{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UQQQGTDVWVT5ZIC7B2PRGK3HGB","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":"964862790092adb046004dd4d37b92a2ee9b793b111ee3040cac6a0bfe53e2cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-09T14:52:21Z","title_canon_sha256":"2add049f7da5bf406e6b92470d290ddc969b8b7475b830a96c17155ff4a9a3e7"},"schema_version":"1.0","source":{"id":"1804.03034","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03034","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03034v2","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03034","created_at":"2026-05-18T00:06:11Z"},{"alias_kind":"pith_short_12","alias_value":"UQQQGTDVWVT5","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UQQQGTDVWVT5ZIC7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UQQQGTDV","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:aa3051ed3d0dbcf6445cd89e599163a073686c95c49ba774b4125a96c1cc8c63","target":"graph","created_at":"2026-05-18T00:06:11Z","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":"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","authors_text":"Jean-Philippe Chancelier (CERMICS), Michel de Lara (CERMICS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-09T14:52:21Z","title":"Fenchel-Moreau Conjugation Inequalities with Three Couplings and Application to Stochastic Bellman Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03034","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":"sha256:051b1c325928ee5c9842e95c74579dd6ee9247563abff964db1335ee0c535c57","target":"record","created_at":"2026-05-18T00:06:11Z","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":"964862790092adb046004dd4d37b92a2ee9b793b111ee3040cac6a0bfe53e2cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-04-09T14:52:21Z","title_canon_sha256":"2add049f7da5bf406e6b92470d290ddc969b8b7475b830a96c17155ff4a9a3e7"},"schema_version":"1.0","source":{"id":"1804.03034","kind":"arxiv","version":2}},"canonical_sha256":"a421034c75b567dca05f0e9f132b67307669f437b7e69bb96a771b8e15a3317f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a421034c75b567dca05f0e9f132b67307669f437b7e69bb96a771b8e15a3317f","first_computed_at":"2026-05-18T00:06:11.656347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:11.656347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"24ep82dVXKPmIJXDkDfom9Lg1K7Lyc+4C1hkKfcMxZD/CHRIXcdLrYU9eLdLqHJu2NUZrEB0QV/fkhZFIItGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:11.657024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03034","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:051b1c325928ee5c9842e95c74579dd6ee9247563abff964db1335ee0c535c57","sha256:aa3051ed3d0dbcf6445cd89e599163a073686c95c49ba774b4125a96c1cc8c63"],"state_sha256":"ba3bfcc8f5a37d7ca31fdb1f3e06691785bda3d234b0f785dc49f21f2d47a6ea"}