{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Y525IQC5QQDYMUBOIFY5DLGROC","short_pith_number":"pith:Y525IQC5","canonical_record":{"source":{"id":"1608.08709","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-31T02:27:14Z","cross_cats_sorted":[],"title_canon_sha256":"781420763e04377e9e9b0efc4510015aec2cd4ccd9dfa8396d4b6e6d4433961d","abstract_canon_sha256":"d2185208b72e3c538f254e3b346c595c903979687c6462d6da1f5b5a22a1e72e"},"schema_version":"1.0"},"canonical_sha256":"c775d4405d840786502e4171d1acd170ace52e46db7600a8d2c497cee5d0b6cf","source":{"kind":"arxiv","id":"1608.08709","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08709","created_at":"2026-05-18T00:30:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08709v4","created_at":"2026-05-18T00:30:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08709","created_at":"2026-05-18T00:30:11Z"},{"alias_kind":"pith_short_12","alias_value":"Y525IQC5QQDY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Y525IQC5QQDYMUBO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Y525IQC5","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Y525IQC5QQDYMUBOIFY5DLGROC","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08709","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-31T02:27:14Z","cross_cats_sorted":[],"title_canon_sha256":"781420763e04377e9e9b0efc4510015aec2cd4ccd9dfa8396d4b6e6d4433961d","abstract_canon_sha256":"d2185208b72e3c538f254e3b346c595c903979687c6462d6da1f5b5a22a1e72e"},"schema_version":"1.0"},"canonical_sha256":"c775d4405d840786502e4171d1acd170ace52e46db7600a8d2c497cee5d0b6cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:11.712718Z","signature_b64":"PFN3GZ+7PDLB5ciE2vq62IvBkiMWhSF44zADGJs6fra30GYZTrpZ1hnro/F54OGddewzI/5MFsBw23FGxIxBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c775d4405d840786502e4171d1acd170ace52e46db7600a8d2c497cee5d0b6cf","last_reissued_at":"2026-05-18T00:30:11.711998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:11.711998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08709","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J84mev7KuUORPtB/Yj8Sveagy0jfK4wD1FwVAeoMcEoYOCpMc+LVmBaOJ07624jTX+wWMUh7ZrqU3QNJ6ybCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:01:30.653983Z"},"content_sha256":"54abd92c417cf5429dff11ca89f640d03f8dd3b0849ff4288a9fde740499aea6","schema_version":"1.0","event_id":"sha256:54abd92c417cf5429dff11ca89f640d03f8dd3b0849ff4288a9fde740499aea6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Y525IQC5QQDYMUBOIFY5DLGROC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector duality via conditional extension of dual pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Asgar Jamneshan, Michael Kupper, Samuel Drapeau","submitted_at":"2016-08-31T02:27:14Z","abstract_excerpt":"A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\\colon X\\to \\overline{L^0}$ is established where $(X,Y,\\langle \\cdot,\\cdot \\rangle)$ is a dual pair of Banach spaces and $\\overline{L^0}$ is the set of all extended real-valued measurable functions. We provide a concept of lower semi-continuity which is shown to be equivalent to the existence of a dual representation in terms of elements in the Bochner space $L^0(Y)$. To derive the duality result, several conditional completions and extensions are constructed.\n  This is an earlier version of arXiv e-print 170"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08709","kind":"arxiv","version":4},"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":"2026-05-18T00:30:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wJaTQu2mnKRPPMY8HknlhqwgyPdGF0raAEMzEbs1S2YmRbgmfkKrnjb0z3/TlBve09QbWG8SgUoXsv+fLf//DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:01:30.654350Z"},"content_sha256":"039a92bc550b32d6d0b26724edc0c4816706d4d7851762ca92deeadf46ef5ef4","schema_version":"1.0","event_id":"sha256:039a92bc550b32d6d0b26724edc0c4816706d4d7851762ca92deeadf46ef5ef4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y525IQC5QQDYMUBOIFY5DLGROC/bundle.json","state_url":"https://pith.science/pith/Y525IQC5QQDYMUBOIFY5DLGROC