{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OX7SI6P5F7XJONI5QU5HCRF3Y6","short_pith_number":"pith:OX7SI6P5","canonical_record":{"source":{"id":"2411.15401","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-23T01:07:45Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"91c0cb40b0cc68cf809566dfd2fb7a30b4be54328bd314eabd46ec7bb2e3d913","abstract_canon_sha256":"d75dbb2829237282ddfbe44ea879077379cf9310602096a82488e6ed6d7ee51c"},"schema_version":"1.0"},"canonical_sha256":"75ff2479fd2fee97351d853a7144bbc78b76c242f645e3ad687d1d98162d4c71","source":{"kind":"arxiv","id":"2411.15401","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15401","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15401v4","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15401","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"OX7SI6P5F7XJ","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"pith_short_16","alias_value":"OX7SI6P5F7XJONI5","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"pith_short_8","alias_value":"OX7SI6P5","created_at":"2026-07-05T10:25:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OX7SI6P5F7XJONI5QU5HCRF3Y6","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15401","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-23T01:07:45Z","cross_cats_sorted":["econ.TH"],"title_canon_sha256":"91c0cb40b0cc68cf809566dfd2fb7a30b4be54328bd314eabd46ec7bb2e3d913","abstract_canon_sha256":"d75dbb2829237282ddfbe44ea879077379cf9310602096a82488e6ed6d7ee51c"},"schema_version":"1.0"},"canonical_sha256":"75ff2479fd2fee97351d853a7144bbc78b76c242f645e3ad687d1d98162d4c71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:25:14.302155Z","signature_b64":"ClZLrcTRMv607zaeuuFJtc1GCJaQXAEHFIw/Y1RszdY9rrgegRGssLfvaE6KaBVdXd7Pnc6GnnUcTRkEQ1gWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75ff2479fd2fee97351d853a7144bbc78b76c242f645e3ad687d1d98162d4c71","last_reissued_at":"2026-07-05T10:25:14.301361Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:25:14.301361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15401","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRvBlMGTC17i3wl427A5QiJIF82U/AJ0lustKdIMLCnOe4k49T4ROLSXkGe0JnXDN1D36etHT61JTleuPxp3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:30:57.776554Z"},"content_sha256":"fde38b4189723bdc231a90b4a1d7e1068037b35cf60bae13215fe2bfe55fcb18","schema_version":"1.0","event_id":"sha256:fde38b4189723bdc231a90b4a1d7e1068037b35cf60bae13215fe2bfe55fcb18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OX7SI6P5F7XJONI5QU5HCRF3Y6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The reference interval in higher-order stochastic dominance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.TH"],"primary_cat":"math.PR","authors_text":"Qinyu Wu, Ruodu Wang","submitted_at":"2024-11-23T01:07:45Z","abstract_excerpt":"Given two random variables taking values in a bounded interval, we study whether one dominates the other in higher-order stochastic dominance depends on the reference interval in the model setting. We obtain two results. First, the stochastic dominance relations get strictly stronger when the reference interval shrinks if and only if the order of stochastic dominance is larger than three. Second, for mean-preserving stochastic dominance relations, the reference interval is irrelevant if and only if the difference between the degree of the stochastic dominance and the number of moments is no la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15401","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.15401/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:25:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPv8AjSg7njo0y7iFwnu8sP1Bq9CUBXJIMJbL047dPOanylKTCfuAgH7ZDbWcjwL8XDKLqHnOHNs7UpIq7rGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:30:57.788178Z"},"content_sha256":"efea3d8bf27fab0f29513deaddcccbe3a136117a69a2f86587c195c5e0bb648f","schema_version":"1.0","event_id":"sha256:efea3d8bf27fab0f29513deaddcccbe3a136117a69a2f86587c195c5e0bb648f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OX7SI6P5F7XJONI5QU5HCRF3Y6/bundle.json","state_url":"https://pith.science/pith/OX7SI6P5F7XJONI5QU5HCRF3