{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:HU7DKRPCR53VINMCIPVMORO4WI","short_pith_number":"pith:HU7DKRPC","canonical_record":{"source":{"id":"2311.17884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T18:31:28Z","cross_cats_sorted":[],"title_canon_sha256":"570622d09c180d2d9fce7fd1c89ebd1e85dc680db0fe4bfcb2dc7b9dc331412d","abstract_canon_sha256":"b39781c796ee0a28df5c3287764d52b62903f89fb88de4526ad8623b7adabdf0"},"schema_version":"1.0"},"canonical_sha256":"3d3e3545e28f7754358243eac745dcb22bd83d58bbd92522b3a05325c9fe1cac","source":{"kind":"arxiv","id":"2311.17884","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.17884","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"2311.17884v1","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.17884","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"HU7DKRPCR53V","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"pith_short_16","alias_value":"HU7DKRPCR53VINMC","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"pith_short_8","alias_value":"HU7DKRPC","created_at":"2026-07-05T07:18:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:HU7DKRPCR53VINMCIPVMORO4WI","target":"record","payload":{"canonical_record":{"source":{"id":"2311.17884","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T18:31:28Z","cross_cats_sorted":[],"title_canon_sha256":"570622d09c180d2d9fce7fd1c89ebd1e85dc680db0fe4bfcb2dc7b9dc331412d","abstract_canon_sha256":"b39781c796ee0a28df5c3287764d52b62903f89fb88de4526ad8623b7adabdf0"},"schema_version":"1.0"},"canonical_sha256":"3d3e3545e28f7754358243eac745dcb22bd83d58bbd92522b3a05325c9fe1cac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:18:20.660526Z","signature_b64":"ia9wFQ53zRW9lyfVIUb7KP+etK+ToCNLOpIWhd4jvxxeQB39Zcacs/5+XcBtTl6i7GJp0aH/RwQKQ3Ac43j4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d3e3545e28f7754358243eac745dcb22bd83d58bbd92522b3a05325c9fe1cac","last_reissued_at":"2026-07-05T07:18:20.660021Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:18:20.660021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.17884","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZvOBjJSEpkh41YQkL2Z/3xc1rjeq4Zns9SUOSLZilgpBHa53WRsoIq4pjQ+yQ5J/xFJHQmDEV9eXJBeUmFzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:02:45.102516Z"},"content_sha256":"c75e94bcfefe91fa75ad730d6c3508993e90e0c43fc915fa607bcd322eb54f94","schema_version":"1.0","event_id":"sha256:c75e94bcfefe91fa75ad730d6c3508993e90e0c43fc915fa607bcd322eb54f94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:HU7DKRPCR53VINMCIPVMORO4WI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Ordering of Symmetric Core Event Probabilities With Respect To Row Margins For Multiple Hypergeometric Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruce Levin","submitted_at":"2023-11-29T18:31:28Z","abstract_excerpt":"Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X satisfies some symmetrical, but otherwise arbitrary, interval constraints in each component decreases as the sample size increases or decreases away from one-half of the population size."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.17884","kind":"arxiv","version":1},"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/2311.17884/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":"2026-07-05T07:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQYA5HRVgtvqAdk7keySrdxCzLEO1RzrpruiV7+CcMjBoAp/FTEOUK3ZaO8py9/QH6p/qpfAGa6ESnUpxcjQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:02:45.102894Z"},"content_sha256":"cd7bad89234a3025e4ec2d320f7a690b60b81b09ab4bb43fa5f3bd6aa8db9e61","schema_version":"1.0","event_id":"sha256:cd7bad89234a3025e4ec2d320f7a690b60b81b09ab4bb43fa5f3bd6aa8db9e61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HU7DKRPCR53VINMCIPVMORO4WI/bundle.json","state_url":"https://pith.science/pith/HU7DKRPCR53VINMCIPVMORO4WI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HU7DKRPCR53VINMCIPVMORO4WI/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":"2026-07-06T10:02:45Z","links":{"resolver":"https://pith.science/pith/HU7DKRPCR53VINMCIPVMORO4WI","bundle":"https://pith.science/pith/HU7DKRPCR53VINMCIPVMORO4WI/bundle.json","state":"https://pith.science/pith/HU7DKRPCR53VINMCIPVMORO4WI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HU7DKRPCR53VINMCIPVMORO4WI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HU7DKRPCR53VINMCIPVMORO4WI","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":"b39781c796ee0a28df5c3287764d52b62903f89fb88de4526ad8623b7adabdf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T18:31:28Z","title_canon_sha256":"570622d09c180d2d9fce7fd1c89ebd1e85dc680db0fe4bfcb2dc7b9dc331412d"},"schema_version":"1.0","source":{"id":"2311.17884","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.17884","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"2311.17884v1","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.17884","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"HU7DKRPCR53V","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"pith_short_16","alias_value":"HU7DKRPCR53VINMC","created_at":"2026-07-05T07:18:20Z"},{"alias_kind":"pith_short_8","alias_value":"HU7DKRPC","created_at":"2026-07-05T07:18:20Z"}],"graph_snapshots":[{"event_id":"sha256:cd7bad89234a3025e4ec2d320f7a690b60b81b09ab4bb43fa5f3bd6aa8db9e61","target":"graph","created_at":"2026-07-05T07:18:20Z","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/2311.17884/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X satisfies some symmetrical, but otherwise arbitrary, interval constraints in each component decreases as the sample size increases or decreases away from one-half of the population size.","authors_text":"Bruce Levin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T18:31:28Z","title":"Stochastic Ordering of Symmetric Core Event Probabilities With Respect To Row Margins For Multiple Hypergeometric Random Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.17884","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:c75e94bcfefe91fa75ad730d6c3508993e90e0c43fc915fa607bcd322eb54f94","target":"record","created_at":"2026-07-05T07:18:20Z","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":"b39781c796ee0a28df5c3287764d52b62903f89fb88de4526ad8623b7adabdf0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-11-29T18:31:28Z","title_canon_sha256":"570622d09c180d2d9fce7fd1c89ebd1e85dc680db0fe4bfcb2dc7b9dc331412d"},"schema_version":"1.0","source":{"id":"2311.17884","kind":"arxiv","version":1}},"canonical_sha256":"3d3e3545e28f7754358243eac745dcb22bd83d58bbd92522b3a05325c9fe1cac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d3e3545e28f7754358243eac745dcb22bd83d58bbd92522b3a05325c9fe1cac","first_computed_at":"2026-07-05T07:18:20.660021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:18:20.660021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ia9wFQ53zRW9lyfVIUb7KP+etK+ToCNLOpIWhd4jvxxeQB39Zcacs/5+XcBtTl6i7GJp0aH/RwQKQ3Ac43j4Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:18:20.660526Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.17884","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c75e94bcfefe91fa75ad730d6c3508993e90e0c43fc915fa607bcd322eb54f94","sha256:cd7bad89234a3025e4ec2d320f7a690b60b81b09ab4bb43fa5f3bd6aa8db9e61"],"state_sha256":"e022faefcaf2e2fb572a5b16100c794b7dd715e1e64aff05e5594d6deda16fbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vyTMQCx0kqVQhi1MvyoUnlKypgoVct0FfO1NFhqZIRNFGFGE921BckhtQkpSP30Vcinr1DlylYvmJXDPDvhsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T10:02:45.104759Z","bundle_sha256":"d25421bbee6086f0c8cd49616234a3a13473cf2a649f8ada5f8c4eaadec1d7b8"}}