{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZXZG57NC277LVLQFM7KFQOIEBM","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":"e3d594a5b1f1d95773560a961b5272c210dc7b4d9cbc61c0dc05780a67858b74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-13T17:40:06Z","title_canon_sha256":"ec0ae97599190572b884368d73877579504f27d171b47e987f6d8e35b8fbccc8"},"schema_version":"1.0","source":{"id":"1012.2811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2811","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2811v1","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2811","created_at":"2026-05-18T04:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"ZXZG57NC277L","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZXZG57NC277LVLQF","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZXZG57NC","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:26bdaa34635c3093b3accd9f8aefcc12203ec0a8fc2c72fea3f3b40759cbe5fa","target":"graph","created_at":"2026-05-18T04:33:27Z","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":"Let $L$ be a linear space of real bounded random variables on the probability space $(\\Omega,\\mathcal{A},P_0)$. There is a finitely additive probability $P$ on $\\mathcal{A}$, such that $P\\sim P_0$ and $E_P(X)=0$ for all $X\\in L$, if and only if $c\\,E_Q(X)\\leq\\text{ess sup}(-X)$, $X\\in L$, for some constant $c>0$ and (countably additive) probability $Q$ on $\\mathcal{A}$ such that $Q\\sim P_0$. A necessary condition for such a $P$ to exist is $\\bar{L-L_\\infty^+}\\,\\cap L_\\infty^+=\\{0\\}$, where the closure is in the norm-topology. If $P_0$ is atomic, the condition is sufficient as well. In addition","authors_text":"Luca Pratelli, Patrizia Berti, Pietro Rigo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-13T17:40:06Z","title":"Finitely additive equivalent martingale measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2811","kind":"arxiv","version":1},"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":"sha256:1bf7e5f79ff1386789b6c55de4922382901c235996af7f29d1c7f7e5d2daec26","target":"record","created_at":"2026-05-18T04:33:27Z","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":"e3d594a5b1f1d95773560a961b5272c210dc7b4d9cbc61c0dc05780a67858b74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-13T17:40:06Z","title_canon_sha256":"ec0ae97599190572b884368d73877579504f27d171b47e987f6d8e35b8fbccc8"},"schema_version":"1.0","source":{"id":"1012.2811","kind":"arxiv","version":1}},"canonical_sha256":"cdf26efda2d7febaae0567d45839040b3237dec6fd79f3b03669c66dd712eb59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdf26efda2d7febaae0567d45839040b3237dec6fd79f3b03669c66dd712eb59","first_computed_at":"2026-05-18T04:33:27.701937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:27.701937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xJzKHswMS1D8Up4BFwbrkuei7kcA73Ho/MA5Zb7OLAafvLHP4saLcb+J9mMnnWa6cutj1YnDqFPRcLwQ5/baAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:27.702675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bf7e5f79ff1386789b6c55de4922382901c235996af7f29d1c7f7e5d2daec26","sha256:26bdaa34635c3093b3accd9f8aefcc12203ec0a8fc2c72fea3f3b40759cbe5fa"],"state_sha256":"04f88948259f01e2cc6ad109fcb208ed29521126d7b2af1e7fee640e58779f5e"}