366070abd35337c022c415019f51b0a0481f0650d49a378e693e7"},"schema_version":"1.0"},"canonical_sha256":"4a0174880e466b64ee1e798ff629e9142b3160895075943708469be8c010abd7","source":{"kind":"arxiv","id":"1511.00940","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00940","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00940v3","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00940","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"pith_short_12","alias_value":"JIAXJCAOIZVW","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JIAXJCAOIZVWJ3Q6","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JIAXJCAO","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JIAXJCAOIZVWJ3Q6PGH7MKPJCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00940","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-03T15:14:00Z","cross_cats_sorted":[],"title_canon_sha256":"7f220b9e6a82e5dd3ce366a4283927167695c147ff9ff6429b3b0118631fd78f","abstract_canon_sha256":"064e4945cff366070abd35337c022c415019f51b0a0481f0650d49a378e693e7"},"schema_version":"1.0"},"canonical_sha256":"4a0174880e466b64ee1e798ff629e9142b3160895075943708469be8c010abd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:03.554402Z","signature_b64":"OpXU1BamFi/m0U+uaqgemyxlrfupsIwCVFYuSVkm9zhcm4pYCCJTl5OIui3vhO7Zm2EPfqvBxPvqEWksFe96AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a0174880e466b64ee1e798ff629e9142b3160895075943708469be8c010abd7","last_reissued_at":"2026-05-17T23:57:03.553810Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:03.553810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00940","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXhCUkA5RtMVy3SI4mvl5sJXij2ZI2ZlOh3qwK95GcG/RJ5UAXf2IZVnyqf3l3z2J35zTLklbZoAngc5ZkMvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:52:01.948402Z"},"content_sha256":"29bdbdc580171588fdb32918696d5c95bd74e05a14814062ec05e42eab94da10","schema_version":"1.0","event_id":"sha256:29bdbdc580171588fdb32918696d5c95bd74e05a14814062ec05e42eab94da10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JIAXJCAOIZVWJ3Q6PGH7MKPJCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some results on the Orlicz space generated from a random normed module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Long Long, Mingzhi Wu, Xiaolin Zeng","submitted_at":"2015-11-03T15:14:00Z","abstract_excerpt":"Noting the important role the abstract $L^p$ space has played in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a random normed module. First, we give a basic dual space representation theorem which identify the dual of the Orlicz heart of a random normed module with the Orlicz space generated from the random conjugate space. Then, we establish the respective equivalence relations of the strict convexity and uniform convexity of this abstract Orlicz space to the random strict convexity and random uniform convexity of the underlyin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00940","kind":"arxiv","version":3},"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":"2026-05-17T23:57:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8p+LkzREfDFXuKOZMOBA+2JjTRzOs1Kd5zmYbGMJpkh1IB1O4VNV0KRE9R3IMKjj+4U4EzB8E4W3c/awymPYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:52:01.948756Z"},"content_sha256":"31792e3f14c3f4a916f95f4b10d0828e487576d6cce190ec4224194a06aaa79c","schema_version":"1.0","event_id":"sha256:31792e3f14c3f4a916f95f4b10d0828e487576d6cce190ec4224194a06aaa79c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIAXJCAOIZVWJ3Q6PGH7MKPJCQ/bundle.json","state_url":"https://pith.science/pith/JIAXJCAOIZVWJ3Q6PGH7MKPJCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIAXJCAOIZVWJ3Q6PGH7MKPJCQ/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":"2026-06-23T23:52:01Z","links":{"resolver":"https://pith.science/pith/JIAXJCAOIZVWJ3Q6PGH7MKPJCQ","bundle":"https://pith.science/pith/JIAXJCAOIZVWJ3Q6PGH7MKPJCQ/bundle.json","state":"https://pith.science/pith/JIAXJCAOIZVWJ3Q6PGH7MKPJCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIAXJCAOIZVWJ3Q6PGH7MKPJCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JIAXJCAOIZVWJ3Q6PGH7MKPJCQ","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":"064e4945cff366070abd35337c022c415019f51b0a0481f0650d49a378e693e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-03T15:14:00Z","title_canon_sha256":"7f220b9e6a82e5dd3ce366a4283927167695c147ff9ff6429b3b0118631fd78f"},"schema_version":"1.0","source":{"id":"1511.00940","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00940","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00940v3","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00940","created_at":"2026-05-17T23:57:03Z"},{"alias_kind":"pith_short_12","alias_value":"JIAXJCAOIZVW","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JIAXJCAOIZVWJ3Q6","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JIAXJCAO","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:31792e3f14c3f4a916f95f4b10d0828e487576d6cce190ec4224194a06aaa79c","target":"graph","created_at":"2026-05-17T23:57:03Z","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":"Noting the important role the abstract $L^p$ space has played in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a random normed module. First, we give a basic dual space representation theorem which identify the dual of the Orlicz heart of a random normed module with the Orlicz space generated from the random conjugate space. Then, we establish the respective equivalence relations of the strict convexity and uniform convexity of this abstract Orlicz space to the random strict convexity and random uniform convexity of the underlyin","authors_text":"Long Long, Mingzhi Wu, Xiaolin Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-03T15:14:00Z","title":"Some results on the Orlicz space generated from a random normed module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00940","kind":"arxiv","version":3},"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":"sha256:29bdbdc580171588fdb32918696d5c95bd74e05a14814062ec05e42eab94da10","target":"record","created_at":"2026-05-17T23:57:03Z","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":"064e4945cff366070abd35337c022c415019f51b0a0481f0650d49a378e693e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-03T15:14:00Z","title_canon_sha256":"7f220b9e6a82e5dd3ce366a4283927167695c147ff9ff6429b3b0118631fd78f"},"schema_version":"1.0","source":{"id":"1511.00940","kind":"arxiv","version":3}},"canonical_sha256":"4a0174880e466b64ee1e798ff629e9142b3160895075943708469be8c010abd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a0174880e466b64ee1e798ff629e9142b3160895075943708469be8c010abd7","first_computed_at":"2026-05-17T23:57:03.553810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:03.553810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OpXU1BamFi/m0U+uaqgemyxlrfupsIwCVFYuSVkm9zhcm4pYCCJTl5OIui3vhO7Zm2EPfqvBxPvqEWksFe96AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:03.554402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00940","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29bdbdc580171588fdb32918696d5c95bd74e05a14814062ec05e42eab94da10","sha256:31792e3f14c3f4a916f95f4b10d0828e487576d6cce190ec4224194a06aaa79c"],"state_sha256":"199774e8b43abaacfae4cf3372ac5663e4bf11d03663c4568dcf9628ac3355e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IG1Gceb0aW43jSa0SaWX222QoVfC7VWHh1xYdcRqKli+YtfUZPwl49cqGk4tGZAUOvP73mhYoqtcaDt3leWkAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T23:52:01.950736Z","bundle_sha256":"6a1a3fc87ff8a07d216b2bcb95fef3b06b76011b2e8a9db6b1e93512deb57f16"}}