{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UQQQGTDVWVT5ZIC7B2PRGK3HGB","short_pith_number":"pith:UQQQGTDV","schema_version":"1.0","canonical_sha256":"a421034c75b567dca05f0e9f132b67307669f437b7e69bb96a771b8e15a3317f","source":{"kind":"arxiv","id":"1804.03034","version":2},"attestation_state":"computed","paper":{"title":"Fenchel-Moreau Conjugation Inequalities with Three Couplings and Application to Stochastic Bellman Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean-Philippe Chancelier (CERMICS), Michel de Lara (CERMICS)","submitted_at":"2018-04-09T14:52:21Z","abstract_excerpt":"Given two couplings between \"primal\" and \"dual\" sets,   we prove a general implication   that relates an inequality involving \"primal\" sets   to a reverse inequality involving the \"dual\" sets.%  More precisely,  let be given two \"primal\" sets $\\PRIMAL$, $\\PRIMALBIS$and two \"dual\" sets $\\DUAL$, $\\DUALBIS$, together with two {coupling} functions  \\(\\PRIMAL \\overset{\\coupling}{\\leftrightarrow} \\DUAL \\) and  \\(\\PRIMALBIS \\overset{\\couplingbis}{\\leftrightarrow} \\DUALBIS \\).  We define a new coupling \\(\\SumCoupling{\\coupling}{\\couplingbis} \\)  between the \"primal\" product set~$\\PRIMAL \\times \\PRIMAL"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.03034","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-09T14:52:21Z","cross_cats_sorted":[],"title_canon_sha256":"2add049f7da5bf406e6b92470d290ddc969b8b7475b830a96c17155ff4a9a3e7","abstract_canon_sha256":"964862790092adb046004dd4d37b92a2ee9b793b111ee3040cac6a0bfe53e2cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:11.657024Z","signature_b64":"24ep82dVXKPmIJXDkDfom9Lg1K7Lyc+4C1hkKfcMxZD/CHRIXcdLrYU9eLdLqHJu2NUZrEB0QV/fkhZFIItGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a421034c75b567dca05f0e9f132b67307669f437b7e69bb96a771b8e15a3317f","last_reissued_at":"2026-05-18T00:06:11.656347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:11.656347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fenchel-Moreau Conjugation Inequalities with Three Couplings and Application to Stochastic Bellman Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean-Philippe Chancelier (CERMICS), Michel de Lara (CERMICS)","submitted_at":"2018-04-09T14:52:21Z","abstract_excerpt":"Given two couplings between \"primal\" and \"dual\" sets,   we prove a general implication   that relates an inequality involving \"primal\" sets   to a reverse inequality involving the \"dual\" sets.%  More precisely,  let be given two \"primal\" sets $\\PRIMAL$, $\\PRIMALBIS$and two \"dual\" sets $\\DUAL$, $\\DUALBIS$, together with two {coupling} functions  \\(\\PRIMAL \\overset{\\coupling}{\\leftrightarrow} \\DUAL \\) and  \\(\\PRIMALBIS \\overset{\\couplingbis}{\\leftrightarrow} \\DUALBIS \\).  We define a new coupling \\(\\SumCoupling{\\coupling}{\\couplingbis} \\)  between the \"primal\" product set~$\\PRIMAL \\times \\PRIMAL"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03034","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.03034","created_at":"2026-05-18T00:06:11.656480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03034v2","created_at":"2026-05-18T00:06:11.656480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03034","created_at":"2026-05-18T00:06:11.656480+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQQQGTDVWVT5","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQQQGTDVWVT5ZIC7","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQQQGTDV","created_at":"2026-05-18T12:32:56.356000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB","json":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB.json","graph_json":"https://pith.science/api/pith-number/UQQQGTDVWVT5ZIC7B2PRGK3HGB/graph.json","events_json":"https://pith.science/api/pith-number/UQQQGTDVWVT5ZIC7B2PRGK3HGB/events.json","paper":"https://pith.science/paper/UQQQGTDV"},"agent_actions":{"view_html":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB","download_json":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB.json","view_paper":"https://pith.science/paper/UQQQGTDV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03034&json=true","fetch_graph":"https://pith.science/api/pith-number/UQQQGTDVWVT5ZIC7B2PRGK3HGB/graph.json","fetch_events":"https://pith.science/api/pith-number/UQQQGTDVWVT5ZIC7B2PRGK3HGB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB/action/storage_attestation","attest_author":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB/action/author_attestation","sign_citation":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB/action/citation_signature","submit_replication":"https://pith.science/pith/UQQQGTDVWVT5ZIC7B2PRGK3HGB/action/replication_record"}},"created_at":"2026-05-18T00:06:11.656480+00:00","updated_at":"2026-05-18T00:06:11.656480+00:00"}