{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PP5KFKO3H6YHHTSLTFFMBQG5GW","short_pith_number":"pith:PP5KFKO3","canonical_record":{"source":{"id":"1309.1228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-09-05T02:33:30Z","cross_cats_sorted":[],"title_canon_sha256":"07b9a5768fe1ac2c7ffb576b3c8ae33dbe4f6d5413aeb7e13547a3d50668419c","abstract_canon_sha256":"943a8c880dce74c0c3a028fcc0ddbcf4b1dd5457b21e5a8c9713e0e9c4d8dd9d"},"schema_version":"1.0"},"canonical_sha256":"7bfaa2a9db3fb073ce4b994ac0c0dd35a7347e9d5244902c727e8072aa9d4a68","source":{"kind":"arxiv","id":"1309.1228","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1228","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1228v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1228","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"PP5KFKO3H6YH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PP5KFKO3H6YHHTSL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PP5KFKO3","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PP5KFKO3H6YHHTSLTFFMBQG5GW","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-09-05T02:33:30Z","cross_cats_sorted":[],"title_canon_sha256":"07b9a5768fe1ac2c7ffb576b3c8ae33dbe4f6d5413aeb7e13547a3d50668419c","abstract_canon_sha256":"943a8c880dce74c0c3a028fcc0ddbcf4b1dd5457b21e5a8c9713e0e9c4d8dd9d"},"schema_version":"1.0"},"canonical_sha256":"7bfaa2a9db3fb073ce4b994ac0c0dd35a7347e9d5244902c727e8072aa9d4a68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:07.935774Z","signature_b64":"nqNOVRzdD2VXyXDYLcfdd4qVN/iPuHl0EzbzqcemS2jh7neXOJehqxpo4eG3PQB/stCgMAlapOlkaktiTLrKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bfaa2a9db3fb073ce4b994ac0c0dd35a7347e9d5244902c727e8072aa9d4a68","last_reissued_at":"2026-05-18T03:14:07.935137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:07.935137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1228","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":"2026-05-18T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6eDAnCMMPlU0KVzKGIbmv2J1NVT8p31p3TJH9U5wgkHfn/6iG7tsNAobqoMUWyvSExHa2G/g/3ueHiMRtj35BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:42:57.099570Z"},"content_sha256":"60506a1ec2623f34fd803e7ee7adfed255f56d799b9c0ef8706777cbc3d855db","schema_version":"1.0","event_id":"sha256:60506a1ec2623f34fd803e7ee7adfed255f56d799b9c0ef8706777cbc3d855db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PP5KFKO3H6YHHTSLTFFMBQG5GW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted regret-based likelihood: a new approach to describing uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Joseph Y. Halpern","submitted_at":"2013-09-05T02:33:30Z","abstract_excerpt":"Recently, Halpern and Leung suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not answer an apparently simpler question: what it means, according to this representation of uncertainty, for an event E to be more likely than an event E'. In this paper, a notion of comparative likelihood when uncertainty is represented by a weighted set of probability measures is defined. It generalizes the ordering defined by probability (and by lower proba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1228","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":"2026-05-18T03:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TT7biTRLFHdo3pmWXlcokv50Y+adeVYSofLzD6m5aaJI5eoWukpct0h7EsQSRK1//xaWylpy+gYTP3lj9FDOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:42:57.099918Z"},"content_sha256":"317a2cbdaf4aa24e8d20cdd0547f6994ec07e6cd2619103d2ca6481a8651ed3a","schema_version":"1.0","event_id":"sha256:317a2cbdaf4aa24e8d20cdd0547f6994ec07e6cd2619103d2ca6481a8651ed3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PP5KFKO3H6YHHTSLTFFMBQG5GW/bundle.json","state_url":"https://pith.science/pith/PP5KFKO3H6YHHTSLTFFMBQG5GW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PP5KFKO3H6YHHTSLTFFMBQG5GW/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":"2026-06-11T09:42:57Z","links":{"resolver":"https://pith.science/pith/PP5KFKO3H6YHHTSLTFFMBQG5GW","bundle":"https://pith.science/pith/PP5KFKO3H6YHHTSLTFFMBQG5GW/bundle.json","state":"https://pith.science/pith/PP5KFKO3H6YHHTSLTFFMBQG5GW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PP5KFKO3H6YHHTSLTFFMBQG5GW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PP5KFKO3H6YHHTSLTFFMBQG5GW","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":"943a8c880dce74c0c3a028fcc0ddbcf4b1dd5457b21e5a8c9713e0e9c4d8dd9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-09-05T02:33:30Z","title_canon_sha256":"07b9a5768fe1ac2c7ffb576b3c8ae33dbe4f6d5413aeb7e13547a3d50668419c"},"schema_version":"1.0","source":{"id":"1309.1228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1228","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1228v1","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1228","created_at":"2026-05-18T03:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"PP5KFKO3H6YH","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PP5KFKO3H6YHHTSL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PP5KFKO3","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:317a2cbdaf4aa24e8d20cdd0547f6994ec07e6cd2619103d2ca6481a8651ed3a","target":"graph","created_at":"2026-05-18T03:14:07Z","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":"Recently, Halpern and Leung suggested representing uncertainty by a weighted set of probability measures, and suggested a way of making decisions based on this representation of uncertainty: maximizing weighted regret. Their paper does not answer an apparently simpler question: what it means, according to this representation of uncertainty, for an event E to be more likely than an event E'. In this paper, a notion of comparative likelihood when uncertainty is represented by a weighted set of probability measures is defined. It generalizes the ordering defined by probability (and by lower proba","authors_text":"Joseph Y. Halpern","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-09-05T02:33:30Z","title":"Weighted regret-based likelihood: a new approach to describing uncertainty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1228","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":"sha256:60506a1ec2623f34fd803e7ee7adfed255f56d799b9c0ef8706777cbc3d855db","target":"record","created_at":"2026-05-18T03:14:07Z","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":"943a8c880dce74c0c3a028fcc0ddbcf4b1dd5457b21e5a8c9713e0e9c4d8dd9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2013-09-05T02:33:30Z","title_canon_sha256":"07b9a5768fe1ac2c7ffb576b3c8ae33dbe4f6d5413aeb7e13547a3d50668419c"},"schema_version":"1.0","source":{"id":"1309.1228","kind":"arxiv","version":1}},"canonical_sha256":"7bfaa2a9db3fb073ce4b994ac0c0dd35a7347e9d5244902c727e8072aa9d4a68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bfaa2a9db3fb073ce4b994ac0c0dd35a7347e9d5244902c727e8072aa9d4a68","first_computed_at":"2026-05-18T03:14:07.935137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:07.935137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nqNOVRzdD2VXyXDYLcfdd4qVN/iPuHl0EzbzqcemS2jh7neXOJehqxpo4eG3PQB/stCgMAlapOlkaktiTLrKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:07.935774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60506a1ec2623f34fd803e7ee7adfed255f56d799b9c0ef8706777cbc3d855db","sha256:317a2cbdaf4aa24e8d20cdd0547f6994ec07e6cd2619103d2ca6481a8651ed3a"],"state_sha256":"ea51447971af30b90f7cc43aa6d24010aefe6c1277dadf439c10411ca9a78894"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVI91H2EOIjYkrGkZUc5quNu/8+xIdiR3qgHo1R08lOF0HwY5qYskYxGK4qO3l4Knwx6RFHh0XuiISaOwBNBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:42:57.101835Z","bundle_sha256":"50b5f62e60799db7a6750feba10ab973e765fc711f79aa1ce6cf0a1d2ba1a87f"}}