{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CVC76WO76B5HB2DEHLO5XMBSVP","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":"b90bfcc4aa06bd0ea5ab8d6b4081230f42647a621eb65a61dcb8fa163f7b4924","cross_cats_sorted":["cs.AI","physics.data-an","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-10-27T21:38:08Z","title_canon_sha256":"24019f17e65db96f8c1dfd11ce9e4df932fc4da91c01fd1dc5982de210e3c7eb"},"schema_version":"1.0","source":{"id":"1610.09018","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09018","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09018v6","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09018","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"CVC76WO76B5H","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CVC76WO76B5HB2DE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CVC76WO7","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:8a3b6bdbe3f6f0f5ef98ebc89b922c415791941c3c5265e20c0d08eadb87fb9f","target":"graph","created_at":"2026-05-18T00:38:39Z","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":"In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how \"embarrassing\" it is to communicate a given approximation. We reproduce and discuss an old proof showing that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. The loss function that is obtained in the derivation i","authors_text":"Reimar H. Leike, Torsten A. En{\\ss}lin","cross_cats":["cs.AI","physics.data-an","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-10-27T21:38:08Z","title":"Optimal Belief Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09018","kind":"arxiv","version":6},"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:f6f5a8a586a0280998aaff2be8985926f266cccecb39beac2ea57e5595567c6e","target":"record","created_at":"2026-05-18T00:38:39Z","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":"b90bfcc4aa06bd0ea5ab8d6b4081230f42647a621eb65a61dcb8fa163f7b4924","cross_cats_sorted":["cs.AI","physics.data-an","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-10-27T21:38:08Z","title_canon_sha256":"24019f17e65db96f8c1dfd11ce9e4df932fc4da91c01fd1dc5982de210e3c7eb"},"schema_version":"1.0","source":{"id":"1610.09018","kind":"arxiv","version":6}},"canonical_sha256":"1545ff59dff07a70e8643adddbb032abf3156e2ca391696fbd0a3b4947a19aae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1545ff59dff07a70e8643adddbb032abf3156e2ca391696fbd0a3b4947a19aae","first_computed_at":"2026-05-18T00:38:39.856842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:39.856842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ByPbUHr6r8XPpUUBRDm7wWSloobKSFsKilgjvQWVsw6zeNk4c4KZZ+F5FHdxTB7dP7HzIQMlgoHw/sPaH0zVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:39.857311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09018","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6f5a8a586a0280998aaff2be8985926f266cccecb39beac2ea57e5595567c6e","sha256:8a3b6bdbe3f6f0f5ef98ebc89b922c415791941c3c5265e20c0d08eadb87fb9f"],"state_sha256":"a2d30308b942b94e40d3bdaa2cae26baf1dbd2cdb6fc772e7a9bcddf61b44213"}