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y525IQC5QQDYMUBOIFY5DLGROC/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":"2026-05-28T16:01:30Z","links":{"resolver":"https://pith.science/pith/Y525IQC5QQDYMUBOIFY5DLGROC","bundle":"https://pith.science/pith/Y525IQC5QQDYMUBOIFY5DLGROC/bundle.json","state":"https://pith.science/pith/Y525IQC5QQDYMUBOIFY5DLGROC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y525IQC5QQDYMUBOIFY5DLGROC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Y525IQC5QQDYMUBOIFY5DLGROC","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":"d2185208b72e3c538f254e3b346c595c903979687c6462d6da1f5b5a22a1e72e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-31T02:27:14Z","title_canon_sha256":"781420763e04377e9e9b0efc4510015aec2cd4ccd9dfa8396d4b6e6d4433961d"},"schema_version":"1.0","source":{"id":"1608.08709","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08709","created_at":"2026-05-18T00:30:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08709v4","created_at":"2026-05-18T00:30:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08709","created_at":"2026-05-18T00:30:11Z"},{"alias_kind":"pith_short_12","alias_value":"Y525IQC5QQDY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Y525IQC5QQDYMUBO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Y525IQC5","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:039a92bc550b32d6d0b26724edc0c4816706d4d7851762ca92deeadf46ef5ef4","target":"graph","created_at":"2026-05-18T00:30:11Z","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":"A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\\colon X\\to \\overline{L^0}$ is established where $(X,Y,\\langle \\cdot,\\cdot \\rangle)$ is a dual pair of Banach spaces and $\\overline{L^0}$ is the set of all extended real-valued measurable functions. We provide a concept of lower semi-continuity which is shown to be equivalent to the existence of a dual representation in terms of elements in the Bochner space $L^0(Y)$. To derive the duality result, several conditional completions and extensions are constructed.\n  This is an earlier version of arXiv e-print 170","authors_text":"Asgar Jamneshan, Michael Kupper, Samuel Drapeau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-31T02:27:14Z","title":"Vector duality via conditional extension of dual pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08709","kind":"arxiv","version":4},"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":"sha256:54abd92c417cf5429dff11ca89f640d03f8dd3b0849ff4288a9fde740499aea6","target":"record","created_at":"2026-05-18T00:30:11Z","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":"d2185208b72e3c538f254e3b346c595c903979687c6462d6da1f5b5a22a1e72e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-31T02:27:14Z","title_canon_sha256":"781420763e04377e9e9b0efc4510015aec2cd4ccd9dfa8396d4b6e6d4433961d"},"schema_version":"1.0","source":{"id":"1608.08709","kind":"arxiv","version":4}},"canonical_sha256":"c775d4405d840786502e4171d1acd170ace52e46db7600a8d2c497cee5d0b6cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c775d4405d840786502e4171d1acd170ace52e46db7600a8d2c497cee5d0b6cf","first_computed_at":"2026-05-18T00:30:11.711998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:11.711998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PFN3GZ+7PDLB5ciE2vq62IvBkiMWhSF44zADGJs6fra30GYZTrpZ1hnro/F54OGddewzI/5MFsBw23FGxIxBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:11.712718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08709","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54abd92c417cf5429dff11ca89f640d03f8dd3b0849ff4288a9fde740499aea6","sha256:039a92bc550b32d6d0b26724edc0c4816706d4d7851762ca92deeadf46ef5ef4"],"state_sha256":"fa4a080e991be9970b7c3e6527e6af93743b702ba30e727853fa4a7498d8dc55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wgTnOv7/S4xUDA/WI7XJi5n22riuXIFaZj8wzOPfn8tPPIUYOMTQGvol8bpTwLOPSZLa7OS7CwEDB5iRE8OrBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:01:30.656687Z","bundle_sha256":"c944d7283129a57ae0460f69c3913c62e643efa5d63829a58cd0532954aaf383"}}