{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FR7KZI2MJZNSTL5ZUS5HVJ5U55","short_pith_number":"pith:FR7KZI2M","canonical_record":{"source":{"id":"1702.02490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-08T16:09:48Z","cross_cats_sorted":[],"title_canon_sha256":"36e9f921550cc8365fef2e780273f5a1c5c793033747a9e6d887894de236a867","abstract_canon_sha256":"c75f3c0103ecb2c4a007c01151105ac9d74029b82f22563ae84241d7ae837821"},"schema_version":"1.0"},"canonical_sha256":"2c7eaca34c4e5b29afb9a4ba7aa7b4ef6b5f5ab247232257dca1f92c8c8949b7","source":{"kind":"arxiv","id":"1702.02490","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02490","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02490v2","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02490","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"FR7KZI2MJZNS","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FR7KZI2MJZNSTL5Z","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FR7KZI2M","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FR7KZI2MJZNSTL5ZUS5HVJ5U55","target":"record","payload":{"canonical_record":{"source":{"id":"1702.02490","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-08T16:09:48Z","cross_cats_sorted":[],"title_canon_sha256":"36e9f921550cc8365fef2e780273f5a1c5c793033747a9e6d887894de236a867","abstract_canon_sha256":"c75f3c0103ecb2c4a007c01151105ac9d74029b82f22563ae84241d7ae837821"},"schema_version":"1.0"},"canonical_sha256":"2c7eaca34c4e5b29afb9a4ba7aa7b4ef6b5f5ab247232257dca1f92c8c8949b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:26.894642Z","signature_b64":"DSfj+YzTjz/XZ5IXczqjuvx5C9mUx9RzvQpHx1z5CfRp5DUAeLTOxgRNKMaM+pREnAzbHT4t220o1ZZ9WTHJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c7eaca34c4e5b29afb9a4ba7aa7b4ef6b5f5ab247232257dca1f92c8c8949b7","last_reissued_at":"2026-05-17T23:54:26.894048Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:26.894048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.02490","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":"2026-05-17T23:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xDphMLUxEPM2f0leNrLRew+DEmtUcpv6mwn9xxHNRuIhB/cddhXG/c1C3xJZ0LXJBOkOpzQt31ue95SJlj2eAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:43:53.669629Z"},"content_sha256":"5e9f4bee3b3eaf560acb4b2091c0604202d27710934c69a7d5d1b2712ce0f3c6","schema_version":"1.0","event_id":"sha256:5e9f4bee3b3eaf560acb4b2091c0604202d27710934c69a7d5d1b2712ce0f3c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FR7KZI2MJZNSTL5ZUS5HVJ5U55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A pointwise bipolar theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Bartl, Michael Kupper","submitted_at":"2017-02-08T16:09:48Z","abstract_excerpt":"We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a version of the transport duality under non-tight marginals, and a superhedging duality for semistatic hedging in discrete time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02490","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":"2026-05-17T23:54:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQm8Y4hn+Yn9HNEGgRnsdxkl8ZIPbzx6YDh+nce9frZZ9RPGWYDtB/oI2KLLYi8sbP4EzICymjFxxPghl+ikDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:43:53.669964Z"},"content_sha256":"1fea78bb40d6e9e7e7013797b057cca19065f4fb692f2b42a8c05ba8802ac7c3","schema_version":"1.0","event_id":"sha256:1fea78bb40d6e9e7e7013797b057cca19065f4fb692f2b42a8c05ba8802ac7c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FR7KZI2MJZNSTL5ZUS5HVJ5U55/bundle.json","state_url":"https://pith.science/pith/FR7KZI2MJZNSTL5ZUS5HVJ5U55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FR7KZI2MJZNSTL5ZUS5HVJ5U55/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":"2026-06-29T12:43:53Z","links":{"resolver":"https://pith.science/pith/FR7KZI2MJZNSTL5ZUS5HVJ5U55","bundle":"https://pith.science/pith/FR7KZI2MJZNSTL5ZUS5HVJ5U55/bundle.json","state":"https://pith.science/pith/FR7KZI2MJZNSTL5ZUS5HVJ5U55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FR7KZI2MJZNSTL5ZUS5HVJ5U55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FR7KZI2MJZNSTL5ZUS5HVJ5U55","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":"c75f3c0103ecb2c4a007c01151105ac9d74029b82f22563ae84241d7ae837821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-08T16:09:48Z","title_canon_sha256":"36e9f921550cc8365fef2e780273f5a1c5c793033747a9e6d887894de236a867"},"schema_version":"1.0","source":{"id":"1702.02490","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02490","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02490v2","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02490","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"FR7KZI2MJZNS","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FR7KZI2MJZNSTL5Z","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FR7KZI2M","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:1fea78bb40d6e9e7e7013797b057cca19065f4fb692f2b42a8c05ba8802ac7c3","target":"graph","created_at":"2026-05-17T23:54:26Z","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":"We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a version of the transport duality under non-tight marginals, and a superhedging duality for semistatic hedging in discrete time.","authors_text":"Daniel Bartl, Michael Kupper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-08T16:09:48Z","title":"A pointwise bipolar theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02490","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":"sha256:5e9f4bee3b3eaf560acb4b2091c0604202d27710934c69a7d5d1b2712ce0f3c6","target":"record","created_at":"2026-05-17T23:54:26Z","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":"c75f3c0103ecb2c4a007c01151105ac9d74029b82f22563ae84241d7ae837821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-08T16:09:48Z","title_canon_sha256":"36e9f921550cc8365fef2e780273f5a1c5c793033747a9e6d887894de236a867"},"schema_version":"1.0","source":{"id":"1702.02490","kind":"arxiv","version":2}},"canonical_sha256":"2c7eaca34c4e5b29afb9a4ba7aa7b4ef6b5f5ab247232257dca1f92c8c8949b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c7eaca34c4e5b29afb9a4ba7aa7b4ef6b5f5ab247232257dca1f92c8c8949b7","first_computed_at":"2026-05-17T23:54:26.894048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:26.894048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DSfj+YzTjz/XZ5IXczqjuvx5C9mUx9RzvQpHx1z5CfRp5DUAeLTOxgRNKMaM+pREnAzbHT4t220o1ZZ9WTHJDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:26.894642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02490","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e9f4bee3b3eaf560acb4b2091c0604202d27710934c69a7d5d1b2712ce0f3c6","sha256:1fea78bb40d6e9e7e7013797b057cca19065f4fb692f2b42a8c05ba8802ac7c3"],"state_sha256":"54dd9c567491f0afcdcfa89045a0a49c68492ef9c85d1bf8e92c0a9e291ea6fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8I6xhKB/CTj1LbBHCBHoYpQ6klzmcEdomroTJJ1WtFK7Op09mJyGH/6DpJhRmpJ/JuSKrEVKq9RcGgRTGMCwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:43:53.671819Z","bundle_sha256":"c6f9c57ddf9c5d1b891e9b618e614f14ba96934f9674885c60947fc0fd881e7e"}}