{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KPZ72IHJBRFFJY4GYF65Z5DN4M","short_pith_number":"pith:KPZ72IHJ","canonical_record":{"source":{"id":"1503.01936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-06T12:53:32Z","cross_cats_sorted":[],"title_canon_sha256":"c193ba3d3685a0cfdd5c8b9461861761ccdd74f0fc1b82aef2f8e75f61ad3b1c","abstract_canon_sha256":"ecb0e0839881db0cea74f72d417397e0316f1d4794a1faf68a4ca1b93bb74a08"},"schema_version":"1.0"},"canonical_sha256":"53f3fd20e90c4a54e386c17ddcf46de303c2e1948ee3088f5d3fb1f795613acb","source":{"kind":"arxiv","id":"1503.01936","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01936","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01936v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01936","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"KPZ72IHJBRFF","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KPZ72IHJBRFFJY4G","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KPZ72IHJ","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KPZ72IHJBRFFJY4GYF65Z5DN4M","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-06T12:53:32Z","cross_cats_sorted":[],"title_canon_sha256":"c193ba3d3685a0cfdd5c8b9461861761ccdd74f0fc1b82aef2f8e75f61ad3b1c","abstract_canon_sha256":"ecb0e0839881db0cea74f72d417397e0316f1d4794a1faf68a4ca1b93bb74a08"},"schema_version":"1.0"},"canonical_sha256":"53f3fd20e90c4a54e386c17ddcf46de303c2e1948ee3088f5d3fb1f795613acb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:27.237735Z","signature_b64":"/DloCKMqxgSWmZdQAK+5ybZ5YMhYOXDt3a+IQd1WcLAOUf+dcDeWEPiCFBj965meemzZzTmo1AHNbrnX83KfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53f3fd20e90c4a54e386c17ddcf46de303c2e1948ee3088f5d3fb1f795613acb","last_reissued_at":"2026-05-18T02:25:27.237028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:27.237028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01936","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":"2026-05-18T02:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ezs+uYp9+n0dD5DZBSakGXsa/wyIKzO3h0z2t9ByCHV4yW8cQRPFTzY5BBLPKrE+ZRU0Og3UV1XjhJt3YzPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:29:14.443704Z"},"content_sha256":"0cfc2b04fa3de4f5f4571133f82a3a3b457b11d505d46772a7201ace3fbd0546","schema_version":"1.0","event_id":"sha256:0cfc2b04fa3de4f5f4571133f82a3a3b457b11d505d46772a7201ace3fbd0546"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KPZ72IHJBRFFJY4GYF65Z5DN4M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Goodman-Nguyen Relation within Imprecise Probability Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paolo Vicig, Renato Pelessoni","submitted_at":"2015-03-06T12:53:32Z","abstract_excerpt":"The Goodman-Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain common extension problem. Most previous work involving this relation is concerned with either conditional event algebras or precise probabilities. We investigate here its role within imprecise probability theory, first in the framework of conditional events and then proposing a generalisation of the Goodman-Nguyen relation to conditional gambles. It turns out th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01936","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":""},"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":"2026-05-18T02:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ydww9E7zNNvv0JAWSa7vyJ5gz6xTTh+HAeJKT4geRiDheBs8zkSaHsw9sKY7LEZcvdFhelBQ7MfDVv8lVaoeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:29:14.444036Z"},"content_sha256":"a9a235c485cfd0d3097e7fa808c1e91890b9f6144723a22e58a4c75d4ed4036b","schema_version":"1.0","event_id":"sha256:a9a235c485cfd0d3097e7fa808c1e91890b9f6144723a22e58a4c75d4ed4036b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KPZ72IHJBRFFJY4GYF65Z5DN4M/bundle.json","state_url":"https://pith.science/pith/KPZ72IHJBRFFJY4GYF65Z5DN4M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KPZ72IHJBRFFJY4GYF65Z5DN4M/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":"2026-06-22T15:29:14Z","links":{"resolver":"https://pith.science/pith/KPZ72IHJBRFFJY4GYF65Z5DN4M","bundle":"https://pith.science/pith/KPZ72IHJBRFFJY4GYF65Z5DN4M/bundle.json","state":"https://pith.science/pith/KPZ72IHJBRFFJY4GYF65Z5DN4M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KPZ72IHJBRFFJY4GYF65Z5DN4M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KPZ72IHJBRFFJY4GYF65Z5DN4M","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":"ecb0e0839881db0cea74f72d417397e0316f1d4794a1faf68a4ca1b93bb74a08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-06T12:53:32Z","title_canon_sha256":"c193ba3d3685a0cfdd5c8b9461861761ccdd74f0fc1b82aef2f8e75f61ad3b1c"},"schema_version":"1.0","source":{"id":"1503.01936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01936","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01936v1","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01936","created_at":"2026-05-18T02:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"KPZ72IHJBRFF","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KPZ72IHJBRFFJY4G","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KPZ72IHJ","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:a9a235c485cfd0d3097e7fa808c1e91890b9f6144723a22e58a4c75d4ed4036b","target":"graph","created_at":"2026-05-18T02:25:27Z","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":"The Goodman-Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain common extension problem. Most previous work involving this relation is concerned with either conditional event algebras or precise probabilities. We investigate here its role within imprecise probability theory, first in the framework of conditional events and then proposing a generalisation of the Goodman-Nguyen relation to conditional gambles. It turns out th","authors_text":"Paolo Vicig, Renato Pelessoni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-06T12:53:32Z","title":"The Goodman-Nguyen Relation within Imprecise Probability Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01936","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":"sha256:0cfc2b04fa3de4f5f4571133f82a3a3b457b11d505d46772a7201ace3fbd0546","target":"record","created_at":"2026-05-18T02:25:27Z","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":"ecb0e0839881db0cea74f72d417397e0316f1d4794a1faf68a4ca1b93bb74a08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-06T12:53:32Z","title_canon_sha256":"c193ba3d3685a0cfdd5c8b9461861761ccdd74f0fc1b82aef2f8e75f61ad3b1c"},"schema_version":"1.0","source":{"id":"1503.01936","kind":"arxiv","version":1}},"canonical_sha256":"53f3fd20e90c4a54e386c17ddcf46de303c2e1948ee3088f5d3fb1f795613acb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53f3fd20e90c4a54e386c17ddcf46de303c2e1948ee3088f5d3fb1f795613acb","first_computed_at":"2026-05-18T02:25:27.237028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:27.237028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/DloCKMqxgSWmZdQAK+5ybZ5YMhYOXDt3a+IQd1WcLAOUf+dcDeWEPiCFBj965meemzZzTmo1AHNbrnX83KfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:27.237735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cfc2b04fa3de4f5f4571133f82a3a3b457b11d505d46772a7201ace3fbd0546","sha256:a9a235c485cfd0d3097e7fa808c1e91890b9f6144723a22e58a4c75d4ed4036b"],"state_sha256":"90dcbde5b0c5288baa09af16c05e09dc40cf67239a281a1601f26b1d7a2718fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IRJkQlFJBtkHfL2DH0HSNzOqHT/947jEwxH3aLtr5UjEjp8z220Q0BEOPJA01AbSW/DCuqSe6L6COC++ws67Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:29:14.445873Z","bundle_sha256":"0f13cb02f03860df923d9939731e5f691fee236276e26be1d77d6b450097a428"}}