Y6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OX7SI6P5F7XJONI5QU5HCRF3Y6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T00:30:57Z","links":{"resolver":"https://pith.science/pith/OX7SI6P5F7XJONI5QU5HCRF3Y6","bundle":"https://pith.science/pith/OX7SI6P5F7XJONI5QU5HCRF3Y6/bundle.json","state":"https://pith.science/pith/OX7SI6P5F7XJONI5QU5HCRF3Y6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OX7SI6P5F7XJONI5QU5HCRF3Y6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OX7SI6P5F7XJONI5QU5HCRF3Y6","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":"d75dbb2829237282ddfbe44ea879077379cf9310602096a82488e6ed6d7ee51c","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-23T01:07:45Z","title_canon_sha256":"91c0cb40b0cc68cf809566dfd2fb7a30b4be54328bd314eabd46ec7bb2e3d913"},"schema_version":"1.0","source":{"id":"2411.15401","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15401","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15401v4","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15401","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"pith_short_12","alias_value":"OX7SI6P5F7XJ","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"pith_short_16","alias_value":"OX7SI6P5F7XJONI5","created_at":"2026-07-05T10:25:14Z"},{"alias_kind":"pith_short_8","alias_value":"OX7SI6P5","created_at":"2026-07-05T10:25:14Z"}],"graph_snapshots":[{"event_id":"sha256:efea3d8bf27fab0f29513deaddcccbe3a136117a69a2f86587c195c5e0bb648f","target":"graph","created_at":"2026-07-05T10:25:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given two random variables taking values in a bounded interval, we study whether one dominates the other in higher-order stochastic dominance depends on the reference interval in the model setting. We obtain two results. First, the stochastic dominance relations get strictly stronger when the reference interval shrinks if and only if the order of stochastic dominance is larger than three. Second, for mean-preserving stochastic dominance relations, the reference interval is irrelevant if and only if the difference between the degree of the stochastic dominance and the number of moments is no la","authors_text":"Qinyu Wu, Ruodu Wang","cross_cats":["econ.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-23T01:07:45Z","title":"The reference interval in higher-order stochastic dominance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15401","kind":"arxiv","version":4},"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:fde38b4189723bdc231a90b4a1d7e1068037b35cf60bae13215fe2bfe55fcb18","target":"record","created_at":"2026-07-05T10:25:14Z","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":"d75dbb2829237282ddfbe44ea879077379cf9310602096a82488e6ed6d7ee51c","cross_cats_sorted":["econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-11-23T01:07:45Z","title_canon_sha256":"91c0cb40b0cc68cf809566dfd2fb7a30b4be54328bd314eabd46ec7bb2e3d913"},"schema_version":"1.0","source":{"id":"2411.15401","kind":"arxiv","version":4}},"canonical_sha256":"75ff2479fd2fee97351d853a7144bbc78b76c242f645e3ad687d1d98162d4c71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75ff2479fd2fee97351d853a7144bbc78b76c242f645e3ad687d1d98162d4c71","first_computed_at":"2026-07-05T10:25:14.301361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:25:14.301361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClZLrcTRMv607zaeuuFJtc1GCJaQXAEHFIw/Y1RszdY9rrgegRGssLfvaE6KaBVdXd7Pnc6GnnUcTRkEQ1gWAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:25:14.302155Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15401","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fde38b4189723bdc231a90b4a1d7e1068037b35cf60bae13215fe2bfe55fcb18","sha256:efea3d8bf27fab0f29513deaddcccbe3a136117a69a2f86587c195c5e0bb648f"],"state_sha256":"222cd8ade6cc3e9e4a2621c9ea11ad185aed068c605bddf9097f83d70ea3ca36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zwc0HigJjr73VFE6IQf9c/OyTGpma0crPqmqqzVrNKbo+ozdDMAQsuX4GWLPHtsWzlLdjQgSN2AsnsalPVUtDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T00:30:57.798460Z","bundle_sha256":"898b3fa502925dd11a5b693b9ee40bfcad43e5743ce55599aa4c8967c6c9e1c7"}}