{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HGOHR63LZEX3PKEPQH63YYDZ57","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":"1ccde53db08e665404b6ff9f08dd1c227cbe721f2693204a8600311e7f907004","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-30T14:59:27Z","title_canon_sha256":"3af86079d9c065f47a008fa2c01c05f7157137e50de3e78d651bbd5c2c463ee8"},"schema_version":"1.0","source":{"id":"1503.08695","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08695","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08695v3","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08695","created_at":"2026-05-18T01:27:24Z"},{"alias_kind":"pith_short_12","alias_value":"HGOHR63LZEX3","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HGOHR63LZEX3PKEP","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HGOHR63L","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:f6b4fd7027e5aede3ab39f016377357a9d9f8f980a963a5a613b2b6f33be96a2","target":"graph","created_at":"2026-05-18T01:27:24Z","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":"To provide a solid analytic foundation for the module approach to conditional risk measures, our purpose is to establish a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of topologies (namely the $(\\varepsilon,\\lambda)$--topology and the locally $L^0$-- convex topology). This paper is focused on the part of separation and Fenchel-Moreau duality in random locally convex modules. The key point of this paper is to give the precise relation between random conjugate spaces of a random locally convex module under the two kinds of topolo","authors_text":"Shien Zhao, Tiexin Guo, Xiaolin Zeng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-30T14:59:27Z","title":"Random convex analysis (I): separation and Fenchel-Moreau duality in random locally convex modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08695","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:bca6d94292882124d322fda47d5eccdac086a53ad649a1fa16a4dec0629fcd78","target":"record","created_at":"2026-05-18T01:27:24Z","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":"1ccde53db08e665404b6ff9f08dd1c227cbe721f2693204a8600311e7f907004","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-30T14:59:27Z","title_canon_sha256":"3af86079d9c065f47a008fa2c01c05f7157137e50de3e78d651bbd5c2c463ee8"},"schema_version":"1.0","source":{"id":"1503.08695","kind":"arxiv","version":3}},"canonical_sha256":"399c78fb6bc92fb7a88f81fdbc6079effebc228b0250577f3c03826bc21bac23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"399c78fb6bc92fb7a88f81fdbc6079effebc228b0250577f3c03826bc21bac23","first_computed_at":"2026-05-18T01:27:24.010357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:24.010357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ARKBnaY24pZFMRhFYJZNc7E88PgwUD+B3F336nWCPKaOszVEcf76G/GSWBRQ4mKhVstoO+/x6+YrHTIhGzO9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:24.010786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08695","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bca6d94292882124d322fda47d5eccdac086a53ad649a1fa16a4dec0629fcd78","sha256:f6b4fd7027e5aede3ab39f016377357a9d9f8f980a963a5a613b2b6f33be96a2"],"state_sha256":"c5ab35dac19fc0eed98f41850f3a88711c763b6db6e2ad7679e55eaf5310f35b"}