{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CJHI2DGRORTOLJWCDNDN3RXEPG","short_pith_number":"pith:CJHI2DGR","schema_version":"1.0","canonical_sha256":"124e8d0cd17466e5a6c21b46ddc6e479881931527e5bbd0c4f843325f351afb8","source":{"kind":"arxiv","id":"1202.4703","version":3},"attestation_state":"computed","paper":{"title":"Maximality and numeraires in convex sets of nonnegative random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Constantinos Kardaras","submitted_at":"2012-02-21T17:06:37Z","abstract_excerpt":"We introduce the concepts of max-closedness and numeraires of convex subsets in the nonnegative orthant of the topological vector space of all random variables built over a probability space, equipped with a topology consistent with convergence in probability. Max-closedness asks that maximal elements of the closure of a set already lie on the set. We discuss how numeraires arise naturally as strictly positive optimisers of certain concave monotone maximisation problems. It is further shown that the set of numeraires of a convex, max-closed and bounded set of of nonnegative random variables th"},"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":"1202.4703","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-21T17:06:37Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2e3341c52293e687bbc969b93252d0d8eaee9729c8a09f7bf3f881cfca138c7f","abstract_canon_sha256":"c8b71551207e8f035502cfcab68df2e3b52f49c1efe702c6d50fe8d2de81374b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:10.408902Z","signature_b64":"gn1fVQc9x2LD647iiBdwl5HtVizRRGZ4XrF5hYzJ7TEl7Ic04mSyaNDlLngbilTc8ne27hz827IWZMEWPyh+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"124e8d0cd17466e5a6c21b46ddc6e479881931527e5bbd0c4f843325f351afb8","last_reissued_at":"2026-05-18T02:41:10.408342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:10.408342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximality and numeraires in convex sets of nonnegative random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Constantinos Kardaras","submitted_at":"2012-02-21T17:06:37Z","abstract_excerpt":"We introduce the concepts of max-closedness and numeraires of convex subsets in the nonnegative orthant of the topological vector space of all random variables built over a probability space, equipped with a topology consistent with convergence in probability. Max-closedness asks that maximal elements of the closure of a set already lie on the set. We discuss how numeraires arise naturally as strictly positive optimisers of certain concave monotone maximisation problems. It is further shown that the set of numeraires of a convex, max-closed and bounded set of of nonnegative random variables th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4703","kind":"arxiv","version":3},"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":"1202.4703","created_at":"2026-05-18T02:41:10.408416+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4703v3","created_at":"2026-05-18T02:41:10.408416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4703","created_at":"2026-05-18T02:41:10.408416+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJHI2DGRORTO","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJHI2DGRORTOLJWC","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJHI2DGR","created_at":"2026-05-18T12:27:01.376967+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/CJHI2DGRORTOLJWCDNDN3RXEPG","json":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG.json","graph_json":"https://pith.science/api/pith-number/CJHI2DGRORTOLJWCDNDN3RXEPG/graph.json","events_json":"https://pith.science/api/pith-number/CJHI2DGRORTOLJWCDNDN3RXEPG/events.json","paper":"https://pith.science/paper/CJHI2DGR"},"agent_actions":{"view_html":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG","download_json":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG.json","view_paper":"https://pith.science/paper/CJHI2DGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4703&json=true","fetch_graph":"https://pith.science/api/pith-number/CJHI2DGRORTOLJWCDNDN3RXEPG/graph.json","fetch_events":"https://pith.science/api/pith-number/CJHI2DGRORTOLJWCDNDN3RXEPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG/action/storage_attestation","attest_author":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG/action/author_attestation","sign_citation":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG/action/citation_signature","submit_replication":"https://pith.science/pith/CJHI2DGRORTOLJWCDNDN3RXEPG/action/replication_record"}},"created_at":"2026-05-18T02:41:10.408416+00:00","updated_at":"2026-05-18T02:41:10.408416+00:00"}