{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QYHSIRJ3C5ZXONCMGAB45OCDCL","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":"365a8148e878ebdb8072d4f4d5c2f261d60c2af0a05361d936913b993872076e","cross_cats_sorted":["cs.AI","q-fin.TR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-10-16T17:37:06Z","title_canon_sha256":"b047a54100e6c0853273f97db9d0dda486cc1729aa9c05eb8bb4e48acc54c0f2"},"schema_version":"1.0","source":{"id":"1210.4853","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.4853","created_at":"2026-05-18T03:32:47Z"},{"alias_kind":"arxiv_version","alias_value":"1210.4853v1","created_at":"2026-05-18T03:32:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4853","created_at":"2026-05-18T03:32:47Z"},{"alias_kind":"pith_short_12","alias_value":"QYHSIRJ3C5ZX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"QYHSIRJ3C5ZXONCM","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"QYHSIRJ3","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:4fb31360840754f855d4726f3f1bb63559ad095c1c94b5afbecb9871b84ae29d","target":"graph","created_at":"2026-05-18T03:32:47Z","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":"We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then","authors_text":"Joseph Y. Halpern, Samantha Leung","cross_cats":["cs.AI","q-fin.TR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-10-16T17:37:06Z","title":"Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4853","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":"sha256:0860f6df24a32d790da91c3a0f2826e0ab88d6076036730fe9fde71201768968","target":"record","created_at":"2026-05-18T03:32:47Z","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":"365a8148e878ebdb8072d4f4d5c2f261d60c2af0a05361d936913b993872076e","cross_cats_sorted":["cs.AI","q-fin.TR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2012-10-16T17:37:06Z","title_canon_sha256":"b047a54100e6c0853273f97db9d0dda486cc1729aa9c05eb8bb4e48acc54c0f2"},"schema_version":"1.0","source":{"id":"1210.4853","kind":"arxiv","version":1}},"canonical_sha256":"860f24453b177377344c3003ceb84312c0cdfda632caa63c854120e662e01bbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"860f24453b177377344c3003ceb84312c0cdfda632caa63c854120e662e01bbb","first_computed_at":"2026-05-18T03:32:47.334353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:47.334353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sCMmiowFPynKkAqxTcbMfLQna65OZdTp8OZepCB2IPdSvprgQ2XQXJbJqnL6OocrqlkOzY2B8ygtdB3xJXd4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:47.335185Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.4853","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0860f6df24a32d790da91c3a0f2826e0ab88d6076036730fe9fde71201768968","sha256:4fb31360840754f855d4726f3f1bb63559ad095c1c94b5afbecb9871b84ae29d"],"state_sha256":"5b4a3717b622b0075953f2b4d23231a3500f231a6b61c0320a370ad46f73aa43"}