{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5Y4KXNDCSCYHTPHW2ZP6A46KU4","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":"854325e17d3ae2bcf0a79e7d708fac11ac8172492cb045c408e8a64889044376","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-21T14:29:00Z","title_canon_sha256":"36511063a9618ad51ad62e1b0852f73539dd93773f0fb7a3964ee01ed670f11c"},"schema_version":"1.0","source":{"id":"1512.06640","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06640","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06640v2","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06640","created_at":"2026-05-18T00:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"5Y4KXNDCSCYH","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5Y4KXNDCSCYHTPHW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5Y4KXNDC","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:4e503e92c5a05c761b68736926cd15df95570309f4a12cda1bf85ddbf918e78d","target":"graph","created_at":"2026-05-18T00:08:16Z","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":"A peacock is a family of probability measures with finite mean that increases in convex order. It is a classical result, in the discrete time case due to Strassen, that any peacock is the family of one-dimensional marginals of a martingale. We study the problem whether a given sequence of probability measures can be approximated by a peacock. In our main results, the approximation quality is measured by the infinity Wasserstein distance. Existence of a peacock within a prescribed distance is reduced to a countable collection of rather explicit conditions. This result has a financial applicatio","authors_text":"I. Cetin G\\\"ul\\\"um, Stefan Gerhold","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-21T14:29:00Z","title":"Peacocks nearby: approximating sequences of measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06640","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":"sha256:1f5b215255115dd048fb8f83a6450cf361cefe6985d6cba3e38c2f9e3e671c6e","target":"record","created_at":"2026-05-18T00:08:16Z","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":"854325e17d3ae2bcf0a79e7d708fac11ac8172492cb045c408e8a64889044376","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-21T14:29:00Z","title_canon_sha256":"36511063a9618ad51ad62e1b0852f73539dd93773f0fb7a3964ee01ed670f11c"},"schema_version":"1.0","source":{"id":"1512.06640","kind":"arxiv","version":2}},"canonical_sha256":"ee38abb46290b079bcf6d65fe073caa70a9937ebf256a4a833eb3b62055368ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee38abb46290b079bcf6d65fe073caa70a9937ebf256a4a833eb3b62055368ce","first_computed_at":"2026-05-18T00:08:16.410854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:16.410854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cIhMa3MVJs8syLksLGb/q2IRZ4+sv//IA0Wln1U9j1mI5oLC5wmwta0K4EaxfhT9z4OlB6/yjLe+Pm4vC/MBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:16.411328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06640","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f5b215255115dd048fb8f83a6450cf361cefe6985d6cba3e38c2f9e3e671c6e","sha256:4e503e92c5a05c761b68736926cd15df95570309f4a12cda1bf85ddbf918e78d"],"state_sha256":"2ed6cc5ec1aed656c8e0fa450d81bc99d0861c2f0d93fd461e21e78143248924"}