{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ACP64NUAIBYOFBPQCQQT7UBDST","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":"aae4333cb6eb8b57f2e276baf58cb7e049c094f7f6e83bb9799213648d7aec5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-15T22:02:09Z","title_canon_sha256":"07d026a69944b4c66b232d8949d109e09150c9e7bb08513a9093003a36c3a817"},"schema_version":"1.0","source":{"id":"1403.3855","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3855","created_at":"2026-05-18T00:39:14Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3855v3","created_at":"2026-05-18T00:39:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3855","created_at":"2026-05-18T00:39:14Z"},{"alias_kind":"pith_short_12","alias_value":"ACP64NUAIBYO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"ACP64NUAIBYOFBPQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"ACP64NUA","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:e444730fb470f043c1557e03674bec86751180a090704161e00662b96d99a32e","target":"graph","created_at":"2026-05-18T00:39:14Z","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":"Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling compatible with respect to the partial order. We consider the case of a countable set and introduce the class of \\emph{finitely decomposable flows} on a directed acyclic graph associated to the partial order. We show that a probability measure stochastically dominates another probability measure if and only if there exists a finitely decomposable flow having","authors_text":"Davide Gabrielli, Ida Germana Minelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-15T22:02:09Z","title":"Stochastic monotonicity from an Eulerian viewpoint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3855","kind":"arxiv","version":3},"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:c02c7d72f2fc7f80cb656ced0fd7b21a916f1db3a377813298389025b2d51c06","target":"record","created_at":"2026-05-18T00:39:14Z","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":"aae4333cb6eb8b57f2e276baf58cb7e049c094f7f6e83bb9799213648d7aec5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-15T22:02:09Z","title_canon_sha256":"07d026a69944b4c66b232d8949d109e09150c9e7bb08513a9093003a36c3a817"},"schema_version":"1.0","source":{"id":"1403.3855","kind":"arxiv","version":3}},"canonical_sha256":"009fee36804070e285f014213fd02394f4383cd0be308d932823abd2be121afb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"009fee36804070e285f014213fd02394f4383cd0be308d932823abd2be121afb","first_computed_at":"2026-05-18T00:39:14.065456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:14.065456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rUlt4DIxWwtRNoLDJngb+wWmXLjhBVB6iOaWEnMHIvi4u8+RCMaXJHN20o1sp+TbQZ0YstLYE6ugOvPWGbMGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:14.066151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3855","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c02c7d72f2fc7f80cb656ced0fd7b21a916f1db3a377813298389025b2d51c06","sha256:e444730fb470f043c1557e03674bec86751180a090704161e00662b96d99a32e"],"state_sha256":"69af9bc55f1c7d6879c955dfb91ae4d6d83c26654093c2b0e2d77df5428af95e"}